Vilma Kisnierien Ė
email: vilma.kisnieriene@gf.vu.lt

Kastytis Beitas
email: kastytis.beitas@gf.vu.lt

Vidmantas Sakalauskas
email: vidmantas.sakalauskas@gf.vu.lt

Algis Daktari Ūnas
email: algis.daktariunas@gf.vu.lt

Information Technologies for Biology Education: Computerized Electrophysiology of Plant Cells

Keywords: biophysical education, data acquisition system, teaching/learning strategies, computerized teaching laboratory

Biology has moved from a bench-based discipline to a bioinformational science in modern times but application of computational and analytical methods of informatics in it is still a problem for many researchers and students of biology. We suggest to integrate cost effective and practical combination of the real and the virtual laboratories into the undergraduate biological science curriculum. This laboratory work illustrates passive and active electrical properties of plant cell membranes while introducing basic principles of electrophysiological recording, data acquisition and analysis. As the object for investigation in this laboratory work large cells of starry stonewort (Nitellopsis obtusa) were used. The simple program for experiment control and express visualization of recorded data was developed. Experiment proposed in this paper is easy implemented with a minimum of laboratory equipment, materials and gives an experience of computerized biological experiment.

Introduction

The application of information technology and informational thinking in the biological sciences leads to the modification of students teaching mode. Biology, like the informatics, is advancing at incredible speed these days. It is very important not only to apply informational thinking and informatics technologies in study of the live world and biotechnologies, but to enrich development of informatics with ideas from informational system of the live world also [START_REF] Kirvelis | Extended informatics paradigm in biological and psychological education[END_REF]. Rapidly increasing power of computers enables detailed simulations of biological systems and inevitably raises the question of whether computers will eventually replace wet labs. Computer-based simulations of experiments provide a cheaper alternative to traditional practical classes. Many experimental problems are concerned with the representation, organization, manipulation, distribution, maintenance, and use of information, particularly in digital form. Virtual laboratories can provide workable alternatives in cases when learning outcomes focus on interpretation and manipulation of data. Because of flexibility in time, location, pace, and process, they are potentially more effective in students learning. In many biology fields virtual teaching laboratories are more ethical also because no real animals are used in them.

Virtual cell laboratories are attempts to use computer simulation for the various cells living process. They are used in scientific studies ("To understand complex biological systems requires the integration of experimental and computational research -in other words a systems biology approach. Computational biology, through pragmatic modeling and theoretical exploration, provides a powerful foundation from which to address critical scientific questions head-on" [START_REF] Kitano | Biological robustness[END_REF])) but they can be very successful in a teaching also. Some "virtual cell biology labs" are just complexes of animated images about important cells processes (e.g., NDSU Virtual Cell Learning Environment (2000)) without possibility to interact and experiment. Interactive Lab gives an opportunity to learn about the terms, principles, and techniques of experiments through electronic simulations and modeling of complex phenomena (for example, BioQ Collaborative, 2006). Web-based interactive virtual laboratories incorporate modeling and electronic journal, ability to collaborate with other researchers. ICT technology makes learning more interactive, enjoyable, and customizable. But this is not always the case. None of the models can reflect live processes exactly and completely, also often the critical approach is missing. Biological data are very complex and interlinked. Inquiry based learning, such as laboratory research investigations, develops students' practical, technical and reasoning skills, as well as important scientific habits of mind. The active and rigorous nature of classroom inquiry can significantly enhance students' understanding of science concepts and processes of life. The ability to use laboratory equipment, reagents and possibility to manipulate organisms or experience of real signals processing is an essential learning outcome of a practical class. When inquiry is systematically implemented in a classroom, the student takes increased control of their own learning through the guidance of their teacher. Students must organize data in logical and meaningful ways, make detailed observations, and sometimes transform raw data to reveal patterns, relationships between variables, or to clarify results. But those who have worked with both kinds of laboratories say this question -real or virtual laboratory -misses the point. Each approach offers certain benefits; the challenge is to blend them together successfully, including statistics, physics, computer science, and engineering. Ability to manipulate materials through the use of common tools and laboratory equipment allows students to create simulations and working models in order to test their ideas. Combination of the real and the virtual can provide a cheaper, easier, and less time-and labour-intensive alternative; it produces a better experience then a separate work in real and virtual laboratories.

In this study we suggest cost effective and practical science inquiry approach that can be integrated into the undergraduate biological science curriculum. The experiment and software described in the paper were developed under the EU programme Leonardo da Vinci II within the pilot project "Computerised laboratory in science and technology teaching".

Bioelectrical Phenomena in Cells

Every live cell generates an electrical potential on cell plasma membrane that may result in the flow of electric current. This bioelectricity of cell membranes is related with selective permeability to common ions and has important consequences for many cellular processes. Understanding of bioelectrical mechanisms is important for comprehension of cell functioning.

Electrophysiology has proven to be a powerful tool in understanding of plant physiology and development. This technique has elucidated the many mechanisms underlying the electrical phenomena of cell membrane in neurons and muscle tissue also. Difference of potential across the membranes of all living cells called the resting potential depends on difference in ionic composition on the two sides of the membrane. Membrane potential responds to changes of numerous physiochemical variables as temperature, pH, extracellular and intracellular concentrations of ions and so on [START_REF] Kitasato | Membrane potential genesis in Nitella cells, mitochondria and thylakoids[END_REF]. The membrane potential is measured as a voltage difference across the membrane.

Internodal cells of fresh-water charophytes are known for their ability to generate action potential [START_REF] Johnson | Action potentials in a giant algal cell: a comparative approach to mechanisms and evoliution oi excitability[END_REF]. The giant alga Nitellopsis obtusa generates action potentials (AP) in response to mechanical stimulation, injury, or direct electrical stimulation. The bioelectrical response of a charophyte cell is rapid and highly sensitive to chemicals in environment.

Action potentials involve a transient influx of Ca 2+ to the cytoplasm, effluxes of K + and Cl - [START_REF] Thiel | Ion channel activity during the action potential in Chara: a new insight with new techniques[END_REF]. The depolarization phase of AP is caused by an influx of Cl -. AP repolarization is comprised of two stages. Repolarization phase is due to the outward K + flow and the activity of the electrogenic pumps at the plasma membrane. It is supposed that the second stage of repolarization during AP is related to the operation of electrogenic H + -pumps in the excitable membrane. K + efflux is controlled by calciumdependent potassium channels, which close when the Ca 2+ cyt decreases [START_REF] Thiel | Ion channel activity during the action potential in Chara: a new insight with new techniques[END_REF].

Object for Investigation of Bioelectrical Phenomena

In laboratory works we propose to use large cells of starry stonewort (Nitellopsis obtusa). The algae grow in aquaria without any special care or treatment. It is known that Characean cells are most suitable material for analysis of the electrical characteristics of plant cells [START_REF] Shimmen | Characean cells as a tool for studying electrophysiological characteristics of plant cells[END_REF]. Cells of charophytes are well explored experimental systems. The giant charophyta cell separated from talloma and kept in artificial pond water can he considered to be a single organism that maintains essential physiological characteristics for a long time. The usefulness of Characeaens in the laboratory depends upon the ability of internodal cells to survive after isolation from the plant, and on the large size and regular shape of these cells. These internodes approximate to cylinders in shape and provide seemingly ideal material for many physiological observations and manipulations. Typically the internodal cells used in electrophysiological experiments are about 10 cm length and 1 mm in diameter. Internodal cells of Characeae are intensively used for studies in electrophysiology [START_REF] Beilby | Perfusion of charophyte cells: a critical analysis of the method[END_REF][START_REF] Kitasato | Membrane potential genesis in Nitella cells, mitochondria and thylakoids[END_REF], ion transport [START_REF] Demidchik | Characteristics of non-specific permeability and H + -ATPase inhibition indused in plasma membrane of Nitella flexilis by exessive Cu 2+[END_REF]Shimmen, 2001) cytoplasmic streaming [START_REF] Kikuyama | Membrane control of cytoplasmic streaming in characeaen cells[END_REF], and ion channel activity, [START_REF] Berecki | Tonoplast Anion Channel Activity Modulation by pH in Chara coralline[END_REF][START_REF] Tazawa | Cell physiological aspects of the plasma membrane electrogenic H + Pump[END_REF], as well as to study ecophysiological characteristics [START_REF] Sakalauskas | Computer assisted system for the assessment of wastewater toxicity using biolectrical response[END_REF].

Equipment for Implementation of Electrophysiological Experiment

The laboratory work described in this paper is a part of teaching material for the undergraduate students of biophysics and illustrates passive and active electrical properties of cell membranes while introducing basic principles of electrophysiological recording, data acquisition and analysis. The cost of equipment can be a critical barrier for introducing electrophysiology exercises in biology teaching programs. Proposed experiment is easy implemented with a minimum of laboratory equipment and materials. When a microscope with video camera is available, the observations of experiment can be demonstrated for all students of the class or for remote students in distant learning.

The equipment for electrophysiological experiments includes multifunction data acquisition system (DAQ), which is a common device for all experiments introduced into the course of biophysics, Plexiglas chamber with Ag/AgCl 2 electrodes for cells stimulation and biopotential registration.

The multifunction data acquisition device used by us is "e-Biol" system (Daktariunas, 2004), which implements features (programmable amplifier, differential inputs, user defined multiplexing of DAQ inputs and other) which are essential for realisation of experiments with biological objects. Membrane potentials of up to 8 cells of green alga Nitellopsis obtusa were simultaneously recorded using a plexiglass chamber. In experiments with microelectrodes an additional multichannel biopotential amplifier was used. The measured cells biopotentials were coded as 12 bits words (or 16 bits -depending on modification of DAQ "e-Biol") in each channel and saved to file. The cells were stimulated electrically, chemically and mechanically. The number and quality of outputs (two 12 bits analog outputs and 24 bits ones) of the "e-Biol" DAQ allow implementation of any stimulation algorithm. Simplified block scheme of data acquisition and control device "e-Biol" is shown in Fig. 2.

Any other data acquisition device can be used in described laboratory works, but few modules are essential for such experiments -amplifier with low input current especially if microelectrodes are used, analog digital converter and timer. Sampling frequency of bio-potential is low, so the data acquisition device can be supplied with interface to any computer port for data input/output, such as COM, LPT or USB. In more complex laboratory works data acquisition device must include multiplexer for multichannel registration, digital-analog converter and module of digital information output for electrical stimulation of the cell.

Next and very important part of equipment is software. Standard full set of software for computerized experiments encompass procedures of control of experiment parameters, data acquisition, data visualization, and data analysis as a finished product. This kind of software usually complicates modification of experiment by user, because of source code unavailability and very limited range of methods and algorithms for data analysis. In the other hand, a vast number of powerful software for data visualization, processing and analysis (e.g., OriginLab, MatLab) that can be used for implementation of any method or algorithm are proposed to the market. Some tasks can be realized with commonly used spreadsheet software. We propose to implement simple programs for experiment equipment control with minimal data visualization, analysis and saving abilities. More advanced data processing is passed to specialized software for data analysis. We developed a simple program for data acquisition that works in conjunction to data analysis freeware program Data Master 2003 (Data Master 2003, 2004).

This program controls hardware of data acquisition device, acquires data and writes data to computer memory and displays the data in real time. The program also is used to define parameters of experiment -sampling interval, number of samples, gain coefficient of programmable amplifier, numbers of channels to be used and etc. At the end of experiment the program transfers data from computer memory to spreadsheet and graphics of Data Master. Screenshot of the program is shown in Fig. 3. Program was written in Borland Delphi.

Implementation of Experiment

The freshwater alga Nitellopsis obtusa were cultured in tap water at room temperature. Prior to an experiment, internodal cells (second or third internode below the tip of growing alga) were separated from neighboring cells. The internodes were kept in the dark at least overnight in artificial pond water (control solution for electrophysiological testing) containing 0.1 mM KCl, 1.0 mM NaCl, 0.5 mM CaCl 2 , and 1.0 mM TRIS buffer, pH 7.5 (adjusted with NaOH). The extracellular registration of membrane parameters (resting and action potential) are carried out according to the K'-anaesthesia method of [14]. Up to several internodes are placed in a plexiglass chamber having distinct yet identical sections (a-pool), as seen in Fig. 4. One end of the cell is placed in the larger a-pool. The node and small segment (about 1 mm) of each cell is positioned in the common central c-pool, filled with 100 mM KCl in control solution. Electrical isolation between the cand a-pools is achieved with 5% boric Vaseline junctions (v), as well as by an air gap (ag) between them (Fig. 4). The cell parts in the a-pools are continuously bathed with control or test solutions.

Bioelectrical signals are obtained from one general reference electrode placed in a reference pool (r), similar to an a-pool, and from appropriate measuring electrodes (me) in (a) pools (Fig. 4). Through out the study, electrodes made of chlorinated silver wire with both high stability and low electrode potential are used. The electrical contact between (r) and (c) pools is enabled through the P-shaped glass tube bridge (b) plugged with 3% (w/v) agar solidified in a 3M KCl solution. The placing of reference electrode (re) in (r) pool instead of in the (c) pool was necessary to avoid the appearance of chlorine ions as a potential component that may interfere in later measuring of the RP value. Such interference could occur due to alteration of the Cl -concentration difference between the constant c-pool and changing test solutions. Action potentials are elicited by injecting depolarizing current between two pools using Ag/AgCl wires.

Electrical signals from electrodes are led directly (or through the high input impedance preamplifier module when microelectrodes are used) to the input of the differ- ential amplifier (ad, Fig. 4) of multifunction data acquisition system. Sampling frequency for registration of resting potential (RP) was selected as 1 Hz.

Students Work

The laboratory works on algal cells electrophysiology can be organized according inquiry based approach in this way: the general applications where electrophysiological cell methods can be used are related with two topics:

-Electrical potentials in plants and algae are similar to potentials in animal neural cells. How plants and algae can be used as models of animal neurons? In what way the use of algal cells can be more convenient then use of animal neurons? On what cellular mechanisms the similarity of plant/algal and animal cells is based? -Electrical potentials of algae depend on chemical composition of water in what they dwell. How this electrophysiological sensitivity of cells can be used in evaluation of quality of environment?

Students are asked to search literature databases about possible use of algal cell electrophysiology and to analyze it. On the basis of information they collect and presented descriptions of laboratory equipment for these experiments they are asked to find directions how measurements of electrical potentials can be used in research of mentioned problems. Students are expected to present ideas how electrophysiological methods can be used as a tool for research of:

-differences and similarities of electrophysiological phenomena of neural and algal cells, -influence of biologically active substances on activities of membrane ion channels, -influence of water pollutants on rest and action potentials.

For example, it is expected that students will find that differences in ion channels composition of animal and algal cells determines differences in potentials generation that can be demonstrated in mathematical models (that are realized as a computer software, for example, "Neuron") and in wet experiments.

The full solutions of mentioned problems can be realized in practical works that are organized as unstructurized large practicum where time limits aren't critical. In practical courses that are divided to small cycles the solving of big problems must be divided to solving of small ones also. In this case after students comprehend and explicate the wide context of electrophysiological investigations with algal cells the continuum of possible experiments can be divided into few parts and, depending on time available, each part can be executed as a separate laboratory work.

First part. Resting potential as a reaction to changes of main ion concentration.

In this stage of the laboratory work students can observe and investigate:

1) very negative resting potentials (up to -250 mV) of the cell;

2) dependence of resting potential from different pH or concentration of potassium and sodium ions in surrounding solution. Second part. Action potential and characteristics of action potential.

During this experiment students can observe and investigate: 1) action potential as a result of electrical or mechanical stimulation; 2) magnitudes with depolarizing peaks over 0 mV; 3) AP durations of seconds; 4) refractory periods up to several minutes.

Third part. Processing (noise removing) and analysis of experimental data, application of theory and statistics knowledge for practical purposes:

1) Nernst potentials calculation for the ions distributed across the Nitellopsis cell membrane to hypothesize the ions responsible for the resting potential and for the depolarizing phase of the AP. These calculations suggest that K + is responsible for the resting potential and that Ca 2+ influx and Ca 2+ -activated Cl -efflux are responsible for depolarizing phases of the AP. 2) Simple statistical data processing. For this calculation the experimental data collected in laboratory works by all students of the group can be used. 3) Comparison of Nitelopsis obtusa cells and other cells (for example neurons) reactions to applied stimulus. In presented laboratory work simulated data of neurons responses are used because experiments with real neurons are much trickier then experiments with algal cells. Bioeth-Fig. 6. Resting and action potentials of Nitellopsis obtusa membrane. Changes of magnitude of action potential depend on interstimular interval. ical requirements limit the use of animal objects in similar experiments also. Programs Neuron [START_REF] Huguenard | Electrophysiology of the Neuron: an Interactive Neuron[END_REF] or NeuroDynamix [START_REF] Friesen | NeuroDynamix: Computer Models for Neurophysiology[END_REF] are used for simulation of neural cell membrane potentials.

The real experiments as ones presented here give experience of real experiments with real biological objects. Virtual experimental part (simulated experiments with mathematical model of neuron biopotentials) gives experience on processes in more tricky biological objects. This doubled experiment can serve as an experimental/simulational core of more enriched learning complex. In case when potential of World Wide Web is used experiment can work as nucleus for seminar part, where students search for additional information, articles and reviews in scientific journals, databases and news strips and discuss issues related to wide range of problems from research in plant ant animal electrophysiology to environmental expertise, prostheses of sensory organs and brain-computer interfaces.

Summing Up

Presented experiment system is a base on what students create an authentic understanding of scientific skills, processes, and habits of mind, interacting with materials, measurements, variables and informational technologies application. Information search in multiple sources (for example, articles in data bases of scientific magazines) and analysis help to connect and to fuse students' observations and the observations of others in students' minds. Study of cell biology by virtual means is helpful, it helps to imagine invisible process in the cell, but wet experiment gives and requires more knowledge integrated from different fields of science even though biological object investigated in wet experiment is a simple one. The students must understand physiology of object, chemistry of used materials, methods of signal registration and data analysis. Lack of knowledge from any field of science necessary for real experiment gives artifacts or loss of experimental data [START_REF] Sorgo | Computerised laboratory in science and technology teaching: the course on biological processes[END_REF]. Investigative science is the way in which science should be taught but the difficulties of managing classroom inquiry, need for expensive hardware, and software, modern bioethical requirements stop wide implementation of purely experimental learning. So combination of wet (real) experiment and virtual experiment that enables virtual experiments with tricky, expensive and bioethically restricted objects, enhanced by discussion and internet-extracted information is the necessary alloy for production of knowledge necessary for specialists in nature sciences and technologies. Presented computerized laboratory work is used in teaching laboratory for biology students but it can be used in education of agriculture, sylviculture, medicine, computer sciences specialists also.

Fig. 1 .

 1 Fig. 1. The internodal cells of Nitellopsis obtusa.

Fig. 2 .

 2 Fig. 2. Simplified block scheme of data acquisition and control device "e-Biol".

Fig. 3 .

 3 Fig. 3. Screenshot of the Data Master program.

Fig. 4 .

 4 Fig. 4. Schematic diagram of the experimental set-up. See text for details.

Fig. 5 .

 5 Fig. 5. Resting potentials of Nitellopsis obtusa membrane. Resting potential changes depend on pH of used solutions.

Fig. 7 .

 7 Fig. 7. Simulated action potentials of neuron. Simulated by program Neuron.

Informacini u technologij u panaudojimas biologijos mokyme: kompiuterizuoti elektrofiziologiniai augalini u l asteli u matavimai

Vilma KISNIERIEN Ė, Kastytis BEITAS, Vidmantas SAKALAUSKAS, Algis DAKTARI ŪNAS Šiuolaikinė biologija gali būti priskiriama informacini u moksl u kategorijai, tačiau informacinio m astymo bei analitini u metod u taikymas nemažai daliai biologijos student u bei tyrėj u vis dar išlieka problema. Šiame straipsnyje siūlome, kaip real u ir virtual u elektrofiziologijos laboratorinius darbus sujungti i vien a darb a, kuris galėt u būti itrauktas ne tik i biologijos, bet ir i medicinos, žemės ūkio, bioinformatikos studij u programas. Laboratoriniame darbe, naudojant menturdumblio Nitellopsis obtusa l asteles, tiriamos pasyvios ir aktyvios augalini u l asteli u membran u elektrinės charakteristikos, susipaž istama su elektrofiziologini u signal u registravimo ir analizės principais. Eksperimento kontrolei ir surinkt u duomen u registravimui bei tiesioginiam pavaizdavimui buvo sukurta paprasta kompiuterinė programa. Siūlomam eksperimentui atlikti užtenka minimalios laboratorinės irangos ir medžiag u. Derinant j i su virtualiais eksperimentais, igyjamos ne tik elektrofiziologijos, bet ir informatikos, signal u teorijos, duomen u analizės, chemijos žinios bei gebėjimai.


Olga Kosheleva
email: olgak@utep.edu

Ana Medina-Rusch

Vera Ioudina
email: vioudina@stat.ucla.edu

Pre-Service Teacher Training in Mathematics Using Tablet PC Technology *

Keywords: technology for teaching and learning, mathematics education, digital divide

This study focuses on the use of innovative Tablet PC technology in learning and teaching mathematics. Specifically the effects of incorporating Tablet PC technology in pre-service teachers' mathematics education were analyzed. The significant impact of technology use in mathematics education was assessed by evaluating and comparing students' final project and course grades. Grade performance of two groups of students was compared. One group was the treatment group where students extensively used Tablet PCs to work on mathematical investigations and explorations and to create lesson plans and animated games through PowerPoint presentations. The other group was the control group where students worked on identical mathematics investigations and created lesson plans without utilizing any technology. The outcome shows that the technology enhanced group achieved significantly higher scores than the control group. This outcome indicates a greater improvement in the treatment group's understanding of mathematical content versus that of the control group's.

Introduction

To benefit from computers teachers should have access to good educational software and be familiar with the available software. Ideally teachers should be able to use appropriate software to create math activities that guide students to higher order thinking. Pre-service (future) teachers should be confident and knowledgeable about effective instructional strategies that incorporate technology including those available using Tablet PCs.

In the beginning of 2004 the team of researchers from the College of Education and College of Engineering at the University of Texas at El Paso (UTEP) received a grant from Hewlett Packard.

This grant allowed UTEP to organize a mobile Tablet PC lab. This lab was readily available for use in the mathematics content and mathematics methods classes taught in a field-based environment. It was this HP grant which provided us the necessary technology for this study.

Methodology

In spring semester of 2005, 38 pre-service elementary teachers were enrolled in mathematics content and mathematics methods courses. These students were also enrolled in internships at local elementary schools. The students' internships and class placement was random.

The study focused on two groups of students. The treatment group consisted of fifteen students that regularly met in a professional development school where they were provided with 14 Tablet PCs for use in their classes. The control group consisted of 23 students who were enrolled in the same courses with the same instructors but met at different times and location. In this control group Tablet PC technology was not used. The method used in teaching pre-service teachers from the control group will be called in this paper standard inquiry based method.

One of the primary goals of the senior-level undergraduate mathematics and mathematics methods courses is to provide capstone-type mathematics classes for future teachers, and significantly increase students' understanding of the mathematics concepts and mathematics pedagogy. The main reason why these two classes are offered together (back to back) is to provide intrinsic connection between abstract mathematics concepts and mathematical pedagogical practices. The scheduling also provided great opportunity to organize team-teaching of these classes.

Rationale for Proposed Intervention

Research findings [START_REF] Mariotti | Influence of technologies advances on students' maths learning[END_REF][START_REF] Hoyles | What can digital technology take from and bring to research in mathematics education[END_REF] supporting the use of innovative technology in teaching mathematics show that it:

• may help students to -deal effectively with multiple representations -learn how to formulate and test hypotheses; -learn to visualize difficult mathematical concepts; -constructively build their own knowledge; -create and experiment with mathematical models;

-further develop problem-solving abilities; • enhances ability of students to focus on the process of problem solving instead of the computational aspect, thus decreasing dependence on procedural aspects of mathematics; • provides an opportunity to introduce mathematically interesting/challenging problems much earlier than in traditional mathematical classroom; • can also provide immediate feedback that allows students to discover their mistakes, analyze them and correct them; in this way, errors stop being obstacles, and may become a gateway to meaningful learning; • encourages explorations and investigations with the use of dynamic software tools.

Description of the Intervention

All mathematics content and mathematics methods classes were team taught using a series of rich mathematical investigations, in-depth discussions on topics in the methods textbook (Van de [START_REF] Van De Walle | Elementary and Middle School Mathematics: Teaching Developmentally[END_REF]) and group lesson preparations and implementations. Specifically, these courses were designed to foster conceptual understanding of mathematics and pedagogy in the following major strands: rational numbers, geometry, algebra, number theory, and functions.

Rational numbers investigations dealt with concepts such as equivalent fractions, meaningful operational algorithms and decimals. Geometry investigations dealt with the concepts of similarity, congruence, transformations, and the area versus length relationship. Number theory investigations dealt with place value, alternative bases and deconstructing operational algorithms while applying them to different bases. The investigation covering functions included linear and non-linear relationships as well as exploring multiple representations. All projects were designed to include open-ended problems that required thorough investigations to achieve successful solutions. Instructors utilized collaborative learning and inquiry based methodology while students worked in small groups.

The treatment group used Tablet PCs to explore the investigations or projects. This technology allowed students to explore each activity fully without being limited to paper and pencil drawings. The real time feedback in the various programs and websites used gave students a good evaluation tool of their problem solving methods. In addition, the ability to iterate calculations allowed students to focus on the "big" picture without getting bogged down with repetitive calculations.

Besides the rich investigations, students from both groups planned individual/group lessons and implemented them in local elementary schools. Students created these lesson plans by applying the concepts investigated in their mathematics content and mathematics methods courses. Students in the treatment group successfully implemented Tablet PCs in their individual and group teachings allowing pupils to engage in meaningful technology based activities. The following diagram illustrates the dynamic structure of the technology-enhanced mathematical classroom. By the end of the four month period both groups had completed and presented several investigations. The students' final exam was an oral presentation covering the functions and algebra investigation.

The students' final grade was a cumulative grade indicative of the students' performances in each investigation, presentation, teaching and methods review.

Implementing the Tablet PCs in a Technology-Enhanced Classroom

Tablet PC's are fully functional PC's running an enhanced version of Windows XP Professional. One of their most interesting feature is the "digital ink" that allows a user to write on the screen using a stylus pen. The same pen is also used as a mouse. The handwriting recognition software allows the written text to be converted to digital text in Microsoft Word. Traditional keyboard and mouse are also available. Tablet PC's also have built-in wireless connectivity, so they can communicate with each other even if there is no internet connection present (ad hoc mode). They can also wirelessly connect to the internet. In newer Tablet PCs battery life can be up to six hours, however in our case our Tablets only had a battery life of three hours.

Students had the opportunity to utilize the Tablet PC during their presentations by connecting the Tablets to a data projector. In addition, since we had 14 Tablets and 15 students, students were able to work with the Tablet PCs individually or in small groups. Faculty used special software to communicate with the students.

First, using VNC software (http://www.realvnc.com/what.html) and internal wireless capability, faculty could connect to any of the students' Tablet PCs and check their work, help them and project their successful solution on the screen.

Second, Discourse software (www.ets.org/discourse) was used for the assessment. Using this software, faculty was able to ask various types of questions including open-ended or multiple-choice questions. Each question could be accompanied by an image guiding students to explore this particular question. In addition to images, faculty could guide students to a specific internet site relevant to the question. Students could answer their questions concurrently or on their own pace.

The faculty was also able to simultaneously monitor each student's answer in real time. Some of the students preferred typing the answers; others opened a writing pad, and recorded their answer on the pad. This writing pad automatically converted it to digital text. Also, students could have discussions using the "chat" option (that can be disabled by faculty).

Pre-service teachers employed the Tablet PCs in their university courses and during their internship teaching in a number of ways. The most popular program was a program called Microsoft Journal, which comes free on Tablets and is used as an electronic whiteboard. The Power Point program was extensively used for presentations and for the creation of animated virtual manipulatives. The students were very successful in creating virtual manipulatives for solving word problems, place value tasks, fractions, and geometrical designs. Similarly, Kidspiration and Inspiration (http://www.inspiration.com/) software was used for the creation of mathematical activities and games. Students also used this software to create concept or mind maps.

Variety of specialized free software was also used. One of the most interesting software was Java Bars (http://tt.uga.edu/tt/jwilson.coe.uga.edu/olive/ welcome.html) that provides a creative workspace to explore fractions. Tangram editor was also extensively used.

Excel was used in mathematical projects by utilizing the different spreadsheet capabilities such as graphing and formula calculator. Another interactive site used for fractions was Cynthia Lainus' website (http://math.rice.edu/˜lanius/Lessons/) from Rice University where students could explore fractions with pattern blocks.

Students also used a variety of internet sites such as the National Library of Virtual Manipulatives (http://nlvm.usu.edu/en/nav/vlibrary.html), NCTM Illuminations (http://illuminations.nctm.org/), Math Playground (http:// www.mathplayground.com/) and InterMath Investigations (http://intermath. coe.uga.edu/). Pre-service teachers used a WebCT portal provided to all students by the university to submit their work for grading and discussion as well as for submitting questions outside of class time.

Results

Formative Assessment

We assessed the progress of the pre-service teachers from both groups throughout the semester using grades from Projects (one and two), Quiz #1 (only one quiz was given), teaching observations, and students' reflections.

We computed students' grade point average (GPA) using only their previous mathematics courses they have taken. This information provided us with good estimation of their initial mathematical knowledge. Typically, pre-service teachers enrolled in our program do not have very strong mathematical background. Specifically, the average math GPA computed for the treatment group was 2.99, and the average math GPA for the control group was 2.98. This indicated that both groups had approximately the same mathematical background and content knowledge prior to the study. Fig. 3 shows comparative performance of both groups on Project #1. As we can see, pre-service teachers from control group demonstrated better performance (more A grades, and the average grade is higher, as shown in Table 1).

Figs. 4, 5, 6 and 7 and Table 1 show that the situation changed, and starting with Project # 2 pre-service teachers from treatment group demonstrated much better performance.

Statistical Results

The effectiveness of the proposed technology enhancement for teaching mathematics was statistically compared to the standard inquiry based method. This comparison was based on the results of two distinct items. The first was the students' Final Exam given at the end of a 4 month learning period. The second was the students' Final Grades which is a cumulative grade based on all the investigations throughout the semester. Of a random sample of 38 students, 15 were taught by the technology enhanced method and were considered our treatment group. The other 23 students were taught by the standard inquiry-based method and were considered our control group. All 38 students were taught by the same qualified instructors under similar conditions. As was mentioned before, students' grade point average (GPA) was computed using only their previous mathematics courses. The average math GPA for the treatment group was 2.99 while the average math GPA for the control group was 2.98. This means that both groups had approximately the same mathematical background and content knowledge prior to the study. We developed descriptive statistics for both samples and both teaching methods see (Table 2).

Based on our observations during the previous semesters, we expected that the new teaching method would be more effective. If we could show a statistically significant difference between these groups, we could conclude this observation to be valid. To do this, we have set up a null hypothesis that the two sample means were the same (or the two groups come from the same population), and attempted to reject that hypothesis.

The standard approach for this situation is to use the small-sample t-test. The first theoretical assumption about the independency of observations was satisfied, based on the information provided about the sampling procedure. The second assumption was about Normality. As we can see in Figs. 8 through 11, the histograms of all four distributions are bell-shaped and approximately symmetric.

To verify the Normality in more rigorous way, we used the χ 2 -test for the Final Exam and Final Grades for both groups. The results of four tests are represented in Table 3.

The test shows that for all four distributions the calculated value chi-square was less than the critical value for the indicated degrees of freedom and α . There was insufficient evidence to reject the null-hypothesis about the Normal distribution for given samples. Consequently, each sample data set appeared to come from a population that is approximately Normal. Moreover, as we know, the t-test is robust to moderate departures from Normality.

The third and weaker assumption was that the two samples come from distributions with approximately the same variance.

For our samples we could see that the ratio of the larger to smaller standard deviation was greater than two, therefore the unequal variance test had to be used. In the case where the sample sizes and variances are different (n 1 = n 2 and σ 2 1 = σ 2 2 ), an approximate small-sample test could be obtained by modifying the standard deviation and the degrees of freedom associated with the t-distribution.

We used the Approximate Small-Size Procedure (McClave and Sincich, 2003, p. 390;Devore, 2004, p. 373) when σ 2 1 = σ 2 2 . We let μ 1 and μ 2 represent the population mean for the Final Grade of the treatment and control groups, respectively. The null hypothesis H 0 : (μ 1μ 2 ) = 0 signified that samples do not differ significantly. The alternative hypothesis was

H 1 : (μ 1 -μ 2 ) > 0. Test statistic is t = X1-X2 √ s 2 1 /n1+s 2 2 /n2
, where t is based on degrees of freedom equal to

df = (s 2 1 /n 1 + s 2 2 /n 2 ) 2 (s 2 1 /n1) 2 n1-1 + (s 2 2 /n2) 2 n2-1
.

The test results are represented in Table 4. Table 4 shows that the t-values for both tests are much bigger than the critical value of the t-test with the 5% Type I Error. The table of t-distribution (Devore, 2004, p.747) shows that the area under the 32 degrees of freedom t-curve to the right of 2.851 for the Final Exam test is 0.0035. So the p-value for the upper-tailed test is also 0.0035, that corresponds to the probability 0.35%. For the Final Grade test the p-value is only 0.001 or 0.1%. With a confidence level 0.95, we estimated the difference in the mean of the Final Exam scores between treatment group and the control group to fall in the interval (2.40, 9.45). This means that with 95% confidence we estimated the mean Final Exam score for the new method to be anywhere from 2.40 to 9.45 points more than the mean of the Final Exam score for the standard inquiry-based method.

The 95% confidence interval for the Final Grade is (2.70, 8.00), so we estimated the mean of the Final Grade for the new method to be anywhere from 2.70 to 8.00 points more than the mean of the Final Grade for the standard inquiry-based method. In other words, the new method was associated with higher mean scores.

Therefore there was enough evidence to indicate that (μ 1μ 2 ) differs from zero and that (μ 1μ 2 ) > 0. Using a significance level of 0.05, we could reject the null hypothesis that the two sample means were the same in a favor of the alternative hypothesis which stated that the treatment group mean was significantly bigger then the control group mean for both, the Final Exam and the Final Grade.

Consequently, the statistical analysis of the data collected showed that the technology enhanced group achieved significantly higher mean scores than the control group. These higher mean scores obtained by the treatment group translated into the treatment group having a greater understanding of mathematics content when compared to the control group. This greater understanding could be directly contributed to the effective implementation of the Tablet PC technology in the mathematics content and mathematics methods courses. Thus, we simultaneously achieved two goals. We increased students' mathematics education software literacy and mathematics content knowledge.

Conclusions and Discussions

NCTM Technology Principle (NCTM, 2000) states: "Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning".

Defining the role of teacher in using technology, it says: "The teacher must make prudent decisions about when and how to use technology and should ensure that the technology is enhancing students' mathematical thinking".

Use of digital technology in the classroom brings innovation. It also may ease the path to successful teaching for some categories of pre-service teachers, while create difficulties and obstacles for others.

Our observations of pre-service teachers' interactions with computers have lead us to the conclusion that some of the future teachers already came from the generation of Digital Natives, while others certainly belong to Digital Immigrants [START_REF] Prensky | Digital natives, digital immigrants[END_REF][START_REF] Prensky | Listen to the Natives[END_REF]. The proportion of these populations varied from semester to semester. Typical response of Digital Natives was "working with Tablet PCs was fun", while typical Digital Immigrant would usually say that "working with Tablet PCs was a hard work, and I had to learn a lot about computers".

The technology-enhanced courses proved to provide a truly transformational experience for the pre-service teachers.

The greatest transformation was occurring in the affective domain. One good example was a student who came to our class with a fear of mathematics. At the end of class, she successfully taught a mathematical lesson using Tablet PCs in her internship classroom. She applied to a NASA Pre-Service Teacher Summer Institute at NASA Langley Education Research Center during June 2005, attended the Institute, and was awarded the best mathematics teaching award at the teaching competition held at the end of the program. She obtained the teaching position in one of the elementary schools, and she is currently pursuing her Master's degree in Mathematics Education. When asked about her experiences, she told that "math was never my strong subject". "I did not understand it, I did not like it". When asked how she survived high school math, she told that her sister helped her in all her classes. Now, incorporation of technology in teaching and learning process changed a lot for her. She was using technology extensively in her everyday life. Therefore, when asked to teach and learn mathematics with the use of Tablet PC technology, she was not scared, but excited. She said that "we never have seen Tablet PC before, but we saw them, it was really cool, and we loved them". "When we actually got to use them with the students, and we would go to the schools and use them, the kids loved them (Tablet PCs, OK) even more. . . everything they did on Tablet PCs related to mathematics was like a game." She says: "when I was exposed to math in a way you taught it, and the way we were learning it at NASA, I realized that it really is not that hard, as it was in my head. I am not much of an algebraic person, so trying to do math that way was really hard. When I was able to do it more physically (with manipulatives), and more conceptually, then I really liked it. Now I really want for students like me to be able to learn mathematics, and know that you can do mathematics in a lot of different ways". This is just one example of a successful story. Here is another one. Typically, pre-service teachers after their graduation have to take the standardized test to acquire teaching license certification. This test proved to be somewhat difficult for some of the students. Sometimes pre-service teachers take the test more than one time.

All the pre-service teachers from the treatment group were able to pass the test immediately after they graduated. The average total score for the treatment group was 259, while the score for the mathematical domain questions was 269.5.

The situation was different for the control group students. Several of them took the test more than one time (one pre-service teacher had to take the test four times). The average total score for the control group (after everybody passed the test) was 232, and the score for the mathematical domain questions was 238.5.

These results once again confirm our conclusion that treatment group achieved a greater understanding of mathematics content when compared to the control group.

There are numerous changes brought by technology in teaching and learning environment. In the beginning the most focus was on the ability to do accurate computations faster. This is what [START_REF] Moursund | Getting to the Second Order: Moving beyond Amplification Uses of Information and Communications Technology in Education[END_REF] has called first-order use of technology, that is, when we use technology to do what we can do already, but technology allows us do these things faster and more accurately. Now it is the time to address and focus on the second-order use of technology, i.e., local and global changes technology brings to different aspects of our society. In this work specific issues in mathematics education were addressed, and successful implementation of Tablet PCs technology was presented.

O. Kosheleva received her MS degree summa cum laude in mathematics and applied mathematics from Novosibirsk University, Russia, in 1978. After coming to the USA in 1989, she received MS in computer science and PhD in computer engineering from the University of Texas at El Paso. In Russia, she participated in organizing mathematical olympiads for high school and middle school students, was actively involved in a special outreach program for teaching mathematics to high school students to better prepare them for the university studies, tutored university students in math, and taught mathematics and computer science to engineers. Since 2001, she is teaching at the University of Texas at El Paso. Her research interests include mathematics education in teacher preparation, embedding technology in learning, cognitive growth in elementary and advanced mathematical thinking, curriculum development, mathematics and applied mathematics. She has more than 40 journal publications, more than 60 papers in peer refereed conference proceedings, and more than 80 published conference abstracts. These publications cover different areas of mathematics education, mathematics and applied mathematics.

B ūsim u matematikos mokytoj u mokymas naudojant planšetinio kompiuterio technologij a

Olga KOSHELEVA, Ana RUSCH, Vera IOUDINA Šiame straipsnyje aptariamas tyrimas, nagrinėjantis planšetinio kompiuterio technologijos taikym a mokant ir mokantis matematikos. Svarbiausias dėmesys buvo sutelktas i planšetinio kompiuterio technologijos poveik i student u -būsim uj u matematikos mokytoj u mokymui. Technologijos poveikis matematikos mokymui buvo nustatytas ivertinus ir palyginus mokini u galutin i projekt a ir mokymosi lyg i. Atliekant tyrim a buvo lyginamos dviej u grupi u mokini u žinios. Viena grupė buvo stebimoji grupė, joje mokiniai naudojo planšetinius kompiuterius atlikdami matematines užduotis ir rengdami nam u darbus arba animuotus žaidimus naudodamiesi pateikči u rengykle. Kita grupė buvo kontrolinė -jos mokiniai atliko tas pačias užduotis nesinaudodami jokia technologija. Hipotezė buvo patvirtinta: technologij a naudojanti grupė surinko daugiau tašk u nei jos nenaudojanti. Taigi technologijos naudojimas turi didel e itak a matematikos supratimui ir išmokimui.

Fig. 1 .

 1 Fig. 1. Diagram describing pre-service teachers' integrated study of mathematics content and mathematical pedagogy in field-based context with technology enhancement (treatment group).

Fig. 2 .

 2 Fig. 2. Tablet PC screen showing Discourse session: questions are provided on the left part of the screen, image can be displayed on the right part of the screen.

Fig. 3 .

 3 Fig. 3. Comparison of the treatment and control group based on the grades from math Project 1.

Fig. 4 .

 4 Fig. 4. Comparison of the treatment and control group based on the grades from math Project 2.

Fig. 6 .

 6 Fig. 6. Comparison of the treatment and control group based on the Final Project grades.

Fig. 7 .

 7 Fig. 7. Comparison of the treatment and control group based on the Overall grades.

Fig. 9 .

 9 Fig. 9. Distribution Histogram for the Control group's Final Exam.

Fig. 10 .

 10 Fig. 10. Distribution Histogram for the treatment group's Final Grades.

Fig. 11 .

 11 Fig. 11. Distribution Histogram for the control group's Final Grades.

A

  . Medina-Rusch received her BChE degree in chemical engineering from the Georgia Institute of Technology in Atlanta, Georgia in 1996. After working as a pulp and paper engineer for GL&V/Celleco, she received her MS in mathematics education from the University of Georgia in 2003. She has taught in the Department of Mathematical Science at the University of Texas at El Paso from 2003 to 2006. More recently she has taught in the Math Department at Georgia Perimeter College from 2006 to 2007. She is currently at the University of Georgia completing her PhD in mathematics education. Her research interests include: pre-service teacher mathematics preparation, enhancing mathematics teaching and learning through the implementation of technology and teaching methods aimed at developing higher order thinking skills. V. Ioudina received her MS degree in mathematics from Irkutsk State University, Russia, in 1977. She conducted her postdoctoral research at the Institute of Economics and Statistics in Moscow (Russia) with main focus on the robust estimation of the parameters of multiple linear regressions and got PhD in economics (statistical methods in economical researches) in 1985. V. Ioudina has taught in the areas of mathematics and statistics for almost twenty-five years at several universities in Russia, Mexico and the United States.Prior to coming to USA she lived in Mexico for three years and taught at the undergraduate and graduate levels at Monterrey Tech (known as the Tec de Monterrey) and at the Autonomous University of Ciudad Juarez. Since 2003 she has been working in the Department of Mathematical Science at the University of Texas at El Paso. Currently she is teaching at the Statistics Department of UCLA. Her main research interests fall within the field of applied statistics and data analysis. She participated in several collaborative research projects whose final product can be applied to social issues and educational improvements.

Table 1

 1 Average grades for treatment and control groups (throughout the semester)

		Project #1	Project #2	Quiz #1	Final Exam	Final Grade
	Treatment Group	86.1	93.	71.7	90.8	93
	Control Group	89.5	88.7	59.7	84.9	87.7

  Fig. 8. Distribution Histogram for the treatment group's Final Exam.

					Table 2
				Sample's descriptive statistics
	Group		Final Exam			Final Grade
		n Mean X Var σ 2 St.Dev.
	Treatment 15	90.8	14.31	3.78	15	93.04	8.95	2.99
	Group 1
	Control	23	84.9	77.55	8.81	23	87.70	42.49	6.52
	Group 2

n Mean X Var σ 2 St.Dev.

Table 3 The

 3 Results for χ 2 -test for Final Exam and Final Grades

			Final Exam
	Group	n	χ 2	df	α	χ 2 critical
	Treatment	15	3.53	1	0.05	3.84
	Group 1
	Control	23	4.37	1	0.025	5.02
	Group 2
			Final Grade
	Group	n	χ 2	df	α	χ 2 critical
	Treatment	15	1.52	1	0.05	3.84
	Group 1
	Control	23	0.78	2	0.05	5.99
	Group 2

Table 4

 4 The results of the Small-Size t-test

		t	df	α	t critical	Confidence Interval
						Lower limit	Upper limit
	Final Exam	2.851	32	0.05	1.694	2.40	9.45
	Final Grade	3.418	33	0.05	1.693	2.70	8.00

Informatics inEducation, 2007, Vol. 6, No. 2, 321-334

* This work was supported by Teachers for New Era minigrant, which is part of the TNE grant from the Carnegie Corporation of New York.