text:
SA NC Doing Investigations/Chapter 7

Materials developed by the winning educators
This resource book is not meant to be a textbook on investigations with pages of ideas for teachers. Any examples given are intended to illustrate how even the most common classroom activities can be done with an investigative bias. The materials here, taken from the portfolios of winners of the MSTotY 2003 demonstrate this clearly. The first activity is the investigation of "fractions" for Intermediate Phase learners. Because it tackles the topic using measurement it is appropriate to both science and mathematics. The second and third activities are common in FET physics (Newton's Second Law and the electromagnetic motor rule). The reader will appreciate that by re-shaping them ever so slightly, even familiar activities can conform to the requirements of an "investigative approach." We might assume that "to investigate" means learners working alone and researching private topics that catch their imaginations. But this is not necessarily the case and activities with a specific focus and educator-directed can also be investigations.

In the first of the three examples learners are given a sequence of activities that follow the logic of fractions and learners study them through measurements. Indeed, measurement itself is an important aspect of investigation. So instead of talking about the "free investigation of private topics" by learners, which is the pure form, we now have what is an "investigative approach" to teaching and learning. Free investigations by learners are a special subset of the investigative approach. The important point is that whether learners follow their own curiosity or are led through a logical sequence by their educator, in both cases they are investigating in a way that follows the logic and nature of mathematics and science. The advantage of educator-led investigations is that learners can be shown a logical approach (e.g. asking and then answering a key question before moving to the next stage) even if it may not be as neat and sequenced in "the real world". By gaining this guided experience learners should adopt a similar approach in their free investigations. The first investigation was produced by Vanessa Thayer, winner of the 2003 award for Maths and Science Educator of the Year. Vanessa acknowledges the original inspiration for the activity and the source of some of the content. It is important for professionals to do this as they, of all people, must be above plagiarism and the unacknowledged use of other people's ideas. Using decimetres to investigate fractions: an investigation into fractions and measurement

SPECIAL NOTE All activities in this module were adapted from teaching material and ideas received at the in-service course for Intermediate Phase mathemaics educators at WCED, Cape Teaching Institute.

The history of fractions
Early Egyptians made mention of fractions even before the pyramids were built, over 4000 years ago. Measurement was used to survey farms. They first used their elbows and fingers, but this did not work too well because elbows and fingers were of different lengths for different people.

In their quest for accuracy, they used standard units as equal parts of a bigger unit, e.g. the decimetre ruler. However, they now found that they had a whole bag of rulers, which was also inconvenient. So they later used tenths, hundredths, thousandths (decimals) but had to keep to common fractions (halves and quarters) and couldn't, for instance, measure of a metre in decimals. (Take the learners back in time and make the context real.)

We teach fractions to provide a basis for decimal fractions. We deliberately investigate common fractions in the context of measurement to allow learners the opportunity to discover the context within which fractions started and, most importantly, to see the logic behind equivalent, simple, mixed fractions etc and the relationship between common fractions and decimals. In this way learners are able to formulate their own rules / methods and will also, in the higher grades, understand the logic behind rules, methods and formulae.

The module of activities offer many opportunities for learners to talk about what they have done and engage with other learners and this is an effective way of making learners aware of how they are learning, building on their communication skills and most importantly, engaging with logic.

Try not to rush the concrete support of using the rulers. In this way learners will internalise the logic and will later be confident in working with abstract contexts. Ensure that the learners get the fraction language correct. Encourage them to say, e.g. 3 quarters and not 3 over 4. In the next module of activities, learners will have the opportunity of working with fractions in many other, varied contexts.

Assessment Plan Learning Area: Mathematics, RNCS Grade 5 Learning Outcome: L 01: Number, Operations and Relationships L 04: Measurement

Grade 4

 * Recognises and represents common fractions with different denominators including halves, thirds, quarters, fifths, sixths, sevenths, eighths, in order to describe and compare them.
 * Recognises and uses equivalent forms of common fractions with denominators that are multiples of each other and decimal fractions of the form 0.5  2,5 etc. in the context of measurement.

Grade 5

 * Recognises and represents common fractions to at least twelfths in order to describe and compare them.
 * Recognises and uses equivalent forms of common fractions with denominators that are multiples of each other and decimal fractions of the form 0.5 2,5 etc. in the context of measurement.

Grade 6

 * Recognises and represents common fractions including specifically tenths, hundredths, and percentages.
 * Recognises and uses equivalent forms of common fractions with 1 digit or 2 digit denominator
 * Decimal fractions to at least 2 decimal places
 * Percentages

Grade 7

 * Recognises, classifies and represents decimals (to at least 3 decimal places), fractions and percentages.
 * Recognises and uses equivalent forms of rational numbers including common fractions, decimals, percentages

Baseline assessment task
Intended Outcome: The learner will be able to demonstrate an understanding of "an hour" in fraction notation. Method: Pen and Paper Technique: Worksheet Assessment Tool: Assessment Grid

The exit assessment task
Intended Outcome: The learner will be able to recognize, represent, describe, compare and convert between equivalent forms of common fractions in the context of measurement. Method: Pen and Paper Technique: Worksheet Assessment Tool: The rubric below, using four achievement level descriptors.

Formative assessment task
[LO1: Number, operations and relationships L 04: Measurement] Grade assessment standard: The learner will be able to recognize, represent, describe, compare and convert between equivalent forms of common fractions in the context of measurement.

RUBRIC for Using Decimetres to Investigate Fractions.
Reporting Code: Comments:

________________________________________________________________________________

________________________________________________________________________________

Measuring with decimeters
Put your ordinary rulers away. You will only work with the special rulers provided here.

You will use the decimetre as a unit. Here you can see approximately how long a decimetre is:

Task 1
1. Cut out a strip of paper as long as the "practice decimetre" above. Now you have made a "one decimetre ruler" for yourself.

2. Use your practice ruler to check whether the pencil below is exactly 2 decimetre long. If not, is it more than or less than or about (approximately) 2 decimetres long?

3. Measure the length and the width of the marble slab below with your practice decimetre. Is it a square?

4. Measure the edges of your desk top with your practice decimetre.

5. Was it possible to measure your desk top accurately with the practice decimetre ruler? Discuss this with a friend.

[Use the next two pages as photocopy masters or as exemplars, if they are copied. Make sure that Rulers ABCD, EFGH and JKMN are all exactly 20cm when they have been photocopied. The pages may require a slight enlargement. If you redraw them make sure that the sub-divisions are all exactly equal in any one ruler. For example, all the small sub-divisions in Ruler D must be exactly 1cm long.]

[KEY: E (30ths), F (15ths), G (24ths), H (16ths), J (20ths), K (25ths), M (40ths), N (50ths)]

Task 2
Cut out the ruler (with Rulers A, B, C and D on it) and fold it along the dotted lines. In this way you will make your own set of decimetre ruler.

1. How long is each small part on the lower section of ruler B? Write down your answer.

2. How long is each small part on the lower section of ruler C? Write down your answer.

3. How long is each small part on the lower section of ruler D? Write down your answer.

Simphiwe has measured each of the pencils on the next page. Here are his results:

 * Pencil A is a bit less than 1.5 decimetres long.
 * Pencil B is about halfway between 1.5 decimetres and 2 decimetres long
 * Pencil C is precisely 2 decimetres long.
 * Pencil D is a bit less than 2 decimetres long.
 * Pencil E is precisely 1.5 decimetres long.
 * Pencil F is precisely halfway between 1.5 decimetres and 2 decimetres long.
 * Pencil G is a bit more than 2 decimetres long.

4. Use your new decimetre ruler to check each of Simphiwe's measurements. When you have completed your measurements, compare your findings with your group.

o0o

Mr. Marota tried to measure this earthworm.

First he tried to measure it with the tenths-ruler:

Can you see that the tenths-ruler does not work well for this worm? You can only say that the worm is a bit longer than 6 tenths of a decimetre, and shorter than 7 tenths of a decimetre.

Then Mr. Marota tried a twelfths-ruler:

Next he tried the eighths-ruler:

Mr. Marota was very happy now. He had succeeded in measuring the earthworm quite accurately. He wrote: The earthworm is 5 eighths of a decimetre long.

Task 3
1. How long is the earthworm below?

2. Measure each of the pencils below. For each pencil you must find the ruler that fits exactly. In each case write your answer down like Mr Marta did.

Task 4
1. Measure pencils B, E and F accurately using your new rulers.

2. Compare your results with your group.

3. Work alone again. Use one of your rulers to draw a line exactly 7 tenths of a decimetre long.

4. Use one of your rulers to draw a line exactly 5 sixteenths of a decimetre long.

5. Explain to your group how you managed to do Question 4.

6. Use one of your rulers to draw a line exactly 17 twentieths of a decimetre long.

Equivalent Fractions

Smaller parts

Simphiwe wants to investigate how fish grow when they get different kinds of food. So he wants to measure this little fish accurately.

Simphiwe tries all the different decimetre rulers that he has.

Task 5
1. Can Simphiwe now say accurately how long the fish is?

2. Ben says the fish is 9 twelfths of a decimetre long. Do you agree?

3. Make two new decimetre rulers, one by cutting out and folding Ruler EFGH and the other by cutting out and folding Ruler JKMN. 4. For each new ruler, count the small sub-divisions of a decimetre and write on the ruler what fraction of a decimetre the y are e.g. Ruler E (30ths).

4. Measure the fish above accurately with Ruler EFGH. Write down your answer.

'The language of fractions (equivalent fractions)

Task 6
Measure these fish accurately using Rulers EFGH and JKMN. Write down your best answer like this: Fish X is 19 twenty fourths of a dm.

Compare your results with your group.

Equivalent Fractions: Different descriptions of the same length

Settling a disagreement

Tswanelo and Simphiwe disagree about the lengths of fishes D, F and G. Here are Tswanelo's results:
 * Fish D is 3 quarters of a decimetre long.
 * Fish F is 8 tenths of a decimetre long.
 * Fish G is 21 twenty-fourths of a decimetre long.

Here are Simphiwe's results:
 * Fish D is 15 twentieths of a decimetre long.
 * Fish F is 16 twentieths of a decimetre long.
 * Fish G is 7 eighths of a decimetre long.

Task 7
Work on your own. 1. Using all of your decimetre rulers, investigate the situation regarding the lengths of fishes D, F and G.

2. Write a letter to Tswanelo and Simphiwe, to help them to resolve their differences. (Group work)

This is how Tswanelo measured Fish D.

Tswanelo sees that he can describe the length of Fish D in two ways. He can say it is 3 quarters of a decimetre.

He can also say it is 6 eighths of a decimetre.

3. Can one also measure Fish D with other rulers?

Simphiwe sees that Fish D can also be measured more accurately using twelfths of a decimetre. Write down the fish's length in twelfths of a decimetre.

4. Vuyo says: Fish D is 4 12 sixths of a decimetre long. Is he correct?

5. Explain in writing why 3 quarters of a decimetre and 9 twelfths of a decimetre are actually the same length. Compare your explanation with your group.

6. Work on your own again. Explain in writing why 4 12 sixths of a decimetre and 9 twelfths of a decimetre are actually the same length. Compare your explanations within your group.

Task 8
Equivalent Fraction problems

1. Use your rulers to check if 15 twentieths of a decimetre is the same length as 9 twelfths of a decimetre? Write down the reason for your answer.

2. Compare your response to question 6 with your group.

3. If Fish C is 23 thirtieths of a decimetre long, do you think it can be measured more accurately in sixtieths of a decimetre? First think about it by yourself and come to your conclusion, do not discuss this with your group just yet.

4. A certain Fish X is precisely 3 fifths of a decimetre long. Write down all the other ways that you can describe the length of Fish X accurately.

5. Compare your answers with your group.

6. Another fish, Fish Y is precisely 10 sixteenths of a decimetre long. Write down all the other ways that you can describe the length of Fish Y accurately.

7. Compare your answers with your group.

Combining parts

Houses are sometimes built with cement building sheets instead of bricks. The cement sheets that are made in factories are not all the same thickness. Since sheets of different thicknesses are used for different purposes and sold at different prices, it is sometimes necessary to measure the sheets quite carefully.

The cement sheet sample below is {frac}3/24 dm (three twenty-fourths of a decimetre) thick, as you can see.

Task 9
Measure the thickness of each of the following cement sheet samples. Use the decimetre rulers that you have cut out, and take trouble to make very accurate measurements.

Compare your answers with your group. You must reach agreement.

Task 10
Two or more sheets are sometimes joined to make one thicker sheet. You can see an example of this below. These combined sheets are called composite sheets. Measure the thickness of the dark and the light part of the composite sheet below. Make the most accurate measurements you can.

1. Using the twentieths ruler (Ruler J),
 * measure the darker sheet:
 * measurement _____________ dm.

 * measure the lighter sheet:
 * measurement _____________ dm

 * measure the composite sheet:
 * measurement _____________ dm

2. Using the twenty fourths ruler (Ruler G),

 * measure the darker sheet:
 * measurement _____________ dm.

 * measure the lighter sheet:
 * measurement _____________ dm

 * measure the composite sheet:
 * measurement _____________ dm

3. Working very accurately, draw your own composite sheet as follows:
 * The total thickness of the composite sheet must be dm. (Use Ruler A)
 * The darker sheet must be dm. (Shade it in.)

4. Give the thickness measurements of the darker, lighter and composite sheets in Number 3 using Rulers, A, E, D, F.

5. Examine all the measurements for your light sheet and compare them with the measurements for the dark sheet. Do you see a pattern? Write down what you notice.

6. Work in a group. Discuss how you can use this pattern to get the measurements of rulers A, E, D and F for your composite sheet without using rulers A, E, D and F.

7. What were the most important conclusions from your discussion? Write them down. ____________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________

Use the logic of equivalent fractions to find a method for working out patterns.

Task 11: classroom assessment
Diane measures some samples of composite sheets and records her results. These are given in the table below. For each measurement show which other rulers could also be used to measure the sheet exactly. Write down the accurate measurement from that ruler in the columns. (Check your answers by comparing rulers. Place them next to one another to do this.)

Copy this table and write in your answers.

3. List all the fraction units on your rulers from largest to smallest. ____________________________________________________________________________ ____________________________________________________________________________

4. What went through your mind when you had written down the sequence? ____________________________________________________________________________ _____________________________________________________________________________

Tenths and hundredths.

This is a very fine decimetre ruler.

It is actually a tenths-ruler, but each tenth of a decimetre is again divided into 10 smaller units.

Task 12
1. How many small units are there in the above ruler?

2. Measure the thickness of all the sheet samples on the next page with one of your "old" decimetre fraction rulers (ABCD, EFGH or JKMN).

3. Now measure the sheet samples with your new (hundredths) ruler.

4. Calculate the thickness of each of the following composite sheets in two ways, first by adding your measurements in other fraction parts of a decimetre, and then by adding your measurements in hundredths of a decimetre.

Using the Tenths and Hundredths Ruler

Group work: Discuss this task only when you have completed it.

1. Circle the rulers that made it easier to measure the thickness of the sheets a. our old dm rulers b. tenths and hundredths ruler

2. When we use the tenths and hundredths rulers to measure, we call this kind of fraction
 * ____________________________.

3. Measure Sheet A (above) using your old dm ruler and your tenths and hundredths ruler. Write down the measurements in numbers and in words.
 * _______________________________________________________________________
 * _______________________________________________________________________
 * _______________________________________________________________________

4. Why do you think the tenths and hundredths rulers were invented?
 * _______________________________________________________________________
 * _______________________________________________________________________
 * _______________________________________________________________________
 * _______________________________________________________________________

5. Do tenths and hundredths rulers do the same job as the old dm rulers?
 * ______________

6. What is the difference between them? What is different?
 * _______________________________________________________________________
 * _______________________________________________________________________
 * _______________________________________________________________________

Writing fractions using decimal notation - A different way to write fractions

Instead of writing 7/10, we can write 0,7. "0,7" is read as "nought comma seven", or just as "comma seven".

Instead of writing 7/100, we can write 0,07. This is read as "nought comma nought seven", or just as "comma nought seven".

Instead of writing 2 37/100, we can write 2,37. This is read as "two comma three seven".

This way of writing tenths and hundredths is called the decimal notation.

Task 13
1. Write each of the following lengths in the decimal notation and then find the sum of the lengths: a. 3 dm + 1/10 dm + 4/100 dm b. 1 dm + 7/10 dm + 4/100 dm c. 3 dm + 5/10 dm + 9/100 dm d. 3 dm + 5/10 dm e. 3 dm + 5/100 dm

2. With a partner or in a group, check your answers and compare the methods you used.

3. Arrange Sheet A-F from thickest to thinnest using your tenths / hundredths measurements.

4. Write down their thicknesses in decimetres using decimal notation.

5. Calculate the thickest composite sheet you could make from any two of these sheets and write down the thickness in decimetres and in decimal notation.

6. Calculate the thinnest composite sheet you could make from any two of these sheets and write down the thickness in decimetres and in decimal notation.

Task 14: Calculator Task
a. Enter ".2 + .05 =" and write the answer:
 * __________

b. Write the answer to (a) as an ordinary fraction:
 * __________

c. 25 hundredths is also equal to a ____ part of a decimetre. ( 1 1/10, 4/12, 3/4, 1/2, 1/4

d. Do the following calculations and write them out in the same way as in (a), (b) and (c) above:
 * .7 + .05 = ___
 * .3 + .45 = ___
 * .12 + .13 = ___
 * .2 + .55 = ___
 * .38 + .12 = ___

FET Physics
The next activities cover two important topics in FET physics. They are presented in a very conventional form but, like the Intermediate Phase investigation of fractions, these activities can be taught in an investigative style. The difference is that if the educator's control is strong, the activity will be less of an investigation. If it is less educator-centred i.e. he/she gives more control over the activity to the learners, it will be more of an investigation way. Again we must make the point that the spirit of investigation lies largely in the approach taken by the individual educator to teaching and learning.

Outcomes
At the end of the lesson, learners should be able to:
 * Draw a graph of force versus acceleration and interpret it.
 * State the relationship between acceleration of an object and the force producing the acceleration.
 * Apply this relationship to their everyday life experiences

Teaching method
Experimental/investigative

Teaching aids
Ticker tape timer, ticker tape, metre rule, runway, books to support the runway, thin string, pulley, some 10g mass pieces, graph paper, worksheets, pencil, rubber, ruler, scientific calculator, chalk, board duster.

Tips
Most Grade 12 textbooks and practical worksheets suggest that when doing this investigation the force can be applied on the trolley with rubber bands or spring balances double or triple the force. Anyone who has tried this method will have found that it is very difficult to move along with the trolley while at the same time stretching one or two rubber bands to a constant length. This difficulty can be avoided by using mass pieces (i.e. "weights" as described) instead of rubber bands. Any identical objects, e.g. 10g mass pieces will do the trick.

 * Tie a mass piece to a thin, strong thread.
 * Use an oiled pulley. (See sketch above.)
 * Start the ticker tape timer and then release the trolley. Prevent it from crashing.
 * Increase the number of mass pieces one at a time and repeat the procedure until the trolley accelerates at too high a rate for useful results.
 * Problems to overcome: ticker tape timer not making clear marks and the trolley running skew.
 * Learners must grasp the concept under investigation AND the fact that experimental results are never "perfect".
 * A runway for the trolley can be made from an old door.

Start of lesson
Divide learners into groups at most four learners per group.

Introduction
The educator draws this diagram on the chalkboard ... ... and asks: "What will happen to the object if the two forces act on it simultaneously?"

 * (Anticipated answer: "The object will remain a rest because there in resultant force on it.")

The educator then draws another diagram ... ... and asks: "What will happen if these two forces are applied to the object?"

 * (Anticipated answer: "The object will move to the right because there is a resultant force of 2N acting on it.")

The educator consolidates the answers by referring to previous knowledge: A body will, if at rest, remain at rest or, if moving, continue moving in a straight line at constant speed forever if there are no resultant forces acting on it. (NI)

The educator then writes the aim of the investigation on the chalkboard.

Aim
To investigate the effect on acceleration when mass is increased

Method

 * The educator distributes prepared worksheets and describes the experimental procedure (no mention of "acceleration" at this point) including how the motion of the object can be determined from the ticker timer and tapes.
 * Mention here that when there are sufficient data, these can be plotted on graphs.
 * Learners gather around the table and observe the educator as he/she produces the first tape.
 * Agree with the class on the series of masses to be used and let the learners produce the rest of the tapes for themselves.
 * Agree on the method of finding the time interval between each dot on the tapes and calculate T.
 * Learners now analyze each tape. (Discard the first few points and the last few points on the tapes and use the middle section.)
 * NOTE: if ticker timers are not available it is possible to make ticker tapes with dots that can be analysed. While this is less than ideal to do it this it is certainly better than doing the activity purely as a textbook exercise.
 * Learners calculate the average velocities for each interval (i.e. between dots on the tape) and record these on their worksheets.
 * On the same sheet of graph paper?, plot graphs of velocity vs time for each tape and calculate the "rate change in velocity" for each tape (i.e. for varying masses).
 * Ask questions that get the learners to understand that by varying the masses on the string, they have varied the force applied to the trolley.

 * Introduce the concept of acceleration: the rate of change of velocity. Work out the units of acceleration.
 * Express the slopes of the graphs on the series of v-t graphs as accelerations.

number of mass pieces.")
 * Ask the question: "what is responsible for the acceleration of the trolley?"
 * (Anticipated answer: "The changing force applied on the trolley by changing the
 * Suggest drawing a graph to look for a relationship between force and acceleration. Plot the graph using "number of mass pieces" as the independent variable (x-axis) against the acceleration (y-axis).
 * Is there a straight line relationship? Draw a "best fit" line (i.e. a line that goes closest to most points) on the acceleration vs resultant force graph.

Discussion
object need not be discussed here since the affect is probably within the experimental error anyway.)
 * Is there a straight line trend on the graph? (Carefully executed tests on this apparatus usually lead to one.)
 * If not, what could affect the experimental procedure? (Friction will affect the size of the acceleration but since it is a force in the direction of movement it will not affect the linearity of the graph. The fact that friction varies with the velocity of the moving
 * The educator discusses the questions with the class and clarifies the meaning of a straight line graph relating acceleration to the resultant force. (10 min)

Conclusion
If there is a straight line trend this shows a linear relationship that can be stated:
 * "a is proportional to 1/F"
 * Explain that this is known as Newton's Second Law of motion and show the class the mathematical formulation including mass (of the trolley and NOT the number of mass pieces) as the constant (of proportionality).

Homework
Learners are asked to bring along written information about situations where the relationship between acceleration and force is evident in their everyday experiences/practical situations e.g. The difference between one and two people pushing a stalled car and the resultant accelerations.

Electromagnetism and electromagnetic forces
''The beauty of this investigation, on electromagnetism, is that it is almost identical to the kind of investigations done by Michael Faraday in England and Joseph Henry in the USA in the early part of the nineteenth century. Their pioneering work has led to the great motors and generators that keep our industries moving today.''

Outcomes
At the end of the lesson, learners should be able to:
 * Apply Fleming's Left Hand Rule to determine the force experienced by an electrical conductor in a magnetic field.
 * State and understand the factors which influence this force.
 * Name practical, everyday applications of this force.

Teaching method
Learner investigation

Teaching aids
Retort stand, U-magnet, copper leads (x2), torch cells (x4), circuit board, copper pieces designed for this experiment.

Start of the lesson
The educator divides learners into 3 groups- at least 8 learners per group.

Introduction
The educator asks the following question: "What effects does the electrical current in a wire show? Describe any you have seen."
 * (Anticipated answers: heating, lighting, magnetic and chemical effect.)

The educator starts with phenomena already known to the learners. Make no explanation at this point of the relationship between electric current and its magnetic effect

The educator writes the day's topic on the board. "Investigating forces on current-carrying conductors in magnetic fields."

Aim
To investigate the force experienced by a current carrying conductor in a magnetic field.

The educator issues worksheets, explains the apparatus (see diagrams below) for the investigation and allows the learners to follow the instructions.

Discussion
The educator discusses any effects of forces observed (i.e. movement &Acirc &shy see NII) and draws out learner observations/opinions on the variables affecting the observed forces e.g. increasing the magnetic field strength or increasing the length of the conductor in the magnetic field. Make a chalkboard summary and let learners note the additional information.

Apparatus
For this investigation, set up this apparatus using the suggested materials or others like them. The apparatus is not complicated and can be assembled using scrap or low costs materials.

NOTE: Magnets are easy to come by in the doors of discarded fridges. Old electrical flex and torch cells can also be found or bought very cheaply.

Obtain 3 metal wires, preferably copper and form them into the three shapes below.

Set up the apparatus for the investigation as shown in the diagram.

When electricity flows in the conducting wires, wire 1 must be able to move freely on the loop joints it makes with wires 2 and 3.

Apparatus for the investigation
Wire1 must be free to move into or out of the magnet as shown by the dotted arrows. Know which end of the U-magnet is its North pole.

Now connect the terminals of the battery to wires 2 ands 3 to complete the apparatus. (In a perfect world and with unlimited time, one would leave learners with the question &Acirc &shy "find the relationship among ... etc." &Acirc &shy  and let them both design the apparatus to test the relationships and come up with answers. Unfortunately few educators can afford this luxury and so the apparatus for the investigation is a "given".)

Method and questions to answer by investigation
1. Set up the apparatus as shown in the diagrams.

2. Close the switch and note what happens to conductor 1.

3. What direction does the conductor move?

4. Change the polarity of your connections. i.e. positive and negative terminals. What direction does conductor 1 move now?

5. Will changing the polarity of the terminals affect the movement of the conductor?

6. Close the switch. Observe and note what happens.

7. Reverse the polarity of your magnetic field. Will this affect the movement of the conductor?

8. Are your observations in 2 &Acirc &shy 7 consistent? Would you have expected what you observed? Respond and explain your response.

9. Draw diagrams that show the relationships between magnetic field direction (convention: North to South), the direction of the current in conductor 1 (convention: from positive to negative battery terminals) and the direction of the force on conductor 1.

10. Having drawn your explanatory diagrams (the three directions are all at right angles to one another i.e. the diagrams must show three dimensions: up-down on page left-right on page  and into-out of page.)

11. With the diagrams complete, return to the apparatus and check the predictive value of your diagrams. Introduce Fleming's Left Hand Rule and let learners check the consistency of this rule with their diagrams.

12. Increase the number of cells in the circuit and note the deflection of conductor 1. Does it deflect more or less than when only one cell was used?

13. Is the direction of the force as you would have predicted it, even though current strength is increased?

14. Does the force experienced by the conductor increase or decrease when the number of cells is increased?

15. What can be concluded from this observation, given that increasing the number of cells also increases the current (Ohm' Law)

16. Draw a concept map and write an overall conclusion about the effect on a current- carrying conductor in a magnetic field.

title: SA NC Doing Investigations/Chapter 7


text:
SA NC Doing Investigations/Chapter 8

Clusters, support networks and communities of practice
The ideal environment in which to bring about change, either system-wide curriculum change or more local efforts to change, say, to a more investigative approach to teaching and learning, is one where teacher support is freely available - when and where needed. Ideally the "when" is all the time and on demand. And ideally the "where" is in the place where educators encounter their problems and difficulties: the classroom. Giving support is not as simple as it sounds. For a start, the giver and receiver should be in a trusting, professional relationship. Secondly, the receiver must trust the support giver's knowledge and skills in that discipline. And thirdly the support giver must be an expert. The fact is that nowhere is the ideal commonplace. Givers and receivers of professional support seldom have the time to develop the perfect "mentor-mentee" relationship. There are never enough experts in school education as their skills are in high demand, making them very mobile. It seems to be the way of the organizational world that experts are promoted away from their areas of expertise as they are probably too competent in too many areas! And then there is the principal limitation: money and not enough of it. No government anywhere can afford the cost of quality support needed to effect major change in a very short time. Finally, we all have responsibilities and lives to live beyond our work and so the demands on people and their own time must be kept reasonable.

Now where does this leave us? Is enduring curriculum change a pipe dream? Well, actually, no. If teachers like our MSTotY finalists and many others like them are anything to go by, it is not. We, the willing, can change the curriculum and provide better science and mathematics to all South African learners. But it will take steady progress, creativity and energy to bring about any changes we desire. This chapter offers a few simple suggestions on one course of action. Quite simply, educators can't wait for "the department" to do everything for them. An answer is to develop educator-to-educator support networks. How to organize these depends so much on local circumstances that it is pointless to go into too much detail but here are some provisos for viable teacher support networks. We must start with teachers who:

 * really want to improve themselves professionally;
 * really want to receive support;
 * are prepared to put in effort to improve themselves and each other;
 * are really prepared to give to others as well as receive from them;
 * live reasonably close together;
 * are prepared to meet regularly;
 * are prepared to try new things and ...
 * are prepared to fail (at first) in their attempts to change without withdrawing.

With a group of like-minded professionals we can establish "communities of practice". In our context a community of practice is a group of educators who live and work in close proximity and who can meet regularly to offer practical and moral support; to share ideas and to recount successful teaching experiences. Together educators can analyze their failures and see them not as sources of embarrassment but as sources of really useful, professional knowledge. Building a community of practice takes time and patience but it is a basis for true professional development. Because a community of practice is teacher-driven it encourages a stronger commitment to professional development than official programmes that are attend reluctantly and infrequently. How does one start a professional growth and development group that will become a healthy community of practice? An approach is for a small, committed group to answer a few, key questions. The questions should be re-visited and possible answers re-negotiated as the group grows. The moral "buy-in" of all members is critical so it is important to give every member the chance to add his or her views to the debate. Here are some guidelines.

Who are you?
Someone needs to take the initiative and put out invitations to local schools and teachers to get together. Once this has been done the ball will roll if there is a perceived need for such a grouping.

What do the group members need in general?
Ask this question and come to a consensus about a programme.

What do the group members need, specifically?
Specific, curricular or teaching support. But be realistic. The group can't equip labs or supply computers!

Why do the group members need these things?
Opens the discussion on group members' circumstances and gets a mutual appreciation of each others' problems.

Needs by phase / grade?
Catalogue needs. This will help with the development of the group's programme. After the initial discussions, is there still a genuinely felt need for the group/network?

Clustering.
Schools within close proximity; with similar needs; and with resources or expertise that they are willing to offer to / share with the whole group.

Optimum size: what can YOU handle?
Don't be over-ambitious. Although there may be a great need to serve this group, you cannot do it alone.

What REAL official support is available?
Survey this and find out from local education authorities.

Cooperating with official bodies and personnel.
Make the co-operation with official bodies and persons a priority. Get their blessing and buy-in for the idea.

Sustaining professional development: communities of practice.
When group members start seeing their efforts and participation as important to the survival of the group; and when the survival of the group becomes professionally important to the individual group members, you have a community of practice.

Limitations / problems / weaknesses / difficulties.
Identify and acknowledge these. Then reduce or solve them.

Where are you?
Know where group members teach and try to have all members visit the schools of all other members.

Committees.
Keep committee work to a minimum and make sure that the bulk of meeting time is spent on doing professional work Â and not talking about trivial, administrative matters.

Functions of committee members / portfolios.
If a small committee is formed, make sure that each member has a portfolio and that there is general agreement in the whole group of roles and responsibilities.

Exam setting by cluster.
This is a useful way to get the group collaborate and to address an important need.

How often to meet?
Balance frequency versus efficiency.

Communicating.
Establishing a "communication triangle so that no-one has to contact more than two people:

[[Image:DoingInvestigations_chp8_1.png

Running successful workshops.
The "workshop" has become a standard in development work, and for good reason. A good workshop involves more doing and less talking; an occasion where participants experiment, investigate, hear and share new ideas, and give themselves time to think of better approaches in an engaging atmosphere. Some key features of successful workshops are:

Participant selection:
Workshop participants begin by selecting themselves, in that they should already have done something to show that they are passionate about improving maths, science and technology (MST) education in their schools or districts. Punctuality and attendance; responsiveness, participation and enthusiasm for MST; and the willingness to share their curricular and content insights are important. The group decides who is welcome and who is not.

Intensive engagement:
Workshops must be intensive with total immersion in MST, the principles of OBE and activity-based teaching and learning. This also means workshops that are not too short or where people are arriving late and leaving early. Teacher participants who cannot cope with intense, hard work should not be part of the group in the first place.

Modeling:
At MST workshops, the presenters should try to model good MST education and OBE practice, from planning to presentation. Participants must be able to imbibe the spirit and application of good teaching and learning, the first principle of which is "maximum learner activity."

Less is more:
Less focus on recallable answers (less "right answer-ism") and more focus on the processes of scientific and mathematical investigation, exploration, discovery and pattern-seeking. Less talking and more doing does not mean no time for critical discussion and reflection. It means a shift in emphasis from talk to action. OBE: The context of all MST work done is set by the spirit of OBE. But worry less about OBE terminology and OBE Policy and give more attention to elements of good MST education that promote OBE.

Technology:
Technology Education is a wonderful means to integrate mathematics and science learning and gives both learning areas relevance. Emphasise mathematical, scientific and technological literacy. (The "literacies" get their meaning from an ability to apply MST knowledge to real life. Technological problems are solved by using science and mathematics in context.)

Resources:
Place an emphasis on using waste and recycle-able materials and on improvisation. Any resource that enables learners to do hands-on work is important. Teachers cannot wait for such materials to be supplied and must work together to create them through ingenuity and improvisation.

Follow up and "Subject Advisors":
A focus of the community of practice model is to develop "lead teachers" who give rather than take the lead in their own group's development. Ideally MST lead teachers should serve a wider, provincial commitment to MST- and HR Development but this is not essential. Subject advisors are ideally placed to take the "community's" lead teachers into a wider development process but again, this does not have to be a primary aim of the home-grown support and development network. Educators should see themselves as professional friends and mentors for the other members of their group. Where possible members should observe each other's teaching.

Keep a reflective journal

 * It is not a report of factual information but a record of personal insights and of expectations, perceptions and feelings about one's teaching activities.
 * Journal entries should include observation, speculation, doubt, questioning, self-awareness, problem stating, problem solving, expressing sentiments and emotions, stating ideas regarding content and direction of one's teaching.
 * What did you learn today that you can apply to your teaching in the future?
 * What questions did today's lessons raise for you?
 * What do you need to learn more about?
 * Did you encounter anything today that was a complete surprise to you?

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: SA NC Doing Investigations/Chapter 8


text:
SA NC Doing Investigations/Chapter 9

Scientific and mathematical literacy
Science and mathematics education, projects and investigations have one, common goal: to develop a scientifically and mathematically literate society. In Chapter 10 of this resource book, you are given a number of internet addresses of "websites" that you can visit if you are connected to the internet. (The government is committed to providing all schools with computers in due course.) Useful websites are being created all the time and even though many more may be available by the time your school is connected, those in Chapter 10 are a good entry point.

The definitions given below of the characteristics of science have been adapted from "Explanations of the Factors in ... Scientific Literacy" which can be found at [www.sasked.gov.sk.ca/docs/chemistry/ns_a.html/]

The website contains material from "Student Evaluation: An Educator Handbook" by Saskatchewan Education (1991). The authors have broken scientific literacy down into its components to help educators to assess learners' progress in science. The examples given apply as much to us in South Africa as they do to Canadian students. As you examine them see which component skills etc. can be developed using an investigative approach to science education.

To be scientifically literate is to understand what science is, its "nature" [A] and its relationship to technology and society [D]; what science is about, the key concepts we study in science [B] and how we study them [C & D]; skills that we need to develop [E] and the values and attitudes that good scientists and scientifically literate people will hold [F & G]. The lists actually tell us about the content of science education. Reflect on them and how investigations can help us to achieve our science education aims. Lists A, B and C are described in detail because they are closely related to investigations.

A. Nature of Science
''Scientifically literate people understand the nature of science and scientific knowledge. Science experiences should expose learners to ... scientific inquiry and discovery as ... ''

public and private: Science is based on evidence developed privately by individuals or groups that is shared publicly with others.

holistic: All branches of science are interrelated. E.g. The principles of chemistry govern how an animal digests food.

replicable: Science is based on evidence that could be obtained by other people working in a different place and at a different time under similar conditions.

empirical: Scientific knowledge is based on experimentation or observation. E.g. Scientists perform experiments and gather data from the things they observe.

probabilistic: Science does not make absolute predictions or explanations. E.g. A weather forecaster predicts a 20% chance of rain tomorrow.

unique: The nature of scientific knowledge and the procedures for generating new scientific knowledge are different from those in other fields of knowledge such as philosophy.

tentative: Scientific knowledge is subject to change. It does not claim to be truth in an absolute and final sense. E.g. As new data become available, theories are modified to encompass the new and the old data. Our views since 1900 of atomic structure have changed considerably for this reason.

related to human culture: Scientific knowledge is a product of humankind. It involves creative imagination and is the product of a culture and its technologies. E.g. The use of biotechnology has resulted in the production of synthetic insulin for the treatment of diabetics.

B. Key Science Concepts
Scientifically literate people understand and accurately apply appropriate science concepts, principles, laws and theories as they interact with society and the environment.

Among the most important concepts of science are: change: Change is the process of becoming different. It may involve several stages. E.g. Seasons change throughout the year. Rocks are eroded.

interaction: This happens when two or more things influence or affect each other. E.g. Some animals living in the same place have to compete for available food and space.

orderliness: This is a regular sequence that either exists in nature or is imposed through classification. E.g. The Earth moves about the Sun in a regular manner.

organism: An organism is a living thing or something that was once alive. E.g. Plants and animals are organisms.

symmetry: This is a repetition of a pattern within some larger structure. E.g. Most animals appear to have matching halves. Most wallpaper patterns exhibit symmetry.

force: It is a push or a pull. E.g. A magnet can pick up a paper clip. Pedaling a bicycle causes it to move.

quantification: Numbers can be used to convey important information. E.g. There are 60 seconds in one minute. There are 206 bones in the human body.

reproducibility of results: Repetition of a procedure should produce the same results if all other conditions are identical.

cause-effect: It is how one thing affects another. E.g. Walking outside in the winter may cause your face to get cold.

predictability: Patterns can be identified in nature. From those patterns we make predictions. E.g. When a seed receives enough moisture in a warm place it will germinate. From this, one might predict that to keep seeds from germinating they should be kept cool and dry.

conservation: An understanding of the finite nature of the world's resources, and an understanding of the necessity to treat those resources with prudence and economy, are underlying principles of conservation. In physics, the term `conservation' also has a unique meaning, as in the conservation of energy. E.g. Insulating a home will save energy. Smaller, more efficient cars can be designed to use less fuel.

energy-matter: It is the interchangeable and dependent relationship between energy and matter. E.g. When a candle burns, some of the energy stored in the wax is released as heat and light.

cycle: Certain events or conditions are repeated. E.g. The seasons change during the year. Some birds migrate in the spring and autumn. A pendulum on a clock swings back and forth in a regular manner.

model: It is a representation of a real structure, event, or class of events intended to facilitate a better understanding of abstract concepts or to allow scaling to a manageable size. E.g. A globe is a model of the Earth. Marbles and styrofoam balls can be used to make models that represent atoms.

system: A set of interrelated parts forms a system. E.g. The Earth is a planet in the solar system. A stereo sound system consists of speakers, an amplifier, input devices such as a CD player, and other parts that are all connected together. field: A field is a region of space that is influenced by some agent. E.g. Two similar magnetic poles repel one another. If a ball is thrown into the air, it returns to earth because of the pull of gravity.

population: A population is a group of organisms that share common characteristics.

probability: Probability is the relative degree of certainty that can be assigned to certain events happening in a specified time interval or within a sequence of events. E.g. The probability of getting some types of cancer increases with prolonged exposure to large doses of radiation.

theory: A theory is a connected and internally consistent group of statements, equations, models, or a combination of these that serves to explain a relatively large and diverse group of things and events. E.g. One theory suggests that there are periodic mass extinctions of species.

accuracy: Accuracy involves the recognition that there is uncertainty in measurement. It also involves the correct use of significant figures. E.g. A watch with a minute hand is more accurate for measuring time than an hourglass.

fundamental entities: They are units of structure or function that are useful in explaining certain phenomena. E.g. The cell is the basic unit of life. The atom is the basic unit of matter.

scale: Scale involves a change in dimensions. This may affect other characteristics of a system. E.g. A paper airplane made from a sheet of notebook paper may fly differently than a plane of identical design made from a poster-size sheet of the same paper. time-space: It is a mathematical framework in that it is convenient to describe objects and events. E.g. An average human being has an extension in one direction of approximately 1,75 metres and in another direction of about 70 years.

evolution: Evolution is a series of changes that can be used to explain how something got to be the way it is or what it might become in the future. It is generally regarded as going from simple to complex. E.g. Organic evolution is thought to progress in small, incremental changes. Similarly, scientific theories undergo change to accommodate new data as they become available.

C. Processes of Science
Scientifically literate people use appropriate processes of science to solve problems, make decisions and further their understanding of society and the environment.

Integrated processes include the more basic skills. Skills are acquired and practised throughout life and information processing and problem solving abilities eventually go beyond any curriculum. The basic processes of science are:

classifying: Classifying is a systematic procedure used to impose order on collections of objects or events. E.g. Objects can be grouped in a variety of ways, such as by size, shape or colour.

communicating: Communicating is any one of several procedures for transmitting information from one person to another. E.g. Writing reports, or participating in discussions in class are examples of communicating.

observing and describing: This is the most basic process of science. The senses are used to obtain information about the environment. E.g. During an investigation a student writes a paragraph recording the progress of a chemical reaction between hot copper metal and sulphur vapour.

working co-operatively: This involves an individual working productively as a member of a team for the benefit of the team's goals. E.g. While one member of a group is stirring a mixture of reactants in a beaker, another is reading the temperature whiles another member of the group is writing down the temperatures.

measuring: An instrument is used to obtain a quantitative value associated with some characteristic of an object or an event. E.g. The length of a metal bar can be determined to the nearest millimetre with an appropriate measuring device.

questioning: It is the ability to raise problems or points for investigation or discussion. E.g. A student should be able to create directed questions about observed events. When migratory birds are observed, questions such as, "Why do birds flock to migrate?", "Do some birds migrate singly?", and "How do birds know where to go?" should direct further inquiry.

using numbers: This involves counting or measuring to express ideas, observations, or relationships, often as a complement to the use of words. E.g. One orange had seven seeds in it, while another orange had no seeds.

hypothesizing: Hypothesizing is stating a tentative generalization that may be used to explain a relatively large number of events. It is subject to immediate or eventual testing by experiments. E.g. Ask students to explain what they think might happen to a plant if it is placed in a dark place for several days. Then ask them to explain how to design and conduct experiments to test their explanations.

inferring: It is explaining an observation in terms of previous experience. E.g. Because clay is a less permeable material, puddles of water do not soak away as quickly on clay soil as they do on sandy soil.

predicting: This involves determining future outcomes on the basis of previous information. E.g. Anticipate whether or not it is likely to rain later in the day based on current cloud conditions.

controlling variables: Controlling variables is based on identifying and managing the conditions that may influence a situation or event. E.g. In order to test the effect of fertilizer on plant growth, all other factors that may be important in plant growth must be identified and kept similar so that the effect of the fertilizer can be seen.

interpreting data: This important process is based on finding a pattern in a collection of data. It leads to a generalization. E.g. The grass under a carpet that is thrown on a lawn turns yellow. Removing it eventually allows the grass to turn green again. One might infer from the observations that a lack of light, or an increase in pressure on the plants, caused them to turn yellow. In a different experiment, leaves turn yellow when a plant is kept in the dark. The leaves on a similar plant kept in the light remain green. From this, one might suppose that there is a link between the amount of light a plant receives and the colour of its leaves. A piece of glass can then be placed on the lawn to see if pressure alone will cause plants to turn yellow.

formulating models: Models are used to represent an object, event, or process. E.g. The globe is a model of the Earth. problem solving: Scientific knowledge is generated by, and used for, asking questions concerning the natural world. Quantitative methods are frequently employed. E.g. A student sees a bat one evening and cannot remember ever seeing one during the day. A question arises: "Why is it that I have never seen a bat before dark?" This leads to a series of investigations and research in an attempt to find an answer to the question.

analyzing: It is examining scientific ideas and concepts to determine their essence or meaning. E.g. Groups of students observe satellite weather images. Each group tries to develop a forecast based on the satellite images and their knowledge of weather patterns, the characteristics of weather systems, the motion of weather systems, and so on.

designing experiments: Designing experiments involves planning a series of data-gathering operations that will provide a basis for testing a hypothesis or answering a question. E.g. Car manufacturers test seat belt performance in crash tests. using mathematics: When using mathematics, numeric or spatial relationships are expressed in abstract terms. E.g. The area of a rectangular surface can be found by multiplying the length by the width.

using time-space relationships: These are the two criteria used to describe the location of things or events. E.g. The position of a star on any given date can be determined from astronomical reference tables.

consensus making: Consensus making is reaching an agreement when a diversity of opinions exist. E.g. Discussion of disposal of toxic waste, based on student research, gives students a chance to evaluate information.

D. Science-Technology-Society-Environment Interrelationships
Scientifically literate people understand and appreciate the joint enterprises of science and technology, their interrelationships and their impacts on society and the environment including issues such as:

 * scientists and technologists are human and fallible;
 * the public understanding gap;
 * resources required for science and technology;
 * taking variable positions on important debates;
 * the limitations of science and technology; and
 * social influences on science and technology.

E. Scientific and Technical Skills
''Scientifically literate people have developed numerous manipulative skills associated with science and technology. Scientific and technical skills include:''

 * using magnifying instruments;
 * using natural environments;
 * using equipment safely;
 * using computers;
 * making measurements;
 * manipulative ability;
 * measuring time as accurately as the instruments allow;
 * measuring volume, temperature and mass;
 * using electronic instruments; and
 * using quantitative relationships.

F. Values That Underlie Science
''Scientifically literate people interact with society and the environment in ways that are consistent with the values that underlie science. Values include ...''

 * longing to know and understand;
 * questioning;
 * searching for data and their meaning;
 * valuing natural environments;
 * respect for logic;
 * consideration of consequences; and the
 * demand for verification.

G. Science-Related Interests and Attitudes
Scientifically literate people have developed a unique view of science, technology, society and the environment as a result of science education and continue to extend this education throughout life. Observable attitudes include their ...

 * interest and interests;
 * confidence;
 * commitment to continuous learning;
 * choices of vocation;
 * preferred methods of explanation; and
 * attitudes to the contributions of others.

Mathematical Literacy
Material from the Programme for International Student Assessment (PISA) is equally useful from a mathematical point of view. It does not analyze the components of mathematical literacy in as much detail as the Saskatchewan group analyzes scientific literacy. PISA starts with the assumption that in order to assess learner achievement of certain outcomes, you must have clear definitions. The PISA definitions, developed between 2000 and 2003, provide us with international standards of mathematical literacy, scientific literacy and cross-curricular problem solving, all of which are Critical Outcomes of the new South African curriculum. Compare the PISA view of scientific literacy with that of Saskatchewan Education. The websites containing the PISA 2003 definitions are:

[www.erc.ie/pisa/maths.html/]

[www.erc.ie/pisa/science.html/]

[www.erc.ie/pisa/probsolve.html/]

The PISA definitions are useful yardsticks against which to assess both one's teaching and the learners' progress. According to PISA, mathematical literacy entails "the use of mathematical competencies at several levels, ranging from performance of standard mathematical operations to mathematical thinking and insight. It also requires the knowledge and application of a range of mathematical content that is drawn from areas such as chance, change and growth, space and shape, quantitative reasoning, uncertainty and dependency relationships. These include specific areas of the mathematics curriculum, such as algebra, statistics and geometry."

PISA assesses mathematical literacy in three dimensions: What is the relevance of this compared with the revised national curriculum statements on assessment?

1. First, the content of mathematics, as defined mainly in terms of broad, overarching concepts underlying mathematical thinking, and only secondarily in relation to traditional curricular strands (such as algebra and geometry). ... The four overarching ideas are: Quantity, Space and Shape, Change and Relationships, and Uncertainty.

2. Second, the process of mathematics as defined by general mathematical competencies. These include the use of mathematical language, modeling and problem-solving skills. The idea is not ... to separate out such skills ... rather, questions are organised in terms of three clusters defining the type of thinking skill needed: a) The Reproduction Cluster - is mathematical competencies consisting of simple computations.

b) The Connections Cluster - requires connections to be made to solve straightforward problems.

c) The Reflection Cluster - consists of mathematical thinking, generalisation and insight, and requires students to engage in analysis, to identify the mathematical elements in a situation and to pose questions and reflect on problems.

3. Third, the situations in which mathematics is used, ranging from private contexts to those relating to wider scientific and public issues. An important reason for distinguishing between different mathematical contexts is to embed mathematical problems in real-life contexts that are broader and less abstract than those found in traditional school curricula. According to PISA, scientific literacy involves the use of key scientific concepts to understand and make decisions about the natural world. It also involves being able to recognize scientific questions, use evidence, draw scientific conclusions and communicate these conclusions. (Compare this with the Saskatchewan facets of scientific literacy.) PISA suggests using scientific concepts relevant to the students' world both now and in the near future. These include concepts related to science in life and health, earth and the environment and in technology.

PISA defines scientific literacy as "the capacity to use scientific knowledge, to identify questions and to draw evidence-based conclusions, in order to understand and help make decisions about the natural world and the changes made to it through human activity."

PISA suggests assessing scientific literacy in three dimensions:

1. First, scientific concepts, which are needed to understand certain phenomena of the natural world and the changes made to it through human activity. ... concepts ... are the familiar ones relating to physics, chemistry, biological sciences and earth and space sciences (but) they need to be applied to real-life scientific problems rather than just recalled. The main content of the assessment is selected from within three broad areas of application: science in life and health; science in earth and environment and science in technology.

2. Second, scientific processes, which are centred on the ability to acquire, interpret and act upon evidence. Five such processes ... relate to:
 * the recognition of scientific questions
 * the identification of evidence
 * the drawing of conclusions
 * the communication of these conclusions
 * the demonstration of understanding of scientific concepts

[(Only) ... the last of these ... requires a pre-set body of science knowledge. ... since no scientific process can be content-free, the PISA science questions will always require understanding of key scientific concepts.] 3. Third, scientific situations, selected mainly from people's everyday lives rather than from the practice of science in a school classroom or laboratory, or the work of professional scientists ... .

Cross-Curricular Problem-Solving
"Problem-solving is an educational objective that is common across countries and school subjects, particularly science, mathematics and technology. Students' ability to solve problems in everyday situations is ... of particular interest to educators ... . Problem-solving is a competency essential to successful participation in society and an integral part of the learning process."

PISA defines problem-solving as

"an individual's ability to use cognitive processes to confront and resolve real, cross-disciplinary situations where the solution path is not immediately obvious and where the literacy domains or curricular areas that might be applicable are not within a single domain of mathematics, science and reading."

PISA assesses problem-solving in three dimensions: 1. Three broad Problem Types:

a) Decision Making, which requires the student to make a decision under certain constraints, and taking a number of features of the situation presented into consideration.

b) System Analysis and Design is concerned with either the analysis of a complex situation in order to find out what is the cause of the problem to be solved, or the design of a system that works and achieves certain goals

c) Troubleshooting problems require students to diagnose a faulty or underperforming system or mechanism, and to suggest solutions.

2. Problem Solving Processes The assessment of cross-curricular problem-solving focuses on five processes that students may implement when attempting to solve a problem. These include:

a) Understanding the information given

b) Identifying the critical features and their inter-relationships

c) Constructing or applying an external representation

d) Solving the problem

e) Evaluating, justifying and communicating the problem solution

3. Real-life Contexts The contextual nature of problems in PISA 2003 involves the use of life skills. Rather than using contexts presented as part of the school curriculum, an attempt has been made to develop questions which simulate real-life situations.

Make three comparisons. First, compare the three PISA definitions and see how much they are interrelated. Second, compare the PISA definition of scientific literacy with the Saskatchewan lists and see how well they are matched. And third, compare your own teaching and assessment with the PISA and Saskatchewan Education aims. You will gather that the international aims of science and mathematics education are very consistent with our own here in South Africa.

Look again at the emphasis placed on "real-life situations" in all three PISA definitions (mathematical- and scientific literacy and problem solving). Now think of this aim in terms of investigations which involve real-life situations in learners' own lives. We hope that you will agree that investigations in science and mathematics education are both a modern and internationally respected approach to teaching these very important subjects.

title: SA NC Doing Investigations/Chapter 9


text:
SA NC Doing Investigations/Chapter 10

Useful "Uniform Resource Locators" (URLs)
If you are fortunate enough to have a computer and access to the internet (the world-wide web or "www") there are wonderful "websites" to visit for information. Each site has a unique URL (e.g. www.enc.org) which is actually its electronic address. Many sites are useful for science-, mathematics- and technology educators. Because so many sites exist these days we can only mention a few examples here.

Once you start visiting websites you will find links to many other sites that you may prefer to the ones below. Develop the habit of collecting useful sites in your computer's "Favourites" box. The Department of National Education has a comprehensive website ("Thutong") that consolidates all available curriculum information for educators. In the near future it will also contain actual materials and lesson plans or links to these. The other websites also provide links to many other educational websites. Browse through these and you will find information that you didn't even know you needed! That's the way of the web.

www.thutong.org.za/

www.curriculum.wcape.school.za/

www.wcsn.org.za/news.php

www.school.za/

A good place to start if you are trying to establish standards for science and mathematics education (i.e. to pinpoint the skills, competences, knowledge, attitudes, values etc. you want children at various grades, ages and stages of development to learn), is at ssdoo.gsfc.nasa.gov/education/standards.html

It gives you links to literature on the whole issue of standards as well as taking you to some of the key sites for the individual subjects of interest to NASA. The site covers selected entries for science, mathematics, technology and geography. The (American) National Council of Educators of Mathematics standards site is at www.enc.org

What they have done is show how the essential concepts are built up from the simplest elements to advanced concepts. They follow certain key concepts in mathematics (which are usually applicable to other subject areas as well e.g. science and geography) such as "change" and show the age- and grade-related steps that one might take in developing the concept.

A most ambitious project by the American science / science education community is Project 2061, so named because that is the year in which Halley's comet next appears. The grand aim is for every American citizen to be scientifically literate by then. So www.project2061.org/ is a great website for science educators. The Project 2061 home page then leads you to their "Benchmarks On-Line" at www.project2061.org/tools/benchol/bolframe.html that sets out what is meant by scientific literacy and the steps for getting there. For a quick, pictorial summary of Project 2001, you can look at www.enc.org/

The National Curriculum On-Line for the United Kingdom gives details of educational expectations by Key Stage and Attainment Targets for education in the UK at www.nc.uk.net/ Unlike most of the American work on standards the British version is not based on grade levels but rather attainment levels, regardless of age. Having said that, the levels of development one would expect for certain age ranges are given and this can be a useful guide for educators.

A review of numeracy Attainment Targets are described at www.standards.dfee.gov.uk/numeracy/

A useful site to begin with if you are new to technology education and still trying to fathom how it differs from technical education is the website of the International Technology Education Association (ITEA) at www.iteawww.org/ In addition it gives their 20 standards (which define technology education for the ITEA) at www.iteawww.org/

If you want something meatier, including academic papers and discussions of the finer points of technology education, why not browse the Journal of Technology Education at scholar.lib.vt.edu/ejournals/JTE/.

The web is literally overflowing with sites containing practical ideas for technology education and challenging material on how things work, for instance at www.howstuffworks.com/

At one time the University of Southern California was said to have the biggest computerized university library anywhere in the world. They have produced a "Science Educator's Glossary" which is at www.usc.edu/dept/education/science-edu/A-Clist.html

Browse through the links that interest you and you may find something useful. There are also some very good commercial encyclopedias. But if you want a site that costs you no more than your service provider fee and which gives you some information on just about everything, try wikipedia.org

Once you start searching for sites with good teaching resources you will enter a world with more information than you can cope with. So be quite focused about your searches unless you want to get sucked in and carried away! Some of the sites are commercial, like www.enchantedlearning.com

Another excellent resource site (over 30,000 lesson plans here) costing $9.95 a year for membership Â less than R70 - is at www.lessonplanet.com/

There are excellent mathematics resources for pre-school to Grade 12 and university students (these are suitable for the high flyers in the senior school) at forum.swarthmore.edu/math.topics.html/. The beauty of the website is that it links you to a whole lot of other mathematics resources as well.

A site that is not commercial and which provides some really interesting activities in a range of learning areas is the American Public Broadcast Service site at www.pbs.org

The education website of the US Geological Survey at info.er.usgs.gov/education/ provides activity sheets and background material in geology, hydrology, biology and geography. The geographical stuff is fantastic. Even though it's all about the USA it can be adapted easily. There are activities for pre-school to Grade 12 learners.

On a slightly whackier note you can visit Beakman at www.geocities.com/TelevisionCity/Set/4567/ex.html to find some weird and wonderful activities and investigations that come out of a TV science show. Learners will love these.

In the end, no matter how much fun we have in the classroom, we have to assess and evaluate. Continuous assessment, rubrics etc. are new to many of us and it is interesting to see what other people are doing. Although materials from other countries may have to be adapted before South African educators can use them, good ideas and examples will always be useful. So have a look at www.techtrekers.com/rubrics.html and www.newburyport.k12.ma.us/middle/educator.htm

One of the best and most useful, all round, mathematics and science education sites must be Kathy Schrock's school.discovery.com/schrockguide Not only do we find masses of ideas, including many on assessment, but we also get mathematics and science activities (classified according to grades) and many links to other sites on the world wide web.

Finally, here's something for a bit of fun. The web is full of interesting sites like these to spice up your class with puzzles and icebreakers. thinks.com Look in the "Web Guides" on this site and you will find more puzzles. Many of them may be too difficult for your learners. If so, just get the idea of the puzzles and make up your own!

There are some nice mathematical puzzles at www.puzzles.com/

Finally there are some good icebreakers and energizers at these two websites: www.eslcafe.com and www.kimskorner4teachertalk.com

Have e-fun!

title: SA NC Doing Investigations/Chapter 10


text:
SAASTE Technology

What is Technology Education?
A definition of technology can be taken from any technology curriculum, but what it means to each individual is dependent on one's understanding of technology.

Below are some teachers' understanding of technology:

 * Technology teaches communication, problem solving, finding solutions (based on informed choices), time and self management. Technology reinforces the fact that there are often many solutions to problems.
 * Ricardo Miller

 * Technology is a process whereby learners identify a need or opportunity. Through the acquisition of knowledge they apply their skills. It stimulates critical thinking and creativity.
 * Averil Nolly

 * It is about using the relevant skills, knowledge, and creativity making a contribution to address the problem in a particular situation by making use of necessary materials. It is a technique of doing something to solve a particular problem.
 * Nonzali Mzizi

 * Technology is about applying the knowledge and skills which was acquired to meet certain needs and wants of society.
 * Cheryl Jafta

 * Engaging in a process (Investigate, design, make and evaluate) to solve human needs and wants.
 * Deon Khan

The RNCS does not say what I must do!
This sets the stage for a basic differentiation between a curriculum and a syllabus...

(TECHNOLOGY Revised National Curriculum Statement (RNCS)) A curriculum states in general terms concepts, skills, attitudes & awareness that should be developed, whilst, a syllabus is specific about what exactly must be developed e.g. a curriculum might say manipulative skills, while a syllabus might say cutting.

The RNCS is a curriculum statement, not a syllabus.

In each of the learning outcomes assessment standards spells out the minimum that a learner should be able to do and know at any particular grade level. What it says are the key concepts and ideas that should be developed. These can be developed through activities that are relevant to the concept of idea. Minimum does not preclude learners functioning at levels higher that those for a specific grade. Many of the assessment standards have some text within brackets. These texts are prefaced with; such as,  e.g.  and some are not prefaced. Interpretation of these texts will depend largely on whether the reader analyses it linguistically, technically, or emotively. Whatever the approach, it must not detract from the core requirement of the assessment standard.

The development of technology in the RNCS through the assessment standards suggests an approach which can be summed up thus:

 * FP - craft-like in the approach to projects focus on the developing of manipulative skills
 * IP - some elements of reproduction and/or adapting of existing products focus on development of cognitive skills while further developing manipulative skills
 * SP - more innovative  no reproduction    focus on the honing of manipulative and specific skills   greater emphasis on creative and lateral thinking.

Teaching and learning in Technology must be aimed at developing Technological Literacy so that learners are empowered to cope with the challenges of a technological society. As all developments are manifested through economic, political, social and environmental context there is a need for an understanding of the interconnections between technology, society and the environment. Inherent in the development towards technological literacy is Technological Capability. In the South African technology curriculum, the development of the skills associated with problem solving lies at the heart of capability.

What are these Learning Outcomes about?
The Learning Outcomes in the Technology Learning Area are interrelated statements that state in broad terms the facets that are considered vital to develop technological literacy in learners. The three outcomes focus on the following:

Learning Outcome 1
The learner is able to apply technological processes and skills ethically and responsibly using appropriate Information and communication Technologies

This outcome is a SKILLS outcome. The technological process is a way of doing something (like the scientific process skills). When a learner does technology he/she is demonstrating the ability to do the skill. But the outcome talks of Process and Skill this refers to the stages of the process (South African) which are: Investigate Design, Make, Evaluate and Communicate. Each of these stages has skills associated with them, viz:
 * Investigate: the skills of Finding out.
 * Design: the skills of Planning / Decision making.
 * Make: the skills of Making / Manufacturing.
 * Evaluate: the skills of Reflecting / Checking.
 * Communicate: the skills of Communication.

Learning Outcome 2
The learner is able to understand and apply relevant technological knowledge ethically and responsibly.

This outcome is about the Content (South African) through which we do our technology. It states the Knowledge and Understanding in the areas that form the focus of our studies. These are; Structures, Processing, and Systems & Control. Each of these are have information (knowledge) associated with them, but acquiring knowledge on its own is of no use unless there is an understanding of it. It is Very Important to note that the knowledge is written in as concepts. Refer to the section on /Key Concepts/ to gain a better understanding of what is required in terms of these areas.

Learning Outcome 3
The learner is able to demonstrate an understanding of the inter-relationships between technology, society and the environment.

This outcome is about the interrelationship between Science & Technology and Society. It is designed to provide opportunities to develop Awareness of and opportunities to come up with strategies to address situations. This outcome is by far the Most Powerful of the outcomes because it gives us reasons for doing Technology. This outcome can provide the context and situations / scenarios for technology modules / projects. Technology exist because of us (our needs, wants and aspirations, to fix the things we do wrong and improve on the things we do right) and Technology is for us (to make our lives easier and comfortable). It is also important to note that this outcome is Exactly the same in the Natural Science learning area.

/Key Concepts/
The key concepts are the results of the lead teachers analysis of all the assessment standards. It talks to the key aspects that need to be addressed in each outcome at any grade level.

 * Grade 4
 * Grade 5
 * Grade 6
 * Grade 7
 * Grade 8
 * Grade 9

/Modules/
Our modules are complete units of work that contain a series of enabling activities / tasks and a challenge.

Each of these modules is designed to provide the learner with an opportunity to apply knowledge and skills in an authentic situation.

 * Processing Grade 8/9
 * Mechanical Systems Grade 9
 * Structures Grade 5
 * Structures Grade 8

/Activities/
The activities have been designed to develop specific knowledge & associated skills that form the core of the assessment standards of the various grades. These must not be considered, nor taken to be "technology" - They are only enabling activities designed specifically to assist you with ideas for the development of concepts, what needs to be taught, learnt, so that learners have a chance at success when engaging in technology. The activities are not contextualised in any module as such and are not about making a product, as our focus is on the development of concepts.

 * Conductors & Insulators
 * Electronic Circuits
 * AND & OR Gates
 * Circuit/Systems Diagram
 * Hydraulics
 * Hydraulics & Pneumatics
 * Technological Products
 * Preservation-1
 * Identifying Materials
 * Properties of Materials
 * Preservation-2
 * Electroplating
 * Conditioning-Strengthening/Waterproofing-1
 * Conditioning-Strengthening/Waterproofing-2
 * Shaping
 * Forming
 * Forces
 * Types of Structures
 * Mechanisms Worksheet

title: SAASTE Technology


text:
SAASTE Technology/Key Concepts

The key concepts are the results of the lead teachers analysis of all the assessment standards. It talks to the key aspects that need to be addressed in each outcome at any grade level.

 * /Grade 4/
 * /Grade 5/
 * /Grade 6/
 * /Grade 7/
 * /Grade 8/
 * /Grade 9/

title: SAASTE Technology/Key Concepts


text:
Conlang/Intermediate/Sound notation

Imagine that you go to another country. You can't speak this country's language, and so you grab a travel book with some common sentences. Let's say you go to France, and you see that the way you ask for the hotel is "S'il vous plaît, où est l'hôtel?". Try to say it. If you don't know how to read French, perhaps you are trying to read it as an English sentence. That's just not good, because you might read it something like "Sil vooze plate, ow ehst low-tel", which doesn't sound like the French sentence you wanted to say.

IPA and CXS
To prevent such things from happening, an alphabet was invented to represent the most common sounds in all languages on Earth, called the International Phonetic Alphabet, or IPA. In order to represent each sound by a single symbol, the designers of the IPA have created a great many new letters — upper- and lower-case Roman letters treated separately, modified versions of Roman letters that rotate them, flip them around, or add hooks, loops, or bars to them, Greek letters, and a few symbols that are partly or completely new. IPA is a very valuable tool for linguists, but there's also a downside to all those special symbols. They aren't easy to add into electronic documents — there isn't a key on a standard keyboard for, say, ɰ — and they're hard to display, too — with all those little details, they require higher resolution than ordinary text (that is, plain ASCII), and many computer programs can't display them at all. To get around these problems, people have invented various alternatives to IPA using standard ASCII characters (though of course these alternatives sometimes need more than one character to represent a single sound). For this book, we're going to use one such alternative designed by and for conlangers, called Conlang X-SAMPA, or CXS for short. (The full name, in case you're curious, is "Conlang Extended Speech Assessment Methods Phonetic Alphabet".)

There is a chart of CXS sound names available in the appendix. Don't worry, you don't need to know all these sounds right now; the next section will introduce you to some of the more common English ones. There are a few general patterns that may help make sense out of the overall arrangement of CXS. (Don't put yourself out trying to memorize these patterns; it should be enough later that you've been exposed to them now.) Most consonants start with a letter; if any additional symbols are needed, the additional symbols usually aren't letters, and if there is an additional letter it's preceded by an underscore, like "" or "". Most digits are used to represent vowels. The backslash, backquote, tilde, and semicolon symbols, "    ", are only used as modifiers after something else to form a different sound — though it will turn out that, of these, backquote, tilde, and semicolon modify the sound in uniform ways, while backslash usually means "something similar to", and occasionally is used to make a new symbol with no relation at all to the old one. The underscore symbol, "", is only used as a separator between other symbols within the representation of a single sound.

CXS is a handy single phonetic alphabet if you only get to learn one, and we won't expect you to learn any other phonetic alphabets for this book. But, that said, you'll also find IPA being used routinely by conlangers in finished documents (like slide presentations, or language descriptions made to be printable on paper); so it will probably pay off for you to become somewhat familiar with IPA as well. To help you along with that, we've set up a chart showing both IPA and CXS together, for comparison.

Distinguishing sounds from letters
You may have noticed during the Beginner lesson on sounds that there was some trouble distinguishing between the sounds that we say and the words that we write. To solve this problem linguists tend to write sounds — that are spoken — between a pair of forward-slashes (//) and letters — that are written — between angle brackets (<>).

For example, the English word ship is written <ship> and pronounced // (in CXS, or in IPA).

title: Conlang/Intermediate/Sound notation


text: SAASTE Technology/Key Concepts/Grade 4

title: SAASTE Technology/Key Concepts/Grade 4


text: SAASTE Technology/Key Concepts/Grade 5

title: SAASTE Technology/Key Concepts/Grade 5


text: SAASTE Technology/Key Concepts/Grade 6

title: SAASTE Technology/Key Concepts/Grade 6


text: SAASTE Technology/Key Concepts/Grade 7

title: SAASTE Technology/Key Concepts/Grade 7


text: SAASTE Technology/Key Concepts/Grade 8

title: SAASTE Technology/Key Concepts/Grade 8


text: SAASTE Technology/Key Concepts/Grade 9

title: SAASTE Technology/Key Concepts/Grade 9