Suming Li

Synthesis and Self-Assembly of Hydroxypropyl Methyl Celluloseblock-Poly(ε-caprolactone) Copolymers as Nanocarriers of Lipophilic Drugs

Keywords: hydroxypropyl methyl cellulose, poly(ε-caprolactone), block copolymer, reductive amination, micelle, self-assembly, drug release

Synthesis and Self-Assembly of Hydroxypropyl Methyl

Cellulose-block-Poly(ϵ-caprolactone) Copolymers as Nanocarriers of Lipophilic Drugs

INTRODUCTION

In the past decades, polymeric nanomicelles have attracted increasing attention as drug delivery systems because of their unique advantages including enhanced drug solubility, prolonged blood circulation, passive targeting to tumor issue by enhanced permeability and retention effect, decreased adverse effects, and improved drug bioavailability. [START_REF] Cabral | Block Copolymer Micelles in Nanomedicine Applications[END_REF] Micelles are generally prepared from amphiphilic block copolymers via various self-assembly approaches. The hydrophobic component aggregates into the core which is capable of encapsulating lipophilic drugs, whereas the hydrophilic component forms the shell to stabilize the micelle structure in an aqueous medium. Generally, amphiphilic copolymers used in drug delivery should be biocompatible, bioresorbable, and nontoxic as they should be metabolized in or excreted from the human body without causing adverse reactions.

Poly(ε-caprolactone) (PCL) is an FDA-approved biocompatible and biodegradable polyester which has been extensively studied as drug carriers, medical implants, and tissue engineering scaffolds. [START_REF] Dash | Poly-small je, Ukrainiancaprolactone based formulations for drug delivery and tissue engineering: A review[END_REF] In drug delivery, many PCL-based formulations have been investigated, including nanoparticles, nanofibers, hydrogels or nanogels, polymersomes, micelles, polyplexes, and drug-conjugates. [START_REF] Grossen | PEG-PCLbased nanomedicines: A biodegradable drug delivery system and its application[END_REF] In fact, PCL can be used as a degradable and hydrophobic block to combine with various hydrophilic polymers, including both natural biopolymers such as starch, [START_REF] Karami Ghaleseiedi | Starch-based dual amphiphilic graft copolymer as a new pH-sensitive maltidrug co-delivery system[END_REF] and chitosan, [START_REF] Liu | Preparation of chitosan-gpolycaprolactone copolymers through ring-opening polymerization of epsilon-caprolactone onto phthaloyl-protected chitosan[END_REF][START_REF] Youssouf | Enhanced effects of curcumin encapsulated in polycaprolactone-grafted oligocarrageenan nanomicelles, a novel nanoparticle drug delivery system[END_REF] and synthetic polymers such as poly(ethylene glycol) (PEG), [START_REF] Grossen | PEG-PCLbased nanomedicines: A biodegradable drug delivery system and its application[END_REF] polyurethane (PU), [START_REF] Irani | Gold coated poly (epsilon-caprolactonediol) based polyurethane nanofibers for controlled release of temozolomide[END_REF] and so forth. Importantly, PCL is compatible with a wide range of drugs. 8,[START_REF] Hakkarainen | Heterogeneous biodegradation of polycaprolactone -low molecular weight products and surface changes[END_REF] It has been reported that PCL-based micelles can encapsulate doxorubicin, [START_REF] Qiu | Self-assembled polyethylenimine-graftpoly(epsilon-caprolactone) micelles as potential dual carriers of genes and anticancer drugs[END_REF][START_REF] Ahmed | Self-porating polymersomes of PEG-PLA and PEG-PCL: hydrolysis-triggered controlled release vesicles[END_REF] 5-fluoro uracil, [START_REF] Gu | Preparation of polysaccharide derivates chitosan-graft-poly(varepsilon-caprolactone) amphiphilic copolymer micelles for 5-fluorouracil drug delivery[END_REF] curcumin, [START_REF] Youssouf | Enhanced effects of curcumin encapsulated in polycaprolactone-grafted oligocarrageenan nanomicelles, a novel nanoparticle drug delivery system[END_REF] paclitaxel, [START_REF] Shuai | Corecross-linked polymeric micelles as paclitaxel carriers[END_REF] nimodipine, [START_REF] Ge | Preparation, characterization, and drug release behaviors of drug nimodipine-loaded poly(ε-caprolactone)-poly(ethylene oxide)-poly-(ε-caprolactone) amphiphilic triblock copolymer micelles[END_REF] sorafenib, [START_REF] Tang | Therapeutic Effect of Sorafenib-Loaded TPGS-b-PCL Nanoparticles on Liver Cancer[END_REF] and so forth. Among them, curcumin has received much attention in the past decades because it is a naturally occurring polyphenol with outstanding biological activities, including anticancer, antiinflammatory, antibiotic, antioxidant, and antiviral activities. [START_REF] Peng | Drug delivery systems for overcoming the bioavailability of curcumin: not only the nanoparticle matters[END_REF][START_REF] Qi | Enhanced In Vitro and In Vivo Anticancer Properties by Using a Nanocarrier for Co-Delivery of Antitumor Polypeptide and Curcumin[END_REF] As a hydrophilic polymer, polysaccharides including cellulose, chitosan, alginate, dextran, cyclodextrin, and so forth have attracted widespread interest because of their biocompatibility, biodegradability, nontoxicity, and the presence of numerous hydroxyl groups allowing chemical modification. [START_REF] Liu | Polysaccharidesbased nanoparticles as drug delivery systems[END_REF] Cellulose is the most abundant polysaccharide which is a linear β-1,4-glucan with an acetal linkage between C1 and C4 carbon atoms. [START_REF] Klemm | Cellulose: fascinating biopolymer and sustainable raw material[END_REF] Cellulose is insoluble in water and in common organic solvents, but it can be dissolved in Nmethylmorpholine N-oxide, ionic liquids, or in water at extreme pHs. The poor solubility of cellulose is referred to strong intrachain and interchain hydrogen bonding. The intrachain hydrogen bonding is dominated by the strong O3-H•••O5 bond which is responsible for the high axial chain stiffness, whereas the interchain hydrogen bonding ensures the cohesion between cellulose chains. [START_REF] Moon | Cellulose nanomaterials review: structure, properties and nanocomposites[END_REF] This poor solubility greatly restrains the potential applications of cellulose for the synthesis of amphiphilic copolymers. Chemical modification of cellulose is performed by substitution of hydroxyl groups with alkyl or hydroxyalkyl ones so as to reduce the hydrogen bonding and thus to improve the solubility. A number of water soluble derivatives of cellulose are commercially available, including hydroxyethyl cellulose, carboxymethyl cellulose, ethyl cellulose, hydroxypropyl cellulose, and hydroxypropyl methyl cellulose (HPMC). [START_REF] Yang | Self-assembled cellulose materials for biomedicine: A review[END_REF] As a biobased polymer, HPMC has been widely used in pharmaceutical and food preparations such as viscolizing or thickening agent, coating polymer, bioadhesive, capsule shell, excipient, and eyedrops. It is one of the most important hydrophilic biopolymers used in oral drug delivery because of its high swellability. [START_REF] Al-Tabakha | HPMC capsules: current status and future prospects[END_REF] Controlled radical polymerization based on hydroxyl groups has been used to synthesize graft copolymers. Bordallo et al. synthesized a series of oxidized carboxymethyl cellulose-graf t-poly(ethylene glycol)-dodecylamine (OCMC-g-PEG-DDA) with different contents of DDA. [START_REF] Bordallo | Self-assembly in aqueous solution of amphiphilic graft copolymers from oxidized carboxymethylcellulose[END_REF] The copolymers are able to form micelles with narrow size distribution. Wang et al. synthesized ethyl cellulose-graf tpoly(2-(diethylamino) ethyl methacrylate) (EC-g-PDEAE-MA). [START_REF] Wang | Synthesis, self-assembly and drug release behaviors of pH-responsive copolymers ethyl cellulose-graft-PDEAEMA through ATRP[END_REF] pH-responsive micelles are obtained from the copolymers which can efficiently encapsulate rifampicin. Das and Pal evaluated hydroxypropyl methyl cellulose-graf tpolyacrylamide (HPMC-g-PAM) as a potential carrier of 5amino salicylic acid. [START_REF] Das | Hydroxypropyl methyl cellulose grafted with polyacrylamide: application in controlled release of 5-amino salicylic acid[END_REF] However, grafting polymerization is poorly controllable because of the large number of hydroxyl groups on the polymer backbone. In contrast, water soluble cellulose derivatives can be used as a hydrophilic component for the preparation of amphiphilic block copolymers because the reducing end (hemiacetal group) of cellulose is easily converted to an aldehyde group. Reductive amination between aldehyde and amino groups is a well-established reaction but is rarely used to synthesize cellulose-based block copolymers because of the lack of common solvent for the two blocks, side reactions induced by lateral hydroxyl groups, and limited availability of the hemiacetal group at the chain end.

In our previous work, linear HPMC-polylactide (HPMC-PLA) and Y-type (HPMC) 2 -PLA block copolymers were synthesized for the first time by combination of ring-opening polymerization (ROP), amination reduction and UV initiated thiol-ene or thiol-yne click reaction. [START_REF] Lu | Synthesis and self-assembly of AB2-type amphiphilic copolymers from biobased hydroxypropyl methyl cellulose and poly(L-lactide)[END_REF][START_REF] Wang | Synthesis and Self-Assembly of Amphiphilic Block Copolymers from Biobased Hydroxypropyl Methyl Cellulose and Poly(l-lactide)[END_REF] More recently, reductive amination was used to synthesize HPMC-PLA diblock copolymers and HPMC-JEFFAMINE diblock, triblock, and three-armed copolymers. [START_REF] Lu | Novel thermo-responsive micelles prepared from amphiphilic hydroxypropyl methyl cellulose-block-JEFFAMINE copolymers[END_REF][START_REF] Lu | Self-assembled micelles prepared from bio-based hydroxypropyl methyl cellulose and polylactide amphiphilic block copolymers for anti-tumor drug release[END_REF] These various amphiphilic and thermo-responsive copolymers are able to aggregate in micelles by self-assembly in an aqueous medium and serve as nanocarriers of lipophilic drugs. In this work, amino-terminated PCL (NH 2 -PCL) was prepared by ROP of ε-caprolactone using tert-butyl-N-(3-hydroxypropyl) carbamate as initiator, followed by removal of the N-tertbutoxycarbonyl (Boc) group. HPMC-PCL block copolymers with different PCL and HPMC block lengths were then synthesized by reductive amination between the amine of NH 2 -PCL and the hemiacetal end of HPMC. The selfassembly, drug loading and drug release behaviors, and the biocompatibility of HPMC-PCL copolymers were investigated to evaluate their potential as nanocarriers of lipophilic drugs in cancer therapy.

EXPERIMENTAL SECTION

2.1. Materials. ε-Caprolactone was purchased from Aldrich and purified by distillation under reduced pressure. HPMC was provided by Dow Colorcon Limited France, and HPMC oligomers with M w of 7000 and 18,000 Da were prepared by enzymatic degradation, as reported in our previous work. [START_REF] Lu | Synthesis and self-assembly of AB2-type amphiphilic copolymers from biobased hydroxypropyl methyl cellulose and poly(L-lactide)[END_REF][START_REF] Wang | Synthesis and Self-Assembly of Amphiphilic Block Copolymers from Biobased Hydroxypropyl Methyl Cellulose and Poly(l-lactide)[END_REF] tert-Butyl-N-(3-hydroxypropyl) carbamate (3-(Boc-amino)-1-propanol), sodium triacetoxyborohydride (NaBH(OAc) 3 ), tin(II) 2-ethylhexanoate (Sn(Oct) 2 ), anhydrous dimethyl sulfoxide (DMSO), and curcumin were purchased from Sigma-Aldrich and used without further purification. Trifluoroacetic acid (TFA) was purchased from Merck KGaA. Dichloromethane was purchased from Sigma-Aldrich, dried by anhydrous calcium chloride (CaCl 2 ), and distilled before use.

2.2. Synthesis of End-Functionalized PCL. End-functionalized PCL was prepared by ROP of ε-caprolactone in the presence of 3-(Boc-amino)-1-propanol as initiator and Sn(Oct) 2 as catalyst, followed by treatment with TFA to remove the Boc group. [START_REF] Ten Breteler | Synthesis and thermal properties of hetero-bifunctional PLA oligomers and their stereocomplexes[END_REF][START_REF] Le Hellaye | Biodegradable polycarbonateb-polypeptide and polyester-b-polypeptide block copolymers: synthesis and nanoparticle formation towards biomaterials[END_REF] Typically, 0.35 g of 3-(Boc-amino)-1-propanol (2 mmol), 4.56 g of εcaprolactone (40 mmol), and 0.0932 g of Sn(Oct) 2 (2.3 mmol) were added into a dried Schlenk flask. Three freeze-pump-thaw cycles were required to degas the mixture, and the reaction proceeded at 120 °C for 24 h. Boc-NH-PCL was then obtained as a white powder using the dissolution/precipitation method. Subsequently, the Boc group of Boc-NH-PCL was removed with TFA treatment using the previously reported method. [START_REF] Lu | Self-assembled micelles prepared from bio-based hydroxypropyl methyl cellulose and polylactide amphiphilic block copolymers for anti-tumor drug release[END_REF] 2.3. Synthesis of HPMC-PCL Block Copolymers. Reductive amination was performed to synthesize HPMC-PCL block copolymers. [START_REF] Moussa | Reducingend "clickable" functionalizations of chitosan oligomers for the synthesis of chitosan-based diblock copolymers[END_REF][START_REF] Abdel-Magid | A review on the use of sodium triacetoxyborohydride in the reductive amination of ketones and aldehydes[END_REF] Briefly, 0.16 g of NH 2 -PCL (0.154 mmol), 1.0 g of HPMC (0.14 mmol) with M w of 7000, and 0.042 g of NaBH(OAc) 3 (0.2 mmol) were added in 20 mL of anhydrous DMSO under stirring. After complete dissolution, the reaction proceeded 72 h at 35 °C under a nitrogen atmosphere. The final product was obtained by 72 h dialysis in deionized water, followed by 48 h freeze-drying.

2.4. Characterization. 1 H NMR was performed on a 300 MHz Bruker spectrometer (AVANCE300), and diffusion ordered spectroscopy (DOSY) NMR was performed on a 400 MHz Bruker AVANCE spectrometer (AQS400) equipped with a Bruker multinuclear zgradient inverse probe head. CDCl 3 , DMSO-d 6 and D 2 O were used as solvent. [START_REF] Cabral | Block Copolymer Micelles in Nanomedicine Applications[END_REF] H NMR spectra were processed by using MestReNova software, and DOSY NMR spectra were processes by using Bruker Topspin and Dosy Toolbox software.

The Kaiser test was performed using Kaiser test kit from Sigma-Aldrich containing KCN in H 2 O/pyridine (Reagent A), 6% ninhydrin in ethanol (Reagent B), and 80% phenol in ethanol (Reagent C). A small amount of polymer was added into a test tube, followed by successive addition of two or three drops of Reagent A, B, and C. Then, the tube was heated at 110 °C for 5 min. The solution color was finally compared to that of the control without addition of the polymer. The tests were performed in triplicate.

Gel permeation chromatography (GPC) was performed on a

Viscotek TDA 305 multidetector GPC/SEC system using THF as the mobile phase and polystyrene standards (Polysciences, Warrington, PA) for calibration. Polymer solutions at 10 g/L were filtered through a 0.22 μm Millipore filter before injection.

Fourier transform infrared (FT-IR) was performed on a Nicolet NEXUS spectrometer with attenuated total reflection accessory. Spectra were recorded in the range from 650 to 4000 cm -1 with a resolution at 4 cm -1 . Thirty two scans were performed for each analysis.

Dynamic light scattering (DLS) was carried out on Anton Parr Litesizer 500 at 25 °C. Micelle solutions were prepared at a concentration of 1.0 mg mL -1 and filtered through a 0.45 μm cellulose acetate (CA) filter. All measurements were performed at a scattering angle of 90°.

The critical micelle concentration (CMC) of copolymers was determined by fluorescence spectroscopy using pyrene as probe. An aqueous pyrene solution (6 × 10 -7 g/L) was used to prepare copolymer solutions at concentrations ranging from 1.0 × 10 -4 to 2.0 mg/mL. The excitation spectra of the pyrene solutions were registered in the 300-360 nm range at an excitation wavenumber of 395 nm.

Transmission electron microscopy (TEM) was carried out on JEOL 1400 plus instrument at an accelerating voltage of 120 kV. Samples at 1.0 mg mL -1 were dropped on a carbon-coated copper grid and stained by exposure to ruthenium oxide vapor for 7 min. Ruthenium(VIII) oxide solution was prepared as follows: sodium periodate (2.0 g) was added in water (50 g), and then, ruthenium(IV) oxide (0.30 g) was added in the solution under stirring at room temperature, yielding a yellow solution of ruthenium(VIII) oxide. [START_REF] Trent | Ruthenium Tetraoxide Staining of Polymers -New Preparative Methods for Electron-Microscopy[END_REF][START_REF] Fielding | RAFT dispersion polymerization in non-polar solvents: facile production of block copolymer spheres, worms and vesicles in n-alkanes[END_REF] 2.5. In Vitro Drug Release. Drug-loaded micelles were prepared using a previously reported method. [START_REF] Lu | Self-assembled micelles prepared from bio-based hydroxypropyl methyl cellulose and polylactide amphiphilic block copolymers for anti-tumor drug release[END_REF] Blank micelles were first prepared by dissolution of 20 mg of copolymer in 20 mL of distilled water. Curcumin (2 mg) was dissolved in 400 μL of ethanol, and the solution was then dropped into the micelle solution under vigorous stirring. The solvent was evaporated overnight, yielding a drug-loaded micelle solution. The solution was filtered through 0.8 μm CA filter to eliminate unloaded drug, lyophilized, and stored at 4 °C before analysis.

In vitro drug release was realized by using Float-A-Lyzer G2 dialysis devices with MWCO of 3 500 Da, as previously reported. [START_REF] Lu | Self-assembled micelles prepared from bio-based hydroxypropyl methyl cellulose and polylactide amphiphilic block copolymers for anti-tumor drug release[END_REF] Briefly, 1 mL of drug-loaded micelle solution at 2.0 mg/mL was added in a dialysis device which was placed in a tube containing 40 mL of phosphate buffered saline (PBS). The release medium was regularly renewed to ensure sink conditions. Drug release was performed in a water bath at 37 °C under constant shaking. An aliquot of 25 μL solution was collected from the dialysis device at each data point, and the same volume of fresh PBS was added.

HPLC-MS was used to determine the concentration of curcumin in solution, using a 50/50 v/v mixture of acetonitrile and pH 7.4 PBS as the mobile phase. Drug loading content (DLC) and drug loading efficiency (DLE) were determined from the following equations 36

2.6. MTT Assay. MTT assay was performed to evaluate the biocompatibility of HPMC-PCL micelles on L-929 cells, as previously reported. [START_REF] Lu | Self-assembled micelles prepared from bio-based hydroxypropyl methyl cellulose and polylactide amphiphilic block copolymers for anti-tumor drug release[END_REF] 3. RESULTS AND DISCUSSION 3.1. Synthesis and Characterization of Amphiphilic Copolymers. Amphiphilic HPMC-PCL block copolymers were synthesized in three steps, as shown in Scheme 1. Boc-NH 2 -PCL was first synthesized by ROP of ε-caprolactone initiated by 3-(Boc-amino)-1-propanol which has a protected amine group and a hydroxyl endgroup. The Boc group was then removed with TFA treatment to obtain end functionalized PCL. HPMC-PCL block copolymers were finally obtained via reductive amination between the hemiacetal endgroup of HPMC and the amine group of PCL in the presence of NaBH(OAc) 3 as the reducing agent. [START_REF] Trache | Microcrystalline cellulose: Isolation, characterization and biocomposites application-A review[END_REF] The synthesis of amino terminated NH 2 -PCL was based on the method reported in literature. [START_REF] Ju | Fast and Convenient Synthesis of Amine-Terminated Polylactide as a Macroinitiator forω-Benzyloxycarbonyl-L-Lysine-N-Carboxyanhydrides[END_REF][START_REF] Gotsche | Amino-termined poly(Llactide)s as initiators for the polymerization of N-carboxyanhydrides: synthesis of poly(L-lactide)-block-poly(α-amino acid)s[END_REF] Boc-NH-PCL was first synthesized by ROP of ε-caprolactone with predetermined monomer/initiator (M/I) molar ratios of 10, 20, or 30. The obtained polymers were characterized by FT-IR, GPC, and quantitative 1 H NMR. As shown in Figure 1A, the signals at S1. The molar mass and dispersity (Đ = M w /M n ) of polymers were determined by GPC, as shown in Figure S1A. A symmetric molar mass distribution is observed. The M n GPC increases from 3180 to 5140 with the increase of DP PCL from 10 to 30, whereas the dispersity ranges from 1.29 to 1.41 (Table S1). The M n GPC values are larger than those from NMR. The difference can be assigned to the fact that M n GPC is obtained from the hydrodynamic volume of polymer chains in solution compared to that of polystyrene standards, in contrast to M n NMR values which are calculated from the integrations of NMR signals.

NH 2 -PCL was obtained by treating Boc-NH-PCL with TFA to remove the Boc group. As shown in Figure S1, Boc-NH-PCL 30 and NH 2 -PCL 30 present almost the same elution time. In other words, deprotection by TFA treatment did not cleave PCL chains. [START_REF] Cabral | Block Copolymer Micelles in Nanomedicine Applications[END_REF] H NMR was performed to evidence the effective removal of the Boc group (Figure 1B). The methyl peak (a) of Boc at 1.42 ppm is not detected on the spectrum of NH 2 -PCL 10 . Meanwhile, the methylene peak (c) shifts from 3.2 ppm for Boc-NH-PCL 10 to 3.0 ppm for NH 2 -PCL10 (c′), in agreement with the conversion of the adjacent acylamino group to the amine group. The intensity ratio between signals c and f remains constant, thus confirming the absence of PCL chain degradation during deprotection.

The Kaiser test is commonly utilized to evidence the presence of primary amines. The main effective constituent of the Kit, ninhydrin, reacts with amine groups to produce an intense blue color. As shown in Figure S1B, Boc-NH-PCL presents almost the same color as the control, while NH 2 -PCL solution is dark blue. This finding demonstrates the presence of primary amino groups in NH 2 -PCL but not in Boc-NH-PCL.

Finally, amphiphilic HPMC-PCL block copolymers were synthesized by reductive amination of NH 2 -PCL and HPMC in the presence of a reducing agent, NaBH(OAc) 3 . Six HPMC-PCL copolymers were obtained in this work, namely, HPMC7K-PCL 10 , HPMC7K-PCL 20 , HPMC7K-PCL 30 , HPMC18K-PCL 10 , HPMC18K-PCL 20 , and HPMC18K-PCL 30 (Table 1). As shown in Figure 2A, the 1 H NMR spectrum of HPMC7K-PCL 10 in DMSO-d 6 presents a signal at 1.05 ppm (q) assigned to methyl protons of the hydroxypropyl substitution group, signals between 2.75 and 4.75 ppm (p) corresponding to the methylene and methine protons of the substitution group, methyl protons adjacent to the oxygen moieties of ether linkage, and the protons of glucose units of HPMC. The signals at 1.30 (h), 1.62 (j), 2.75 (f), and 4.0 (i) ppm belong to the methylene protons of PCL blocks. The Kaiser test also corroborates with the effective reductive amination (Figure S1B). In fact, HPMC-PCL almost shows the same color as the control, indicating the absence of primary amines. In other words, all the terminal amino groups of NH 2 -PCL 30 have reacted with aldehyde groups of HPMC. H NMR in selective solvents allows us to evidence the core-shell structure of micelles prepared from amphiphilic block copolymers. Water is able to dissolve the hydrophilic block, that is, the shell block of micelles, but not the hydrophobic block. Thus, only the signals corresponding to HPMC are visible on the NMR spectrum in deuterated water. As shown in Figure 2B, signals belonging to PCL blocks are not observed due to their limited movement. This finding well corroborates with the micelle structure composed of a hydrophilic HPMC shell and a hydrophobic PCL core.

DOSY-NMR was also used to evidence the synthesis of HPMC-PCL block copolymers. The DOSY-NMR spectrum is a 2D diagram: one dimension shows the chemical shift, and the other dimension provides separation based on the self-diffusion coefficients of the dissolved species. [START_REF] Pages | Pulsedfield gradient nuclear magnetic resonance measurements (PFG NMR) for diffusion ordered spectroscopy (DOSY) mapping[END_REF][START_REF] Jiang | Aqueous solution behaviour of novel water-soluble amphiphilic copolymers with elevated hydrophobic unit content[END_REF] As shown in Figure 3, all the signals corresponding to PCL and HPMC are detected at the same diffusion coefficient. This finding suggests that the both blocks are combined in the same polymer chain, thus confirming the successful synthesis of HPMC-PCL block copolymers. FT-IR was also used to analyze the chemical structure of HPMC-PCL copolymers and precursors (Figure 4). Boc-OH presents characteristic absorption bands at 3260, 1689, 1527, 1392, and 1366 cm -1 which belong to O-H, CO, CO-NH, and C-H (methyl) groups, respectively. These bands become less intense on the spectrum of Boc-NH-PCL and invisible on the spectrum of NH 2 -PCL because of the deprotection. The carbonyl band of PCL is detected at 1760 cm -1 . On the spectrum of HPMC, absorption bands of O-H, C-H, and C-O bonds are detected at 3480, 2890, and 1047 cm -1 , respectively. Signals corresponding to both HPMC and PCL are observed on the spectrum of HPMC7K-PCL 30 , which corroborates with the presence of both blocks in the copolymer.

3.2. Self-Assembly of Amphiphilic Block Copolymers. HPMC-PCL amphiphilic block copolymers are able to selfassemble into nanoscale micelles with the shell-core structure by direct dissolution in water. The self-assembly properties of copolymers were investigated by means of DLS, TEM, and fluorescence spectroscopy.

The CMC is a key parameter of self-assembled polymeric micelles. Fluorescence spectroscopy allowed determination of the CMC of copolymers, using pyrene as the fluorescent probe. Once hydrophobic association of copolymer chains occurs in the aqueous medium, pyrene molecules significantly migrate into hydrophobic regions, resulting in changes of its photophysical properties. [START_REF] Li | Synthesis of folate mediated carboxymethyl cellulose fatty acid ester and application in drug controlled release[END_REF] As shown in Figure 5A, the red shift of absorption indicates pyrene migration into the nonpolar core of micelles, in agreement with micelle formation. The CMC is derived from the two tangent lines of the intensity ratio of I 336 / I 334 versus polymer concentration plots (Figure 5B). As summarized in Table 1, the CMC decreases from 0.012 for HPMC7K-PCL 10 to 0.0009 g/L for HPMC7K-PCL 30 and from 0.009 for HPMC18K-PCL 10 to 0.003 g/L for HPMC18K-PCL 30 . Therefore, longer hydrophobic block or shorter hydrophilic block facilitates micelle formation, thus leading to lower CMC, as reported in literature. [START_REF] Hu | Preparation and drug release behaviors of nimodipine-loaded poly(caprolactone)-poly(ethylene oxide)-polylactide amphiphilic copolymer nanoparticles[END_REF][START_REF] Ge | Preparation, characterization, and drug release behaviors of drug nimodipine-loaded poly(ε-caprolactone)-poly(ethylene oxide)-poly-(ε-caprolactone) amphiphilic triblock copolymer micelles[END_REF][START_REF] Yang | carriers for tumor diagnosis and treatment[END_REF] The micelle size, size distribution, and zeta potential of micelles are determined by DLS. The diameter of HPMC7K-PCL micelles is in the range of 179.0-195.9 nm with a narrow polydispersity index (PDI) from 0.12 to 0.17 (Table 1). The size of HPMC18K-PCL micelles ranges from 205.1 to 222.0 nm that is larger than that of HPMC7K-PCL ones, suggesting that longer hydrophilic blocks yield larger micelles. It is also noticed that the micelle size is only slightly affected by the hydrophobic PCL block length. The zeta potential of micelles is slightly negative because there are no charged groups at the surface of the HPMC shell (Table 1). The morphology of micelles was visualized by TEM, as shown in Figure 6B. Spherical micelles are observed in all cases. The diameter of micelles by TEM ranges from 50 to 100 nm that is smaller than that obtained by DLS. This difference could be attributed to dehydration of micelles during TEM observation. [START_REF] Bordallo | Self-assembly in aqueous solution of amphiphilic graft copolymers from oxidized carboxymethylcellulose[END_REF] 3.3. Drug Loading and In Vitro Drug Release. Curcumin was selected as the lipophilic model drug to assess the drug loading and release behaviors of HPMC-PCL copolymer micelles. Curcumin is a wide spectrum chemotherapeutic drug with outstanding antiproliferative and proapoptotic activities. In addition, it has been demonstrated that curcumin is able to regulate the intracellular levels of ATPbinding cassette drug transporters, which helps to prevent multidrug resistance.

Curcumin-loaded micelles were prepared using a two-step procedure: direct dissolution of block copolymers in water to yield blank micelles, followed by introduction of a curcumin solution in ethanol into the micelle solution. As shown in Table 1, the DLC and DLE are higher for HPMC-PCL micelles with longer hydrophobic PCL blocks. In the case of the HPMC7K-PCL series, the DLC increases from 4.3% for HPMC7K-PCL 10 to 8.2% for HPMC7K-PCL 30 , whereas the DLE increases from 41.5% for HPMC7K-PCL 10 to 75.8% for HPMC7K-PCL 30 . Similar phenomena are observed for HPMC18K-PCL copolymer micelles. Nevertheless, HPMC7K-PCL presents higher DLC and DLE than HPMC18K-PCL with the same PCL block length. In other words, micelles with a higher hydrophobic/hydrophilic ratio present stronger encapsulation ability, as reported in literature. The DLC and DLE of curcumin encapsulated in PCL-PEG micelles increase from 15.9 to 20.6% and from 65.4 to 82.3%, respectively, with an increase of the PCL/PEG ratio from 2 to 5. [START_REF] Kheiri Manjili | Pharmacokinetics and in vivo delivery of curcumin by copolymeric mPEG-PCL micelles[END_REF] Nimodipine-loaded PCL-PEG-PCL micelles also present an enhanced DLC by increasing PCL/PEG ratio. [START_REF] Ge | Preparation, characterization, and drug release behaviors of drug nimodipine-loaded poly(ε-caprolactone)-poly(ethylene oxide)-poly-(ε-caprolactone) amphiphilic triblock copolymer micelles[END_REF] In the case of amiodarone-loaded PEG-PCL micelles, the DLC increases from 2.4 to 7.8% with increase of PCL molar mass from 5000 to 24,000. [START_REF] Elhasi | Solubilization of an amphiphilic drug by poly(ethylene oxide)-block-poly(ester) micelles[END_REF] The increase of DLC and DLE with an increasing PCL block length can be attributed to the interaction between curcumin and the hydrophobic part of micelles. Gou et al. prepared curcumin-loaded nanoparticles derived from natural silk fibroin. Circular dichroism spectra showed that blank nanoparticles had much more β-structures than curcumin-loaded ones, which was assigned to interactions of curcumin with the hydrophobic domains of nanoparticles, hindering formation of β-sheet structures. [START_REF] Gou | Multi-bioresponsive silk fibroin-based nanoparticles with on-demand cytoplasmic drug release capacity for CD44-targeted alleviation of ulcerative colitis[END_REF] In curcumin-loaded PCL-PEG micelles, the interface area between PCL and curcumin was estimated by simulation ten times larger than that between PEG and curcumin, suggesting that the main interaction occurs between hydrophobic PCL of the copolymer and hydrophobic curcumin. [START_REF] Peng | Drug delivery systems for overcoming the bioavailability of curcumin: not only the nanoparticle matters[END_REF] In vitro drug release was realized by using the dialysis method in pH 7.4 PBS at 37 °C. As shown in Figure 7, a biphasic release profile is observed for all curcumin-loaded micelles, including a rapid initial release within the first 6 h and a slower release in the remaining period up to 120 h. The initial burst release could be attributed to the fact that a part of drug is located at the interface of the core-shell structure. [START_REF] Tyrrell | Fabrication of micellar nanoparticles for drug delivery through the self-assembly of block copolymers[END_REF] HPMC18K-PCL 10 presents the largest burst release of over 80% in the first 6 h, whereas HPMC7K-PCL 30 presents a burst of 15% only. The total release at 120 h is 99.8, 97.4, 94.9, and 96.5% for HPMC18K-PCL 10 , HPMC18K-PCL 20 , HPMC7K-PCL 10 , and HPMC7K-PCL 20 , respectively. In contrast, the total release at 120 h is 74.4% for HPMC7K-PCL 30 and 76.1% for HPMC18K-PCL 30 , which is much lower than those of copolymers with a shorter PCL block length. Therefore, the release rate and release percentage from HPMC-PCL copolymer micelles is dependent on the hydrophobic block length and the hydrophobic/hydrophilic ratio. The longer hydrophobic block, the larger the hydrophobic/hydrophilic ratio, the lower the release rate. It should also be noted that micelles with longer hydrophobic block have higher drug load. Hu et al. reported that curcumin-loaded P(NIPAAm-co-DMAAm)-b-PLLA copolymer micelles with a higher drug load present a slower release rate compared to those with a lower drug load. [START_REF] Hu | Thermoresponsive release of curcumin from micelles prepared by selfassembly of amphiphilic P(NIPAAm-co-DMAAm)-b-PLLA-b-P-(NIPAAm-co-DMAAm) triblock copolymers[END_REF] Therefore, the release rate is also dependent on the DLC because drug solubility in the medium could be a limiting factor which significantly affects drug release. Sink conditions are often used to minimize the effect of drug solubility. Nimodipine-loaded PCL-PEG-PCL micelles also present a decrease of the drug release rate with the increase of the PCL block length. [START_REF] Ge | Preparation, characterization, and drug release behaviors of drug nimodipine-loaded poly(ε-caprolactone)-poly(ethylene oxide)-poly-(ε-caprolactone) amphiphilic triblock copolymer micelles[END_REF] Similarly, Danafar et al. reported that curcumin release from PCL-PEG micelles in 120 h decreases from 80.2 to 57.1% with the CL/EG ratio increase from 2 to 5. [START_REF] Kheiri Manjili | Pharmacokinetics and in vivo delivery of curcumin by copolymeric mPEG-PCL micelles[END_REF] 3.4. Biocompatibility of Micelles. The MTT test was applied to assess the cytocompatibility of HPMC-PCL micelles on L929 cells. MTT can react with succinate mitochondrial dehydrogenases which are present in living cells to yield formazan, a purple dye. The latter is insoluble in water but soluble in DMSO. Thus, the absorbance of formazan in DMSO solution is measured to assess the number of living cells.

L-929 cells are a commonly used murine fibroblast cell line for cytocompatibility evaluation. Figure 8 shows the relative activity of L929 cells after culture with HPMC7K-PCL 10 and HPMC7K-PCL 20 micelle solutions at various concentrations. The viability of cells is well above 80% in the whole concentration range. After 72 h incubation, the cell viability is around 90% in all cases. These results indicate that HPMC-PCL copolymer micelles are well compatible with L-929 cells.

CONCLUSIONS

In this work, a series of biobased amphiphilic HPMC-PCL block copolymers were synthesized by reductive amination between the hemiacetal reducing endgroup of HPMC and end functionalized PCL. The copolymers and precursors were characterized by NMR, DOSY-NMR, FT-IR, GPC, and the Kaiser test. The self-assembly of copolymers was evidenced by fluorescence spectroscopy, DLS, and TEM measurements. All the copolymers are able to self-assemble in water into spherical nanoscale micelles with narrow distribution. The longer hydrophilic HPMC block leads to a larger micelle size. The CMC of copolymers decreases with an increasing hydrophobic PCL block length. Curcumin was successfully encapsulated in the micelle core as a lipophilic anticancer drug. Higher drug loading was obtained for copolymers with a longer PCL block length. The drug release rate is dependent on the PCL block length and drug load. The PCL block length or a higher drug load leads to slower drug release. The MTT test shows that HPMC-PCL micelles present outstanding cytocompatibility. In conclusion, biocompatible and biodegradable HPMC-PCL block copolymers could present great potential as nanocarriers of lipophilic drugs.

■ ASSOCIATED CONTENT

* sı Supporting Information

1. 42

 42 (a), 4.18 (e), 1.84 (d), and 3.20 (c) ppm belong to the methyl and the methylene protons of the terminal Boc group, respectively, and the signals at 1.30 (h), 1.62 (j), 2.75 (f), and 4.0 (i) ppm are assigned to the methylene protons of the PCL backbone. The degree of polymerization (DP) of PCL was estimated from the integration ratio of signals f to c. The obtained DP PCL is 10.8, 22.4, and 30.5, which is rather close to the monomer/initiator ratio. The number average molar mass (M n NMR ) was calculated from the DP values. It varied from 1320 to 3600, as shown in Table

Scheme 1 .Figure 1 . 1 H

 111 Scheme 1. Synthesis of HPMC-PCL Block Copolymers via Reductive Amination

1

 1

Figure 2 . 1 H

 21 Figure 2. 1 H NMR spectra of HPMC7K-PCL 10 in DMSO-d 6 (A) and D 2 O (B).

Figure 3 .

 3 Figure 3. DOSY-NMR spectrum of HPMC7K-PCL 30 in DMSO-d 6 .

Figure 4 .

 4 Figure 4. FT-IR spectra of Boc-OH (a), Boc-NH-PCL 30 (b), NH 2 -PCL 30 (c), HPMC7K-PCL 30 (d), and HPMC7K (e).

Figure 5 .

 5 Figure 5. Fluorescence excitation spectra (A) and plot of intensity ratio I 336 /I 334 vs concentration (B) of HPMC7K-PCL 20 copolymer solutions.

Figure 6 .

 6 Figure 6. Size distribution by DLS (A) and TEM image (B) of HPMC7K-PCL 20 copolymer micelles.

Figure 7 .

 7 Figure 7. Cumulative release of curcumin from HPMC-PCL copolymer micelles. Data points represent mean ± SD from triplicate samples, and error bars represent the standard deviation (n = 3).

Table 1 .

 1 Self-Assembly and Drug Loading Properties of HPMC-PCL Block Copolymers

	sample	size (nm)	PDI	ZETA (mV)	CMC (mg/mL)	DLC (%)	DLE (%)
	HPMC7K-PCL 10	179.0 ± 2.1	0.16	-4.5 ± 0.3	0.012	4.3	41.5
	HPMC7K-PCL 20	182.8 ± 1.2	0.17	-2.3 ± 0.4	0.0058	5.1	48.2
	HPMC7K-PCL 30	195.9 ± 2.5	0.12	-6.7 ± 0.2	0.0009	8.2	75.8
	HPMC18K-PCL 10	205.1 ± 3.4	0.19	-6.8 ± 0.2	0.009	3.8	36.4
	HPMC18K-PCL 20	216.9 ± 1.3	0.16	-8.9 ± 0.4	0.005	4.4	41.7
	HPMC18K-PCL 30	222.0 ± 3.0	0.11	-5.4 ± 0.2	0.003	7.2	67.0

https://dx.doi.org/10.1021/acsanm.0c00498 ACS Appl. Nano Mater. 2020, 3, 4367-4375 Downloaded via UNIV MONTPELLIER on June 19, 2020 at 14:31:55 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

https://dx.doi.org/10.1021/acsanm.0c00498 ACS Appl. Nano Mater. 2020, 3, 4367-4375

https://dx.doi.org/10.1021/acsanm.0c00498

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsanm.0c00498.

Characterization of Boc-NH-PCL polymers by NMR and GPC, GPC curves of Boc-NH-PCL 30 and NH 2 -PCL 30 in THF, and the Kaiser test of Boc-NH-PCL 30 , NH 2 -PCL 30 , and HPMC7K-PCL 30 (PDF)


Manuel Philippe

Maurizio Emile Garcon

Maurizio Alì

Nathanaël Rosmery Fundora Cruz
email: rosmeryfundora@gmail.com

André Nicar

Calcolo Mentale

E Competenze Matematiche

Nella Scuola

Primaria Una

Prospettiva Comparativa

Tra Due

Sistemi Scolastici

Martinica E Senegal

Émile Garçon

Nathanaël André Nicar
email: nathanael.nicar@ac-martinique.fr

Mental Arithmetic and Mathematical Skills in Primary School. A Comparative Perspective Between Two Post-Colonial Education Systems: Martinique and Senegal

Keywords: Didactics of mathematics, Martinique, Mental calculation, School difficulties, School performance PAROLE-CHIAVE Calcolo mentale, Didattica della matematica, Difficoltà scolastiche, Martinica, Risultati scolastici

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The relationship between socio-cultural contexts and mathematics learning has been deeply explored since the second half of the 20 th century, especially in the framework of an emerging field of research, the ethnomathematics (D' Ambrosio, 1980;[START_REF] Ascher | Ethnomathematics[END_REF]. Mathematical skills are often described as a gateway to succeed in life; nevertheless, for too many students, academic success in this area is often elusive, especially within communities that, due to their socioeconomic situation, have been historically marginalised [START_REF] Adelman | International comparisons: What your fourth-grade math can reveal[END_REF][START_REF] Halai | Research rationalities and the construction of the deficient multilingual mathematics learner[END_REF][START_REF] Chronaki | Unfolding global/local policies, practices and/or hybrids in mathematics education worldwide: utopias, pleasures, pressures and conflicts[END_REF]. Some authors consider that the low achievement of these students is due to the fact that, in such contexts, mathematics is often taught in a way that is disconnected from their socio-cultural environments [START_REF] Harding | Is science multicultural? Post-colonialisms, Feminisms and Epistemologies[END_REF][START_REF] Martin | Mathematics success and failure among African-American youth: The roles of sociohistorical context, community forces, school influence, and individual agency[END_REF] and that the methodological foundations of the discipline, as articulated in school curricula, remain essentially Western-led [START_REF] Rosa | Ethnomathematics: the cultural aspects of mathematics[END_REF].

To take part in this discussion, this article presents the results obtained in the framework of the research project Train to teach, to calculate mentally: a comparative perspective from Senegal and Martinique and the construction of teacher training 1 . The primary objective of the project was to test the mental calculation skills of primary school pupils in post-colonial environments, but also to understand their mental construction of the concept of number and its numerical representation. It was based on a comparative analysis of two territories, which were once subject to the same imperial power (the France Empire) but which have undergone different decolonization processes: Senegal (an autonomous country that has been independent of France since 1960) and Martinique (an overseas department that has been administratively integrated to France since 1946). The secondary objective of the project was to develop and propose ways of improving pupils' performance in mental arithmetic based on participatory work involving Franco-Senegalese teams to build teaching tools adapted to local needs and cultures.

The results obtained enabled us to specify the objectively measurable level of primary school pupils in the field of mental arithmetic but also to better understand the role of context in the construction of mathematical knowledge.

The research process: research problem, methodology and study population

The teaching methods of mathematics practised in Martinique and in Senegal are the subject of close observation because of their development, but above all because of their effectiveness in the field of mental calculation. The educational policies of each of these territories have invested in establishing new curricula and making recommendations to optimise and develop existing practices. This is also reflected in the introduction of the Malaysian Universal Concept of Mental Arithmetic Systems programme in some Senegalese schools for children aged 5 to 15; while in France the Ministry of Education, Youth and Sports has strongly recommended for several years that the sense of numbers and operations as well as the development of automatic calculation skills be ritualised from the earliest grades, in this case, from nursery school (MENJS, 2018).

To investigate the performance of Martinique and Senegal primary school pupils we used a psychometric tool, the Test de Repérage de Difficultés en Mathématiques (TRDM) developed by Sandrine Mejias, Claire Muller and Christine Schiltz (2019). It is a tracking tool built from a social-cognitive approach that has already been validated by other scientific studies [START_REF] Georges | The importance of visuospatial abilities for verbal number skills in preschool: Adding spatial language to the equation[END_REF][START_REF] Ghazali | A Systematic Review on the Definition of Children's Number Sense in the Primary School Years[END_REF][START_REF] Martini | Identifying math and reading difficulties of multilingual children: Effects of different cut-offs and reference groups[END_REF]. The TRDM contains tasks whose difficulty is adapted to each school level: dictation of numbers, comparison of numbers (integers, decimals, fractions), rapid resolution of written operations (arithmetic fluency). This last test is timed and must be completed within a limited time (1 minute per operation). The instructions are given orally by the examiner and, at the time of evaluation, one point is awarded for each correct answer. To facilitate the study of correlations, the scores obtained by the participants were listed anonymously in an Excel™ spreadsheet according to the participants' school, grade, gender, and examiner. The results obtained through the large-scale deployment of the TRDM allowed us to identify not only the average performance of students according to certain variables but also the best performances, to determine the rate of students who obtained the highest scores in each test.

The population of our study is made up of pupils enrolled in public and private primary schools located in the region of Thiès for Senegal (N=2973) 2 and of public primary school pupils spread throughout the island of Martinique (N=2710) 3 . As the gender distribution of pupils in Martinique was not available from the statistical services concerned, we chose to divide our sample equally between girls and boys (Table 2). The research corpus is freely accessible from DOI: 10.17632/j9yfh482r4.1 [START_REF] Garçon | Corpus de recherche. Résultats du projet Calcul Mental Africa2020 (volet 1 : test de calcul mental en Martinique)[END_REF].

In Senegal, the focus was on the type of school, private or public. The 11 schools from which the students in this study came are spread throughout the Thiès district, which counts 988 public schools (about 79% of pupils) and 258 private schools (about 21% of pupils. Inspection d'académie de Thiès, 2021. In parallel to this main study, we also carried out a complementary survey with a small sample of our study population (89 primary school pupils in Martinique and 470 primary school pupils in Senegal). The questionnaire consisted of six questions on mathematical activities in the family environment (to identify the habits and tools used by families) and on attitudes towards mathematics and mental arithmetic (to detect the mental representations of children). Although the sample for this secondary survey is not statistically representative, the analysis of the children's responses allows us to interpret the results of our main study, particularly to explain certain statistical trends and inconsistencies. In addition, this approach has provided a better understanding of the relatively strained relationship that students have with mathematics and mental arithmetic.

Pupils' performance

The Test de Repérage de Difficultés en Mathématiques (TRDM) allowed us to identify the average skills of the pupils surveyed in four basic areas:

-Dictation (which assesses pupils' ability to associate a number correctly with its numerical representation); -Comparison of quantities (which assesses pupils' ability to identify two quantities, to associate them with the corresponding numbers and to position these numbers correctly on a scale of sizes); -The resolution of numerical complements (which corresponds to the basic cognitive mechanism necessary for mental calculation); -Rapid calculation (which requires both speed of execution and precision but also the ability to control the result).

The first three areas constitute the first part of the test, which is devoted to number construction, while the second part is limited to the speed test.

The TRDM was administered in classrooms during school hours in the presence of a teacher and one or more researchers associated with the project 4 . Each student was asked a series of questions adapted to his or her age and school level, following the instructions and procedures provided by the TRDM developers 5 .

All domains combined, the average total score of the pupils who took part in our study ranged in Senegal, depending on the level, from 50% (for CE2 level6 ) to 58% (for CP level 7 ) of correct answers. In Martinique, the average total score of the pupils who participated in our study varies from 19% (for CE2 level) to 27% (for CM2 level 8 ). These initial results raise questions: indeed, the test designers suggest that scores between 7% and 30% are often associated with difficulties arising from a lack of investment in mathematics activities (at school or at home). In contrast, at the general level but also after a domain analysis, our study did not reveal significant differences between the performance of girls and boys.

The first part of the test was better passed in Martinique by first graders (86% correct answers), while those in second and third grade had an average score of 54% and 68% respectively. We also observed that CE2 pupils were more successful overall in the number comparison exercises -than those assessed based on number dictations -and obtained the lowest score for the calculations of complements to a number (to 10, 100 and 1000).

4 Some of the test-taking sessions were recorded by a team attached to the Division de la Radio-Télévision Scolaire (DRTS/Senegal), a public operator of the national Ministry of Education in charge of producing and publishing educational resources and a partner in our project. These recordings will then be used for the development of study and teaching resources that will be broadcast in France and Senegal. 5 We collaborated with the designers of the TRDM to create a version of the test adapted to the territories of Martinique and Senegal. The starting point was to design an assessment that would cover the common parts of the official curricula of both territories. Optimisation work was carried out with the Mission Mathématiques 1er degré of Martinique in order to find a form of the test (layout of the questions, size of the characters, presence of images, etc.) close to the national assessments and guaranteeing a good context for the test.

On the other hand, the results of this first part of the test are rather homogeneous for Senegal. Indeed, apart from the CE2 level, which obtained 69% of correct answers, the four other levels presented results of between 73% and 74%. It would seem, in fact, that the rate of acquisition of skills in number construction is rather regular. We also observe a surprising phenomenon concerning number dictation and number comparison. We can consider that dictation and knowledge of numbers is a prerequisite for comparison. However, for the CP, CE19 and CE2 levels, the percentage of correct answers is higher for the comparison than for the dictation. This trend is reversed in CM110 and CM2, with better results in dictation than in comparison, which is what we expected. We also observed that CE2 pupils were more successful overall in the number comparison exercises than in the number dictation exercises, and that they obtained the lowest score for calculations of complements to a number (to 10, 100 and 1000).

It is precisely around complements that the pupils participating in our study obtain the lowest scores. The average score of CM1 pupils is 38% of correct answers and that of CM2 pupils 44% in Martinique, while that of CM1 pupils is 64% of correct answers and that of CM2 pupils 63%. It would also seem that the rate of acquisition of number construction skills is not similar in the populations studied. We observe an irregularity in one group, while the other group shows a palpable regularity. In short, this means that the average pupil leaves primary school and enters secondary school with an insufficient mastery of basic calculation skills in our two post-colonial populations.

On the other hand, the second part of the test, devoted to rapid calculations, was much better performed by the CM2 pupils for the whole sample (Tables 6 and7), with an average score of 91 operations performed in 4 minutes in Martinique and an average score of 51% of operations correctly performed in Senegal. The following tables show the correct answers obtained for each of the four operations. As a reminder, the students had one minute for each of the operations: addition, subtraction, multiplication, and division. As might be expected, addition was the operation best mastered at all levels.

However, the scores obtained in operations requiring the use of division are clearly lower, in all school levels (between 7% in CE2 and 13% in CM2 in Martinique and between 17% in CE2 and 32.5% in CM2 in Senegal). This leads to the observation that there is a gradual and moderate increase in rapid calculation skills throughout a pupil's schooling in primary school.

As regards the exercise of rapid calculations within the island population, we also wanted to record the highest scores, in order to detect the presence of pupils with exceptional performance: the highest score in absolute terms was obtained by a pupil in CM1 with a score of 98 correct multiplications within the time allowed. For comparison, the highest score in the division domain was obtained by a pupil in CM2 who performed 61% of the operations correctly and within the time limit. As the table shows, first graders were not tested in this second part of the test. The results we have obtained help us to confirm and clarify the observation suggested, before us, by other researchers who have investigated the Senegalese territory, but also by those who have worked on the West Indian context, namely that the average performance of pupils in the field of mathematics is rather disappointing and that the typology of the school (thus, the school ecosystem or, more simply, the school context) has an impact on the development of certain skills (Dieng and Ibrahima, 2020), particularly in the construction of numbers (Diagne, Kafano and Ounteni, 2006) and mental arithmetic (Ndoye, 1999 and[START_REF] Arneton | Bilinguisme et apprentissage des mathématiques : études à la Martinique[END_REF].

Pupils' overall attitudes

Among the pupils tested for their mental arithmetic skills, we chose 556 (470 in Senegal and 86 in Martinique) to explore their relationship with mathematics and arithmetic, but also about their domestic habits (in order to detect whether they carried out mathematical-type activities at home). To guarantee the homogeneity of the data, the sample was composed of approximately one hundred pupils per level in Senegal (CP, CE1, CE2, CM1 and CM2) and three classes for each school level in Martinique (15 classes in total). Data collection was carried out using a questionnaire with six non-gendered questions, focusing on pupils' interest in mathematics and mental calculation. The first four questions were closed and the last two were open-ended. The first four questions were closed, while the last two were open-ended, so that the student could let his or her experience run wild and fill in the questionnaire without being restricted.

The answers we obtained seem to suggest that students from both populations have a relatively positive conception of mathematics. Indeed, 97% of the respondents said that they liked mathematics among the mainlanders (a little, well, and a lot) -93% said that they liked mathematics among the islanders, while an average of 5% disliked it (Tables 9). This can be explained by the teaching methods proposed by the teachers, but also by the diversity of the educational offer. In Senegal, we note that the pupils' relationship to numbers on the one hand and to mental calculation on the other does not fluctuate. These results are therefore identical. This could be directly linked to the need to use mental arithmetic and numbers. In interviews with some of the students who participated in this study, the previous hypothesis was confirmed. Furthermore, it was found that mental manipulation of numbers is a common task in everyday life (for indeed, shopping).

In Martinique, this relationship is more variable. Although 94% of the pupils interviewed expressed an interest in numbers (as an area of activity) and mental arithmetic (as a school exercise), they were divided into three distinct typologies. Firstly, the enthusiasts (58%), the good students (those who like the exercise itself, 36%), and finally those who do not like mathematics-related activities (6%. Table 10). In Martinique, the results reveal that 30% of the pupils who participated in this survey do not use numbers and mental arithmetic at all in the family context, whereas 69% of the pupils in the same sample say they use numbers and mental arithmetic when they are at home. However, few of them are really able to correctly identify activities that require the performance of quick calculations (e.g. following cooking recipes or counting points in a board game) and to differentiate them from other games or household tasks that do not necessarily require the use of calculation.

In Senegal, pupils are very clear about their intentions and uses of numbers and mental arithmetic. 95% of pupils attest to using mental arithmetic. 85% of them clearly target their use by testifying to a daily and practical use of the tool. The Martinican pupils' relationship with mathematics is largely positive, despite their general performance and a domestic context that does not seem to be in the habit of integrating calculation automatisms into everyday activity. Summarizing the general view, one of the pupils in our study admitted to us that: "mental arithmetic is useful in many board games such as Triomino, Trianglué, Uno, Jeu de l'oie, Jeu de 7 familles, Domino and even Loto".

In contrast, among their Senegalese counterparts, the concepts studied in mental arithmetic are directly applied in everyday life, often for commercial purposes, in order to participate in family life, or to accompany their parents in their daily activities (going to the shopkeeper's, helping in the family business). 65% of young Senegalese reflect this pattern, 19% remain on a completely academic pattern and only 16% remain unaffected by the use of the mathematical notions studied.

Finally, the results also seem to suggest that the discipline is valued more in its operational dimension (calculation) than in its conceptual dimension (mathematics as an abstraction).

Discussion of the results

This research, based on a sociological approach, made it possible to succinctly expose the level of mathematical skills of many pupils in Martinique and Senegalese elementary schools, using a reliable psychometric tool validated by the scientific community on a large scale and relying on a statistically representative sample. Above all, we confirm the ease of use and validity of this tool, the TRDM, which could easily be deployed in other post-colonial overseas contexts to facilitate the comparison work.

It is important to note that in our study we did not detect significant differences between the performance of girls and boys. This statistical consistency could be explained by considering that the gender gap12 in STEM (probably already at work in childhood, as suggested by some authors including [START_REF] Makarova | The gender gap in STEM fields: The impact of the gender stereotype of math and science on secondary students' career aspirations[END_REF][START_REF] Miller | The development of children's gender-science stereotypes: A meta-analysis of 5 decades of US Draw-a-Scientist studies[END_REF], only becomes stronger and more visible from adolescence onwards13 . On the other hand, other sociological variables must be considered to explain certain differences in performance. The results confirm that the type of school (which generally reflects the socio-economic status of the students' families) partly determines the level of performance achieved by the students (in line with the findings of Mc [START_REF] Mc Andrew | La réussite scolaire des élèves issus de l'immigration: une question de classe sociale, de langue ou de culture ?[END_REF] and that students from public schools as well as students from schools located in reinforced priority education networks have the most difficulties with mathematics. In the future, it would be desirable to examine this aspect in greater depth, trying to detect more precisely the impact of certain variables such as the cultural capital of families [START_REF] Bourdieu | Les trois états du capital culturel[END_REF], the school effect [START_REF] Cousin | L'effet établissement : construction d'une problématique[END_REF] or the teacher effect [START_REF] Bressoux | Réflexions sur l'effet-maître et l'étude des pratiques enseignantes[END_REF].

The results that we obtained suggest that in both territories, the rate of acquisition of skills in the construction of numbers varies according to several parameters (systemic, socio-economic). Indeed, in contrast to the results of pupils in Senegal, where the progression curve of acquisitions is rather slow and stable, those obtained by pupils in the academy of Martinique show a loss of speed between the first and the third grade. Even though mathematics teaching begins in nursery school with various activities relating to the construction of numbers and their representation in figures, it seems essential to consolidate these acquisitions.

Our two postcolonial populations are confronted with the plurality of languages in their region. As a result, the linguistic barrier can be considered as a hypothesis. Indeed, some authors have hypothesised that the mastery of the language, but also the specificities of the latter (notably in the field of semantics and nomenclature associated with mathematics) may have an impact on the learning of numeration, and then of calculation (Jarlégan, Fayol and Barouillet, 1996). Mélissa Arneton, in her doctoral thesis (2010), explored the Caribbean context based on this hypothesis, although in her study she finally concluded that "whatever the school level considered, the linguistic type has no link with school performance in either French or mathematics. Bilingual students do not perform worse than monolingual students" (Arneton, 2010: 339). However, his work did not consider the very particular linguistic construction of cardinal numbers -the natural integers -which is specific to the Wolof language (Eglash, 1997) and also specific to the Creole language (and which are also linked to the vigesimal system specific to the French language). The linguistic construction of numbers, which requires many exercises to be mastered, could explain the initial difficulties of pupils who construct numbers from their mother tongue (Wolof or Creole)14 , especially during the first years of school.

Finally, regarding our secondary survey, which served as a corollary to the TRDM, we suggest that the relatively positive relationship to mathematics and more specifically to mental arithmetic in our two territories could be explained in a few points.

In Martinique and Senegal, teaching of mathematics in primary school is often associated (by teachers or in textbooks) with a playful or cultural approach (which is moreover recommended by the respective official curricula) and by representations that are not yet contaminated by the context effect. There is a political will to improve the level of students in mathematics and the evolution of its place in the official curricula testifies to this (for indeed, in Senegal it operates the Project for the reinforcement of the teaching of mathematics, science, and technology, PREMST).

The fact that students value the operational dimension (calculation) over the conceptual one (mathematics as an abstraction) has been confirmed by other studies [START_REF] Papp | Gamification effects on motivation and learning: Application to primary and college students[END_REF][START_REF] Swacha | State of research on gamification in education: A bibliometric survey[END_REF]. It invites us to imagine innovative didactic strategies that take advantage of the opportunities offered by gamification and the use of serious games, escape games and other similar activities to facilitate the learning of computational automatisms.

Conclusions

This research shows us an updated and statistically representative panorama of social representations towards mathematics and the performance of primary schools' pupils in Martinique and Senegal, in the field of number construction and mental calculation. We hope that other similar studies can be carried out in the future: the large-scale deployment of the MDRT combined with a sociological survey would provide the competent public authorities with a more complete panorama that would facilitate the detection of territorial inequalities and to refine the strategies aimed at improving the results and performance of pupils.

Gender Total number of pupils Proportion in relation to the sample

	Girls	1261	49%
	Boys	1331	51%
	Total	2710	100%

Table 2 : Distribution of the sample by gender in Martinique As

 2 for the gender distribution of pupils in the Senegalese sample, it is consistent with that of the region (Inspection d'académie de Thiès, 2021. Table3).

	Gender

Total Number of pupils Proportion in relation to the sample Proportion in relation to the study population

	Fille	1509	51%	52%
	Garçon	1464	49%	48%
	Total	2973	100%	100%

Table 3 : Distribution of the sample by gender in Senegal

 3

	We chose to distribute our sample with the same proportion of pupils per type of
	schooling to guarantee, once again, the statistical representativeness of our study.
	In Martinique, the 32 schools we tested are spread over 10 school districts. The
	department has 50 schools in the Réseau d'Éducation Prioritaire Renforcée (REP+,
	High Priority Education Network, hosting the 23% of island pupils), 65 schools in the
	Réseau d'Éducation Prioritaire (REP, Priority Education Network, from which 29%
	of the island's primary school pupils are drawn), and 107 not-priority schools (HEP,
	48% of pupils. Académie de Martinique, 2021. Table 4).

Schools types Total number of schools Proportion in relation to the sample Proportion in relation to study population

	REP	802	31%	29%
	REP +	512	18%	23%
	HEP	1341	51%	48%
	Total	2710	100%	100%

Table 4 : Distribution of the sample based on school type in Martinique 3

 4

Table 5 ). Schools types Total number of schools Proportion in relation to the sample Proportion in relation to study population

 5

	Public	2258	76%	79%
	schools
	Private	715	24%	21%
	schools
	Total	2973	100%	100%

Table 5 : Distribution of the sample based on school type in Senegal

 5

Table 6 : Results of the mental arithmetic test by level in Martinique The

 6 observation of the results according to the typology of the school of enrolment reveals significant differences. Indeed, the first part of the test was better passed by schools located outside the priority network for islanders in Martinique. It is the schools located in REP that have the best performance in rapid calculations. Schools in REP+ remain at the bottom of the table for both parts of the test (Table7).

		Averages
	HEP	REP	REP +

construction of a number) Average number of correct answers

	Sub-
	Number dictation	89%	85%	80%
	Number comparison	89%	85%	83%
	Complement to a number	47%	36%	28%

total part 1 65% 65% 65% PART 2 (speed calculation) Average number of correct answers

	Additions	57,5%	70%	55%
	Subtractions	47,5%	52,5%	42,5%
	Multiplications	37,5%	45%	30%
	Divisions	25%	25%	15%
	Sub-total part 2	40%	47%	34%

Table 7 : Results of the mental arithmetic test per school type in Martinique In

 7 Senegal, we observed better performances in private schools (Table8).

	Averages
	Public	Private

construction of a number) Average number of correct answers

	Number dictation	79%	91%
	Number comparison	80%	88%
	Complement to a number	51%	61%
	Sub-total part 1	67%	77%
	PART 2 (speed calculation)	Average number of correct answers
	Additions 1 minute	54%	65%
	Subtractions 1 minute	35%	51%
	Multiplications 1 minute	44%	44%
	Divisions 1 minute	24%	27%
	Sub-total part 2	39%	47%

Table 8 : Results of the mental arithmetic test per school type in Sénégal

 8

Do you like maths ? Number of pupils Percentage

		Martinique	Sénégal	Martinique	Sénégal
	I don't like Maths at all	4	1	5%	1%
	I don't like maths	2	11	2%	2%
	I like maths a bit	14	19	16%	4%
	I like maths	14	47	16%	10%
	I like maths very much	52	392	61%	83%
	Total	86	470	100%	100%

Table 9 : Pupils and their relationship to mathematics

 9

Table 10 : Distribution of pupils according to their relationship to numbers and mental calculation

 10

Also known by its short title in French, Calcul Mental Africa2020, the project is led by the Institut National Supérieur du Professorat et de l'Éducation de Martinique (Université des Antilles, France), and funded by the Saison Africa

2020, an initiative of the President of the Republic implemented by the Institut de France, an operator of the French Ministry of Europe and Foreign Affairs and the Ministry of Culture.

The research corpus is freely accessible from DOI: 10.17632/7vm4x2b7hw.1[START_REF] Garçon | Corpus de recherche. Résultats du projet Calcul Mental Africa2020 (volet 1 : test de calcul mental en Martinique)[END_REF].

CE2 is the third grade of primary schools and corresponds to a

7-8-year-old student. 7 CP is the first year of primary schools and corresponds to a 5-6-year-old student. 8 CM2 is the fifth and last year of primary schools and corresponds to a 10-11-year-old student.

CE1 is the second year of primary schools and corresponds to a 6-7-year-old student.

CM1 is the fourth year of primary schools and corresponds to an 8-9-year-old student.

That is, the gender inequality that is generated in certain contexts by the effect of certain traditions, norms or socio-cultural values and that produces differences in treatment or performance between men and women.

This explains why this research item is considered by the Program for International Student Assessment (PISA) studies, conducted by the Organization for Economic Cooperation and Development (OECD), which focus on secondary school students. In the most recent rounds of PISA, France was positioned in the group of the most unequal countries (behind Venezuela), where the rate of boys outperforming girls in mathematics is the highest[START_REF] Stoet | Sex differences in mathematics and reading achievement are inversely related: Within-and across-nation assessment of 10 years of PISA data[END_REF].

-One example is the name associated with the number 32. In French, we say trente-deux, id est, thirty plus two. The pupil must know that thirty is three tens. In Wolof, we say nettfukk ak ñaar, i.e. three times ten plus two. The modality common to French and Wolof calls for the concept of multiplication. It is explicit in Wolof but not in French. An example is the name associated with the number 92. In French, we say quatre-vingt-douze, i.e., four times twenty plus twelve. In Creole, we say katrèvendis dé, i.e., four times twenty plus ten plus


Choosing when to work and when to play: How mindset impacts psychology students' decision to allocate effort and time to school activities

Léa Tân Combette, Jean-Yves Rotgé, Liane Scmhidt

Theories from social and developmental psychology propose that humans very early on hold beliefs (i.e., mindsets) about whether or not their intelligence is malleable over the course of a lifetime [START_REF] Dweck | Goals: An approach to motivation and achievement[END_REF]. Such growth mindset of intelligence is beneficial for dealing with challenges, learning, investing effort (2), and experiencing well being at school (3). However, it is unknown if and how intelligence mindsets affect a person's preferences to engage in studying rather than leisure. Models of economic choices propose that decision-making involves two phases, valuation and action selection. Much work has been done to better understand the valuation phase, which involves the integration of motivational features of choice options into a subjective value that then drives the selection of choice outcomes (4).

Here we combined these two research streams and asked: If intelligence mindset affects decision making about engaging in school activities (vs. leisure activities), and how they potentially affect the valuation of school activities during decision-making ? Second year psychology students (n = 54, 20.59+/-0.04, 47 female/ 7 male) were randomly assigned to a Growth mindset (GM) or a Fixed mindset (FM) intervention. They were told that the aim of the study was to help future students to better prepare for exams, and were encouraged to answer spontaneously. Following the mindset intervention all participants performed a forced choice task during which they had to imagine to be one week or one month before an exam. Under these two contextual scenarios they had to choose between a leisure and a default school activity. Participants also rated each activity on its subjective value (how much they like to engage in this activity), and motivational features such as pleasantness (intrinsic motivation), intellectual enrichment (identified motivation), importance for school (extrinsic motivation) and its difficulty (cost).

The results showed that during the forced choice task, and according to the cover story of contributing to an optimal revision schedule for future students, participants chose more often the school activities, but these choices were influenced by mindset and contextual scenario. The GM intervention group chose more often the school activity than the FM intervention group, and especially one week before exams. In the rating task, school activities valuation was influenced by the pleasantness, enrichment, importance for school and difficulty of each activity. Importantly, the intervention moderated the impact of difficulty on valuation. Taken together these findings indicate that short mindset interventions influence activity choice but also the valuation phase during decision-making by changing the weight of the difficulty of school activities.

The impact of intervention was larger one week than one month before exams.

Binomial General Linear Mixed Model

VALUE PLEASANTNESS ENRICHMENT IMPORTANT DIFFICULTY

Learn how to do a t-test

How much do you want to do this activity?

--------|-----------100

Learn how to do a t-test

How pleasant is this activity?

--------|-----------100

Learn how to do a t-test

How personaly enriching is this activity? 0 --------|-----------100

Learn how to do a t-test

How important is this activity for school?

--------|-----------100

Learn how to do a t-test

How difficult is this activity?

School activities valuation was impacted by all features:

• Pleasantness, enrichment and importance for school Impacted positively school activity values • Difficulty Impacted negatively school activity values • Intervention * Difficulty Activities valuation was less impacted by the difficulty after the growth mindset intervention than after the fixed mindset intervention.

Linear Mixed Model

Students the rated 100 activities on: