**Academic Literacy Supporting Sustainability for Mathematics Education—A Case: Collaborative Working as a Meaning Making for "2**/**3"?**

**Päivi Perkkilä and Jorma Joutsenlahti**

#### **1. Introduction**

Sustainable education is currently being developed, in many countries, in many areas of basic education, vocational education and training, polytechnics, and universities. *Education for sustainable development* (ESD) as a long-term learning process supports a better life in various areas, such as social, economic, and environmental. To support a good and sustainable learning culture in different fields of education, we should build sustainable development so that we can understand the constantly changing world and its challenges. In the field of mathematics education, this means that we must develop students' *academic literacy in mathematics* (ALM) and 21st Century competences so that students have creativity to solve and model ESD-based mathematical problems, namely in the social, economic, and environmental fields. These kinds of skills can support the lives of students in the present and future (Widiaty and Juandi 2019).

#### *1.1. Education for Sustainable Development*

Zehetmeier and Krainer (2011) have argued that sustainability mainly belongs to ecological and economical vocabulary, but is more and more employed in the educational realm too. Already in 1657, Comenius highlighted sustainability in educational in his book "Didactica Magna" (Flitner 1970), with a chapter about the "foundation of lasting teaching and learning". This "foundation of lasting teaching and learning" refers to the view of ESD. Fullan (2006) observed sustainability in the light of educational change as "the capacity of a system to engage in the complexities of continuous improvement with the deep values of human purpose". Fullan (2006) rests his definition about sustainability on Hargreaves and Hargreaves and Finks' (2003) viewpoint, that is "sustainability does not simply mean whether something will last. It addresses how particular initiatives can be developed without compromising the development of others in the surrounding environment now and in the future".

All these definitions of sustainability are based on durable continuation. In the educational realm, we can understand this durable continuation as lifelong learning. Concerning education, good teaching and learning that matters lasts for life, and both are inherently sustaining processes. Supporting and maintaining such deep aspects of teaching and learning, which endure and foster sophisticated understanding and lifelong learning for all, builds the main core for sustainable development in education. In this respect, we want to uncover how the collaborative aspect (working in pairs) helps prospective class teachers with meaning making for the mathematical symbol "2/3". In 2019, we published an article about "What kind of meanings alone working prospective class teachers found for the mathematical symbol "2/3"" (Joutsenlahti and Perkkilä 2019). In the abovementioned article, students worked alone and tried to find different meanings for the mathematical symbol "2/3" and the subject of our study was the separate answers given by each student. In the research at hand, sustainability does not simply mean whether prospective class teachers' meaning making will last; we want to see if collaborative working enriches prospective class teachers' skills to produce their meaning making of the symbol "2/3" compared with the situation when they were working alone (cf. Fullan 2006; Hargreaves and Finks' 2003; Zehetmeier and Krainer 2011). In this sense, we can consider how pedagogical practices such as collaborative working methods support mathematical insights and mathematical thinking. Collaborative working methods, here meaning making collaboratively, are part of academic literacy, which is linked to ESD and 21st Century competences (see Figure 1).

#### *1.2. Academic Literacy and 21st Century Competences*

In the present study, we have expanded the ALM framework to support sustainable development in mathematics education (see Figure 1). Especially we have new interpretations in the context of collaborative mathematical thinking and its impact on meaning making for the symbol "2/3". In this way, we want to see if the collaborative aspect reinforces and enriches the students' meaning making for the mathematical symbol "2/3" and whether collaborative mathematical thinking could be robust enough for ALM skills and for the ESD. In Figure 1, we have described how ALM relates to ESD and to 21st Century competences.

for the article "Academic Literacy Supporting Sustainability to Mathematics Education – A Case: Collaborative Working

**Figures and Tables / Perkkilä and Joutsenlahti**

as a Meaning Making for "2/3"?"

**Figure 1.** Linking Academic Literacy in Mathematics (ALM) to Education for Sustainable Development (ESD) and 21st Century Competences (adapting Moschkovich 2015a, 2015b, 2018; Widiaty and Juandi 2019). **Figure 1.** Linking Academic Literacy in Mathematics (ALM) to Education for Sustainable Development (ESD) and 21st Century Competences (adapting Moschkovich 2015a, 2015b, 2019; Widiaty and Juandi 2019).

On the one hand, in Figure 1, good skills in ALM support both ESD and 21st Century competences, but on the other hand, ESD and the mentioned competences challenge ALM skills. We see that good 21st Century competencies as future citizen skills support both the ALM and sustainable development perspectives in developing mathematics teaching and learning. These future citizen skills include the following areas: civic literacy, global awareness, and cross-cultural skills; critical and inventive thinking; communication, collaboration and information skills (Ministry of Education Singapore 2018; cf. Partnership for 21st Century Learning 2019; Valli et al. 2014). Previously mentioned competences are central abilities of thinking, working, and mastery of tools, and they are considered future competences that future citizens will need (see Valli et al. 2014). As far as ALM skills are concerned, these competences are recognizable in the subareas of ALM skills. However, both ESD and the 21st Century competences are broader than the skills of the ALM, so ESD and 21st Century competences are also challenging ALM skills.

Moschkovich (2015a, 2015b, 2019) uses the term *academic literacy* to refer to literacy in mathematics studies. Generally, the concept *literacy* has been interpreted and studied from many different perspectives and there are several related concepts, for example, technological literacy, information literacy, online literacy, image literacy, and visual literacy (Kupiainen et al. 2015). Multiliteracy has emerged

as the overarching concept that combines the different perspectives. It should be remembered that this is a diverse area of competence, not only in reading but also in writing or production (Kupiainen et al. 2015). The concept "literacy" is based on the English term multiliteracy, which means that there are different textual practices in different social contexts; for example, these social contexts may be related to different disciplines such as mathematics (Kalantzis and Cope 2012). In this article, we illustrate the connection mainly between the ALM framework (see Moschkovich 2015a) and ESD. We also partly observe the meaning of ALM and ESD in the 21st Century competences viewpoint. ALM is understood here through three integrated components: mathematical proficiency, mathematical practices, and mathematical discourse (cf. Kilpatrick et al. 2001). We concentrate, especially, on two components of ALM: mathematical practices and mathematical discourse (languaging). Concerning sustainability in mathematics education, we see that good ALM skills in mathematics support Shulman's (1986) three categories of teacher's content knowledge: subject matter content knowledge, pedagogical content knowledge, and curricular knowledge. We must take these three areas into account if we want to develop teachers' and trainees' expertise in mathematics education and sustainable development in mathematics learning (Joutsenlahti and Perkkilä 2019).

Mathematics is seen as a gatekeeper in education: Good skills in ALM (see Shulman's (1986) three categories of teacher's content knowledge) ensure better chances of success in studies and, thus, a commitment to lifelong learning (Díez-Palomar et al. 2018). Joutsenlahti and Perkkilä (2019) have pointed out that if the mathematical content knowledge and pedagogical content knowledge were deepened in teacher education by making them a more sustainable basis through pedagogical arrangements (e.g., collaborative thinking), this will help to build a sustainable basis for future generations' mathematics education. Concerning pedagogical arrangements, ALM (Moschkovich and Zahner 2018) includes both sociocultural and discursive aspects of mathematical activity. These mean participation in mathematical practices and mathematical discourse. This view assumes that mathematical proficiency, mathematical practices, and mathematical discourse—the elements of ALM—work together and support collaborative mathematical thinking and languaging to build sustainable understanding in mathematics.

#### **2. The ALM Framework Supporting Sustainability in Mathematics Education**

The mission of the fourth goal of the Agenda for Sustainable Development of The United Nations (UN 2018) for 2030 is to secure inclusive and quality education for all and, in this way, promote lifelong learning. As mentioned before, mathematics

learning acts like a gatekeeper in education: those who succeed in mathematics education and have better scores in mathematics will end comprehensive school with better educational trajectories than those who underachieve in this subject (Díez-Palomar et al. 2018). To develop sustainable mathematics education, teachers' mathematical knowledge and skills for building innovative learning situations act like a gatekeeper concerning pupils' development in creating sustainable and meaningful understanding about school mathematics. In this sense, it is important to explore prospective class teachers' conceptual interpretations and, as a case example, their interpretations for the mathematical symbol "2/3", especially in collaborative situations, from the perspective of sociocultural situations of ALM.

#### *2.1. The Components of ALM*

Widiaty and Juandi (2019) treated, in their article, education for sustainable development (ESD) from the mathematics education point of view. They interpreted mathematics as a tool for understanding, analyzing, and solving problems in the neighborhood and surrounding society. To understand the aspect of sustainable development in mathematics, we need to develop the skills and creativity of teachers to plan for the problems of the surrounding society. To guide pupils to apply mathematics in the spirit of ESD, teachers need to have a good conceptual understanding of mathematics. Through conceptual understanding, they will promote sustainability in their own mathematical thinking and professional development in mathematics. Teacher education has great responsibility because conceptual understanding should be strengthened during teacher education by paying attention to the importance of ALM and reinforcing ESD thinking with ALM and 21st Century competences. As mentioned before, Moschkovich (2015a, 2015b, 2019) has defined ALM as three integrated aspects: mathematical proficiency, mathematical practices, and mathematical discourse (cf. Kilpatrick et al. 2001). In the following figure (Figure 2), we present the ALM components from the perspective of this study.


**Figure 2.** The modified Components of ALM of this study (adapting Kilpatrick, Swafford and Findell 2001; Moschkovich 2015a, **Figure 2.** The modified components of ALM of this study (adapting Joutsenlahti and Kulju 2016; Kilpatrick et al. 2001; Moschkovich 2015a, 2015b).

In this article, we will focus especially on the sociocultural aspects (see the mathematical practices and languaging in Figure 2) of the ALM framework in the context of prospective class teachers' mathematics education. These sociocultural aspects include participation in mathematical practices and participation in mathematical discourse. Mathematical proficiency includes the traditional cognitive aspects of mathematical activity such as mathematical reasoning, thinking, conceptual development, and metacognition (Kilpatrick et al. 2001; Moschkovich 2019; Moschkovich and Zahner 2018). We agree with Moschkovich (2019) and Moschkovich and Zahner (2018) that the sociocultural aspects of the ALM framework will not be separated from mathematical proficiency. The sociocultural aspects more likely assume that all the fields of ALM work together. When these three aspects are socioculturally included in mathematics learning, it will make the learning situations dynamic and will improve the meaning making of conceptual understanding in mathematics. These situations involve multiple modes of languaging like oral and written texts, gestures, drawings, objects, tables, graphs, symbols, etc. We need to account for all three ALM categories that develop mathematics teaching toward greater sustainability in mathematical meaning making and in achieving better learning results. Our focus is on education for sustainable development in prospective class teachers' mathematics education because as in-service teachers, they will act as key roles in building the quality of mathematics education for all and promoting sustainable meaningful learning in mathematics education. Next, we will clarify the components of ALM in this study.

#### 2.1.1. Mathematical Proficiency

b; Joutsenlahti and Kulju 2016).

Moschkovich (2015b) stated that the mathematical competence model published in 2001 (Kilpatrick et al. 2001) is still valid for describing the cognitive domain of

academic literacy. This model by Kilpatrick et al. (2001) presents mathematical proficiency, consisting of five features: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition (see also Joutsenlahti 2005).

The feature of conceptual understanding includes an understanding about mathematical concepts and relationships between them, as well as mathematical operations and their relationship to mathematical concepts (Joutsenlahti 2005; Kilpatrick et al. 2001). Conceptual understanding is reflected in the meanings that the mathematical problem solver gives to the solution (What does the result mean for the assignment?), the solution process (Why do the selected procedures and methods work in this solution?), and the final question (Why is the answer correct for this problem?) (Moschkovich 2015b). Procedural fluency is demonstrated by the ability to use mathematical procedures flexibly, carefully, efficiently, and expediently (Joutsenlahti 2005; Kilpatrick et al. 2001). In schools, the role of mechanical computing is particularly emphasized, but computational competence is often an essential part of conceptual understanding, and vice versa (Moschkovich 2015b). Strategic competence is the ability to formulate, present, and solve non-routine mathematical problems. The feature described above is central to problem solving. Adaptive reasoning is logical thinking, reflection, finding explanations, and witnessing. The last mentioned aspect of mathematical competence, productive disposition (the view of mathematics), reflects the learner's perception of the importance and usefulness of mathematics, as well as his or her own diligence and effectiveness in mathematics study (Joutsenlahti 2005; Kilpatrick et al. 2001). The five characteristics of mathematical proficiency (Figure 2) are in fact the cognitive component of academic literacy (Joutsenlahti and Kulju 2016). We can see that the cognitive component of academic literacy works like a tool which supports ESD and gives tools to formulate, present, model, and solve, for example, non-routine problems in the neighborhood and surrounding society. It is also connected to the meanings of 21st Century competences. This means that students should not only have the skills to think mathematically but they should have sensitivity to the problems found in the surrounding society, especially in the social, economic, and environmental fields (Widiaty and Juandi 2019); this is a real challenge for sustainable mathematics education.

#### 2.1.2. Meaning Making by Mathematical Practices

In the United States, the Common Core State Standards (2019) define eight mathematical practices (see Figure 2) that can be interpreted in teaching mathematics from preschool to high school. The practices described guide students starting and

mastering mathematical problem-solving processes. The mathematical practices are (the Common Core State Standards 2019): make sense of the problems and persevere in solving them, reason abstractly and quantitatively, construct viable arguments and critique the reasoning of others, model with mathematics, use appropriate tools strategically, attend to precision, look for and make of use structure, and look for and express regularity in repeated reasoning.

The first goal is to understand a given problem, whereby a mathematically proficient student begins problem-solving by first explaining to themselves the relevant features of the problem. The student uses typical problem-solving methods (for example, analogue problems, and trying special cases and simpler forms of the original problem in order to gain insight into the solution) in a consistent and persevering manner while monitoring and evaluating his/her own solution process. Secondly, the student must draw abstract and quantitative conclusions from the problem assignment. A mathematically proficient student understands the significance of the numbers or variables given in the problem assignment and their relationship to the problem assignment. He/she can contextualize the problem in such a way that he/ she is able to describe mathematical symbols in the problem and the relationships between them, as well as to simplify expressions and solve equations (the Common Core State Standards 2019; Moschkovich 2015b). Meaning making by mathematical practices includes several important competences, which researchers have related to sustainable development: 1. problem solving, critical thinking (e.g., construct viable arguments and critique the reasoning of others), action competence, and system thinking (e.g., model with mathematics, use appropriate tools strategically, attend to precision); 2. imagination, critical thinking and reflection, system of thinking, partnership, learning to work together, and participation in decision-making (e.g., meaning making, perseverance, constructive criticism); 3. systems thinking—the ability to see the interconnections between different dimensions and the complexity of systems and situations (e.g., abstract reasoning, precision, structures). The previously mentioned competences related to Sustainable Development are those skills which strengthen facing and solving mathematical problems, namely in the social, economic, and environmental fields, to support better life in the present and future (cf. Widiaty and Juandi 2019).

#### 2.1.3. Languaging and Collaborative Mathematical Thinking

Moschkovich (2015a, 2015b) highlights mathematical discourse as the third component of ALM. She emphasizes that mathematical discourse is a broader concept than the language used to study mathematics. Moschkovich (2015b) defines

mathematical discourse more precisely as communication competence that enables participation in mathematical practices. According to her, mathematical discourse includes not only oral and written texts, but also many modes (or symbol systems) such as gestures, activity materials, drawings, tables, graphs, and mathematical symbols. Interaction involves various registers such as school mathematics and home language. Moschkovich (2015b) emphasizes that in defining mathematical discourse, confrontation between the use of formal mathematics, such as the textbook definitions of concepts, and the student's own everyday register should be avoided. However, when looking at academic literacy and its components, we have chosen the third component as the "expression of mathematical languaging", instead of the student studying mathematics and discourse. In other words, the features of mathematical competence describe the cognitive potential of said learner, and the adoption of the mathematical practices given to the learner describes mathematical activity in the study and decision processes. The expression of mathematical languaging controls the abovementioned activity. It is based on the pupil's mathematical thinking, which is built on existing knowledge and skills (see Joutsenlahti 2005). This construction of thinking is also accompanied by the expression of thinking, where the student expresses his or her thinking in typical manners for mathematics by utilizing languages in a versatile way (e.g., Joutsenlahti and Rättyä 2015). Mathematical activity is also guided by collaborative working with other students and this interaction can generate mathematical knowledge and understanding. From the literacy point of view, the student expresses his or her mathematical thinking through natural language, mathematical symbolic language, pictorial language, and/or tactile functional language (Joutsenlahti and Kulju 2016; Joutsenlahti and Rättyä 2015). Likewise, mathematical thinking can be expressed using different symbolic systems (or languages) in different texts, for example, in verbal assignments, narratives, or in the oral presentation of a lesson (Joutsenlahti and Kulju 2017). By collaborative mathematical thinking, we mean here common work in pairs, where students share their ideas with each other (the other pair member) and produce joint solutions. In Figure 3, we clarify languaging as mathematical thinking. As mentioned before, languaging is divided in to four different parts.

**Figure 3.** Languaging as multimodality in expressing mathematical thinking (adapting Joutsenlahti and Perkkilä 2019; Joutsenlahti and Rättyä 2015). **Figure 3.** Languaging as multimodality in expressing mathematical thinking (adapting Joutsenlahti and Perkkilä 2019; Joutsenlahti and Rättyä 2015).

We call the process in which, for example, a pupil expresses his/her thinking as "languaging". We describe languaging in mathematics as referring to expressing one's mathematical thinking by different modes, either orally (by natural language) or in writing (by natural language, mathematical symbolic language, or pictorial language) (Joutsenlahti and Kulju 2017). In learning situations, especially with elementary school students, a tactile, functional language (working with manipulatives) is also involved as a fourth language, referring to expressing one's mathematical thinking. In mathematics textbooks, we can recognize three languages, which mathematics textbooks use as meaning making tools for mathematical concepts and procedures. Languaging of mathematical thinking helps pupils to structure their thinking and, in that way, understand mathematical concepts and procedures (Joutsenlahti and Perkkilä 2019; Kilpatrick et al. 2001; Moschkovich 2015b).

Collaborative learning aims at a relatively lasting change in a student's knowledge, collaboration, thinking, and attitudes. Collaborative thinking in groups/pairs facilitates verbal inference, explanation, evaluation, and reflection on what the individual knows. Through a shared reflection process, knowledge becomes meaningful and integrates into meaning structures (Hellström et al. 2015). In our study, collaborative mathematical thinking was manifested in pair work, where students must express their thinking to each other by languaging the meanings of the mathematical symbol "2/3".

#### **3. Case: What Kind of Meanings Do the Prospective Class Teachers Find for the Mathematical Symbol "2**/**3"?**

We have chosen the concept of fractions and the symbol "a/b" as a case from school mathematics. Fractions are one of the most challenging areas in school mathematics (e.g., Martin et al. 2008; Morgan 2001; Perkkilä 2001; Vosniadou 1999). Pupils have trouble with fractions, especially understanding fractions as numbers that extend the whole number system to rational numbers (e.g., Joutsenlahti and Kulju 2017; Siegler et al. 2013). One must have a clear picture of the different meanings of fractions to understand this extension. The different meanings of fractions are introduced separately without clear context in the Finnish mathematics textbooks, in which the fractions are often taught emphasizing a procedural perspective. The conceptual understanding about fractions and their different meanings is left with less attention (cf. Lemke 2002).

#### *3.1. Literature Review of Meanings of the Symbol "a*/*b"*

Researchers have found different subconstructs which are related to the symbol "a/b". Each subconstruct creates a context for the fraction that gives it a contextual meaning and these subconstructs also refer to the extension of whole numbers to rational numbers. Pantziara and Philippou (2012), for example, highlighted that the diverse constructs of fractions make it difficult for pupils understanding the concept of fractions. They described the following five subconstructs: part-whole, ratio, quotient, measure, and operator. We collected, from the literature, some typical approaches to the mathematical symbol "a/b" in Table 1.


**Table 1.** The approaches and the meanings of the symbol "a/b".

In Table 1, we separate two different approaches: (1) mathematical and historical and (2) pedagogical. The first one is based on how the symbol "a/b" has been described and used from the point of view of mathematics and takes into account the historical development of the meanings of fractions. The pedagogical approach is based on analysis of the concept "fraction" in school mathematics and, especially, how it appears in mathematics textbooks. The more detailed description of the meanings of the symbol "a/b" can be found in the writers' earlier article (Joutsenlahti and Perkkilä 2019).

The meanings of the concept could be presented in many different ways: mathematical symbolic language (e.g., "2/3"), natural language (e.g., "two of three parts"), or pictorial language (e.g., Figure 3) (Joutsenlahti and Perkkilä 2019; Shaughnessy 2005). Student's own meaning making processes need the use of natural language (most often, the student's mother tongue) and visual representations in learning activities (e.g., in studying new mathematical concepts and doing exercises) (Joutsenlahti and Perkkilä 2019; Lemke 2002; Morgan 2001).

If we want to learn mathematical concepts by understanding, we must have an awareness of how the new concepts are related to other concepts, and the ability to use them meaningfully in new contexts. We can distinguish the following expressions when we see mathematical symbolic language, mathematics by natural language, or by pictorial language: (1) from the point of view of a concept, we can speak of representations of the concept (Díez-Palomar et al. 2018; Joutsenlahti and Perkkilä 2019; Vosniadou 1999); (2) when a student expresses mathematical thinking, the student can use different multimodal approaches; and (3) when a reader makes meanings for a mathematical text, the languages can be seen as a multisemiotic approach (Joutsenlahti and Perkkilä 2019). In this article, we concentrate on connecting mathematical symbolic language and pictorial language by interpreting students' expressions in natural language.

#### *3.2. Research Questions*

In this article, we study the same phenomena related to the concepts (see Table 1) fraction, rational number, ratio, division, and probability as we did in our earlier article (Joutsenlahti and Perkkilä 2019). Now we have new data, which have been collected by a different study design: the prospective teachers (class teachers) answered the research questions in small groups (mainly two students in a group). We think that it is interesting to research how collaborative work helps students find meanings for the mathematical symbol "2/3" in different given contexts. If we consider prospective class teachers, we can understand the difficulties in the conceptual learning of fractions and find new development targets for teacher education. The modified components of ALM (Figure 2) give us the useful theoretical frame, because they take into account the features of mathematical proficiency and practices. The third

component of ALM is central from the point view of the interpretations and what kind of meanings the students found for the symbol "2/3".

In this article, the focus was to compare the answers given, by a single person (one student in a group) and in pairs (two students in a group), to the questions (Joutsenlahti and Perkkilä 2019):


#### *3.3. Materials and Methods*

Our data were collected in two phases: in 2017, first-year students (N<sup>2017</sup> = 102) completed the research in single-person groups and in 2018, first-year students (N<sup>2018</sup> = 136) completed the research in two-person groups. The students were from the University of Tampere and the University of Jyväskylä. The data were collected during the mathematics didactics course for first-year students by questionnaires in spring 2017 and in spring 2018. In 2017, the questionnaire had two pages: on the first page students gave their opinions spontaneously about what different meanings the mathematical symbol "2/3" can have and on the second page the students were asked to describe in natural language (Finnish) how the pictures A–D (Figure 4) were connected with the mathematical symbol "2/3". In 2018, the questionnaire was answered in the computer environment, but the questions were mostly the same (there were some more questions). The idea of the questionnaire was based on our theoretical background (see Table 1). In both controlled tests, the students had the same time (1 h) to give answers. From the answers to the questionnaire, we wanted to obtain an understanding about students' perceptions of the meanings of the mathematical symbol "2/3", and, on the other hand, how a multisemiotic approach supports the interpretations of collaborative thinking.

The data were analyzed by mixed methods. We used the IBM SPSS statistics 24 program for typical statistical analysis (e.g., mean and standard deviation). The qualitative analysis was done by theory-guided content analysis (e.g., categorizations). We used the classification into the six categories presented earlier in the theoretical part of the article and, on the other hand, the categories generated by the answers.

ports the interpretations of collaborative thinking.

during the mathematics didactics course for first-year students by questionnaires in spring 2017 and in spring 2018. In 2017, the questionnaire had two pages: on the first page students gave their opinions spontaneously about what different meanings the mathematical symbol "2/3" can have and on the second page the students were asked to describe in natural language (Finnish) how the pictures A–D (Figure 4) were connected with the mathematical symbol "2/3". In 2018, the questionnaire was answered in the computer environment, but the questions were mostly the same (there were some more questions). The idea of the questionnaire was based on our theoretical background (see Table 1). In both controlled tests, the students had the same time (1 h) to give answers. From the answers to the questionnaire, we wanted to obtain an understanding about students' perceptions of the meanings of the mathematical symbol "2/3", and, on the other hand, how a multisemiotic approach sup-

**Figure 4.** The second question of the research questionnaire: How the figures A–D describe mathematical symbol "2/3" (Joutsenlahti and Perkkilä 2019). **Figure 4.** The second question of the research questionnaire: How the figures A–D describe mathematical symbol "2/3" (Joutsenlahti and Perkkilä 2019).

#### The data were analyzed by mixed methods. We used the IBM SPSS statistics 24 **4. Results**

program for typical statistical analysis (e.g., mean and standard deviation). The qualitative analysis was done by theory-guided content analysis (e.g., categorizations). We used the classification into the six categories presented earlier in the theoretical part of the article and, on the other hand, the categories generated by the answers. **4. Results**  In the first question of the questionnaire, the first-year students (N2017 = 102 and N2018 = 136) gave as many meanings as they discovered for the mathematical symbol "2/3". If we study the results from the point of view of groups, we can see that, in In the first question of the questionnaire, the first-year students (N2017 = 102 and N2018 = 136) gave as many meanings as they discovered for the mathematical symbol "2/3". If we study the results from the point of view of groups, we can see that, in 2017, there were 102 students who worked alone (single/one student per group) and, in 2018, there were 68 groups (two students per group). Student groups spontaneously found different numbers of meanings for the symbol "2/3". The proportional quantities of the frequencies for each number (one, two, ..., five) are shown in Figure 5. We can see that working in pairs produced relatively more different meanings.

**Figure 5.** The proportional quantity of different meanings per a group that found single-student groups (single) and two-student groups (pair).

In the first question of the questionnaire, groups' (N2017 = 102 and N2018 = 68) spontaneous understanding about the mathematical symbol "2/3" was, in most cases, as a fraction (N2017 = 77 and N2018 = 62 groups gave "two thirds of a given whole" (Frac1) and N<sup>2017</sup> = 43 and N<sup>2018</sup> = 36 groups gave "two of three parts" (Frac2)), which are typical also in the Finnish mathematics textbooks. Ratio, rational numbers, and probability were mentioned the least.

In Figure 6, we can see that two-student groups found relatively more meanings "Division", "two thirds of a given whole" (Frac1), "two of three parts" (Frac2), and rational number (RatNum), but less meanings for probability (Prob) and ratio.

**Figure 6.** Proportional quantity (percent) of different meanings per a group (Single—single-student groups (N<sup>2017</sup> = 102); Pair—two-student groups (N<sup>2018</sup> = 68); Frac1—"two thirds of a given whole"; Frac2—"two of three parts"; Prob—probability; RatNum—rational number).

In the second question of the questionnaire, the groups' problem was writing how four figures (Figure 4) described the symbol "2/3". In Table 2, proportional frequencies (percent) are calculated as the observed frequencies for each group (single or pair). From the table, we can see that the groups' interpretations are mostly the same (highlighted with yellow), but the two-student groups have interpretations focused more on typical meanings (fraction in Figure A, division in Figure C, and rational

number in Figure D). Figure B (Table 2) is an exception because single-student groups found relatively more ratio meanings. "Other" meanings (Table 2) are meanings other than what have been given in the table. Most of these "other" meanings were vague descriptions that could not be meaningfully interpreted in this study. On the other hand, it is interesting to notice that two-student groups found, concerning Figure B, several different meaningful meanings. For example, the interpretation of the connection between Figure B and Frac1: "*The figure has one whole, or three white squares, next to each other. Next to it is two-thirds of it, or two blue squares*" (Two-student group 13). Collaborative thinking seems to be creative.

**Table 2.** Proportional frequencies (quantity per each group) of the interpretations how mathematical symbol "2/3" is connected to figures A–D (Figure 3). (S—single-student groups (N<sup>2017</sup> = 102); P—two-student groups (N<sup>2018</sup> = 68); Frac1—"two thirds of a given whole"; Frac2—"two of three parts"; Prob—probability; RatNum—rational number).


Two-student groups (N<sup>2018</sup> = 68) had a new problem where they had to consider if the given Figure A or B (see Figure 3) could somehow describe the symbol "2/3" and if they answered in the affirmative, they gave an example about the meaning. In Table 3, we can see that the groups invented, by collaborative thinking, mostly good argumentations for Figures A and B, but, particularly, the meanings "two of three parts" (Frac2) and division were difficult to connect meaningfully to Figure B. Some of the argumentations for Figure B (e.g., Frac1 and division) show creative thinking, probably supported by collaborative thinking in the groups. The students invented new contexts guided by the Figures and they unequivocally adapted the content of the chosen concept to themselves.

**Table 3.** Two-student groups' (N<sup>2018</sup> = 68) problem: Is it possible connect the given figure (A or B in Figure 3) to the symbol "2/3"? If the answer is "yes", then explain how. (N("yes"): frequency of "yes" answers, N("good"): frequency of "good" answers). **Table 3.** Two-student groups' (N2018 = 68) problem: Is it possible connect the given figure (A or B in Figure 3) to the symbol "2/3"? If the answer is "yes", then explain how. (N("yes"): frequency of "yes" answers, N("good"): frequency of "good" answers). **Table 3.** Two-student groups' (N2018 = 68) problem: Is it possible connect the given figure (A or B in Figure 3) to the symbol "2/3"? If the answer is "yes", then explain how. (N("yes"): frequency of "yes" answers, N("good"): frequency of "good" answers).


28

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three equal parts and divided into three white boxes evenly. This can illustrate the division of two into three and at the same time it is noticed that one blue box does not go full blue, so 2:3 must be less than one whole. (Group 58), (2)

three equal parts and divided into three white boxes evenly. This can illustrate the division of two into three and at the same time it is noticed that one blue box does not go full blue, so 2:3 must be less than one whole. (Group 58), (2)

If the circle is set to two, the sectors can

If the circle is set to two, the sectors can

division by two divided by three. (Group 47), (7)

division by two divided by three. (Group 47), (7)

DIVISION 31

DIVISION 31

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#### **5. Discussion**

#### *5.1. Collaborative Aspect*

The students interpreted the symbol "2/3" most frequently as a fraction or division (Figure 6). The two-student groups (pair) found, spontaneously, a proportionally bigger quantity of different meanings (Figure 5) and mainly gave, proportionally, more different meanings (Figure 6) than the single-student groups. Collaborative thinking and discussions with the peer (languaging) in two-student groups obviously strengthened the student's conceptual understanding and strategic competence, which they needed in the problem-solving situation.

Figures A–D (Figure 4) were interpreted typically, with Figure A meaning fraction (Frac1 and Frac2), Figure B meaning ratio, Figure C meaning division, and Figure D meaning rational number (RatNum) or fraction (Frac1) (Table 2). The two-student groups found proportionally more of those typical meanings for the figures (especially A, C, and D), but Figure B was an exception (Table 2). In the interpretations of the meanings of Figures A–D, we noticed that the students connected three different languages (Figure 3): pictorial and mathematical symbolic languages were present and in the students' task to combine the meaning they found the two languages and expressed them by natural language. Collaborative thinking and peer discussion helped solve the problem of how the three languages are connected by the given information. Students need meaning making, justification skills, modeling with mathematics, structure understanding, and skills to find regularities during the solution process (mathematical practices in ALM).

The two-student groups thought systemically that the given figures A or B could somehow be interpreted as symbol "2/3". Table 3 shows that the groups found a lot of possible contexts for almost every option. Collaborative thinking in each group brought good examples for the typical connections (compare Table 2). It is interesting that the students invented contexts of new kinds for the familiar meanings of symbol "2/3" by oral languaging, in which they reached a shared view. At the same time, when students create their own contexts for the different meanings of the symbol "2/3", they deepen their own and their mutual understanding about the concept and concept network.

Contradictions the students faced in the problems (e.g., Table 2) illustrated the narrowness of the learning materials, which were mainly constructed as definition-based, without an inquiry approach to concepts. These exercises help students understand that, e.g., the meanings of mathematical symbols are constructed only in their contexts. The curriculum (2014) emphasizes wide-ranging entities as

part of sustainable development, which requires multiliteracy skills (e.g., languaging skills). Therefore, the learning materials should also include a variety of contexts for concepts (including symbols) and guide students to recognize different meanings. Working as described above enables students to deepen the concepts they have already learned as well as to acquire new concepts and integrate them into existing conceptual networks.

In general, the results show that collaborative mathematical thinking in pairs helped students find more meaning for the mathematical symbol "2/3" (cf. Moschkovich 2015a, 2015b, 2019). Students took part in a math discussion that gave them good tips on the meaning of the discussion and how to share their thinking in mathematics learning situations (cf. Joutsenlahti and Kulju 2016). By considering the meaning of the mathematical symbol "2/3" together, they also deepened their understanding about the meanings of the fraction (cf. Joutsenlahti and Perkkilä 2019).

#### *5.2. ALM Supporting Sustainability*

Re-examining our research from a languaging point of view in the data collection situation, we noted that when the students were answering our questionnaire they were codeswitching between pictorial, natural language, and mathematical symbolic language. At the same time, they explained their mathematical thinking to each other. There was a relationship between language and mathematical thinking in this situation. We can image that by solving the problems of our questionnaire, students had to have literacy in understanding pictorial language and understanding about mathematical language. Solving these problems together, students had to have proficiency in the content of mathematics but also competences in collaborative mathematical thinking and languaging, and mathematical practices. (cf. Moschkovich 2019; see also Figures 1 and 2). We can cautiously think that the ALM components were present in the research situation, helping students to deepen their mathematical thinking (see Figures 1 and 2). Students took part in mathematical discussions that gave them experiences on the meaning of discussion about sharing their thinking in mathematics learning situations (see Figures 1 and 2; collaborative mathematical thinking and languaging; mathematical practices). By considering the meaning of the mathematical symbol "2/3" together, they also deepened their understanding of the meanings of the fraction (see Figures 1 and 2; mathematical proficiency). Moschkovich (2019) and Moschkovich and Zahner (2018) highlighted that sociocultural aspects of the ALM framework work together with mathematical proficiency. We can assume that these aspects were socioculturally

included in our data gathering situations and made the learning situations dynamic and possibly improved the students' meaning making of conceptual understanding in mathematics, especially about the meaning making of fractions (see Figures 1 and 2). In this way, the sociocultural aspects supported the deepening of mathematical thinking and, at the same time, broadened the students' perspective of fractions. Through collaborative mathematical thinking, students promoted sustainability in their own mathematical thinking and professional development in mathematics (cf. (Widiaty and Juandi 2019)). Collaborative mathematical thinking has connected ALM with 21st Century competences. Pair-working in the research situations included fields of the 21st Century competences subareas: civic literacy, global awareness, and cross-cultural skills; critical and inventive thinking; and communication, collaboration and information skills. In the meaning making situations, students had to use civic literary (languaging), global awareness and cross-cultural skills (different learners worked together), critical and inventive thinking (meaning making for "2/3"), collaboration (collaborative mathematical thinking), and information skills (multimodality in expressing mathematical thinking) (cf. Figure 1). Based on our study, we noted that during teacher education, prospective class teachers should have experiences (e.g., collaborative mathematical thinking, languaging) that promote their mathematical knowledge and understanding and contribute to the building of their and future generations' basis of sustainable mathematics understanding. In addition, this will support sustainable education and 21st Century competences. We summarize, in Table 4, the factors that support the understanding of key concepts and concept networks in mathematics education from the perspective of 21st Century skills. The objectives presented in Table 4 are objectives for both teacher education, teachers, and students, and they support ALM and ESD in mathematics learning (See Figures 1 and 2).

**Table 4.** Sustainable development goals for teacher education, teachers and students in mathematics teaching and studies.


From a teacher's standpoint, contextualization (see Table 4) means that a teacher's knowledge of his/her students' mathematical skills must be good in order to contextualize mathematical concepts in phenomena that are familiar to students. When the learning atmosphere is good and a teacher knows his/her students, the teacher can focus on the potential for progress in what students say and do. Therefore, the students are free to bring multiple perspectives to learning situations,

e.g., by contextualizing their own examples and self-invented assignments in relation to the mathematical concepts at hand, and also interpreting mathematics as a tool for understanding, analyzing, and solving the problems in the neighborhood and surrounding society (cf.Widiaty and Juandi 2019). Often (e.g., in Finland) mathematics teaching is 'textbook driven'. Due to this, the nature of mathematics and the contents of school mathematics might appear for pupils only through textbooks. Then, there is no room left for the pupils to question and to ask questions about mathematical concepts and solutions and express their own thinking (cf. Joutsenlahti and Perkkilä 2019). The critical use of the textbook in teaching (see Table 4) gives students more time and space to question and to ask questions about mathematical concepts and solutions. Students also have time to construct their own mathematical concepts solution processes and *create* analogies and applications for the mathematical concepts to be studied. Asking questions, reasoning, logical thought, creating analogies and applications for mathematical concepts, describing and explaining, and justification are closely related to conceptual understanding, which is one of the five intertwined strands of the description of mathematical proficiency (see Kilpatrick et al. 2001; Moschkovich 2019). As mentioned in Section 2.1.1, mathematical proficiency includes following intertwined strands: procedural fluency, strategic competence, adaptive reasoning, and productive disposition (see Figures 1 and 2). These strands are included in Table 4. Languaging as a teaching method provides teachers and students space to express and explain mathematical concepts in versatile ways. Therefore, codeswitching can serve as a resource during teaching and learning (tactile functional language, pictorial language, natural language, and mathematical symbolic language; see Figure 3). Languaging of mathematical thinking helps students to analyze and structure their thinking and, in that way, understand mathematical concepts, procedures, and solution processes (Joutsenlahti and Perkkilä 2019; Kilpatrick et al. 2001; Moschkovich 2015b). From the sociocultural perspective, we can think that languaging as a teaching model involves students in discipline-based practices in mathematics learning situations that involve reasoning and justification, sharing different views, understanding, and communication. Collaborative mathematical thinking is involved in languaging situations, and by working in small groups or in pairs, students share their ideas with each other, produce their joint solutions and learn to give feedback to each other. In Table 4, the sustainable development goals for teacher education, teachers, and students in mathematics teaching and studies involve the elements of ALM. These goals are created to give tools for teaching and learning mathematical concepts and mathematical networks in sustainable ways. ALM supports ESD and 21st Century competences but, on the other hand, ESD and

21st Century competences also challenge ALM skills (see Figure 1). The goals in Table 4 give versatile ways to build a solid mathematical knowledge base, so that teacher education, teachers, and students can have better tools to solve and model ESD-based mathematical problems, e.g., in the social, economic, and environmental fields. The results (e.g., in Table 4) could be a base for mathematics education for a new curriculum of teacher education in universities.

**Author Contributions:** The authors contributed equally to this work.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


Kupiainen, Reijo, Pirjo Kulju, and Marita Mäkinen. 2015. Mikä monilukutaito? In *Monilukutaito Kaikki Kaikessa*. Edited by Tapani Kaartinen. Tampere: Tampereen Yliopiston Normaalikoulu, pp. 13–24. (In Finnish)


© 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### **Outstanding Performance or Reversal of Fortune in Burundi's Education System?**

**Yasmine Bekkouche and Philip Verwimp**

#### **1. Introduction**

Since the success of the Millennium Development Goals to get children into school, the focus of the international community has been reoriented towards the quality of schooling. The fourth goal of the Sustainable Development Goals set by the UN targets exactly that. It wants the global community not only to make sure that children attend school, but that schools also offer adequate training in reading and mathematics, tools that form the basis for all further cognitive development of a child (UNESCO 2017).

Burundi forms an interesting case study, as it experienced a massive increase in enrolment in primary school, but access to good quality education was not equally distributed over the country. The capital and the southern provinces were privileged by former presidents who came from the south and belonged to the Tutsi minority. Since his ascent to power, President Nkurunziza, a Hutu from the northern province of Ngozi, during his first mandate (2005–2010) heading a coalition government, and after a landslide victory in his second (2010–2015) and third mandate (2015–2020), has directed public funding to the northern provinces, Ngozi province in particular. Recent work has demonstrated that the population in the north benefits at multiple levels. Jadin (2020) uses household panel data with three waves (1998–2007–2012) and shows how income from agricultural activities as well as from coffee harvest increased in the north after the second wave, but not in the south, whereas both parts were on a parallel trend prior to the second wave. Verwimp (2019) highlighted the strong increase in school test scores obtained by schools in the north in the Concours National from 2010 onwards.

Education data worldwide are the product of an administrative process aggregating pupil-, teacher-, school- and district-level data as well as data from countries' national budgets. Researchers, donors, agencies and policymakers rely on the accuracy of these data to inform future policies, to draw a picture of the current state of affairs, to compare the performance of their country with neighbors and so on. Moreover, even the availability and accuracy of education data does not mean that national policymakers will take the evidence to heart. While, generally speaking,

there are no grounds not to have confidence in a country's education data, it often takes an outside look or evaluation to wake up national policymakers. This is all the more evident in the reactions to the results of the Program for International Student Assessment (PISA) in the national press, in particular when the results show that one's country is lagging behind compared to others.

In this study, we use an independent source of information on school quality and school test score data produced by the CONFEMEN (Conférence des ministres de l'Education des Etats et gouvernements de la Francophonie) Program for the Analysis of Education Systems (PASEC), in 2009 and in 2014, to find out if we are indeed witnessing a reversal of fortune in Burundi's northern versus southern provinces (see PASEC 2010, 2015, in the corresponding order). At the same time, we scrutinize Burundi's overall exceptional performance compared to other countries tested in PASEC (Programe d'Analyse des Systèmes Educatifs de la Confemen). This allows us not only to compare test score data over time, but also between countries, making these data a valuable source for the analysis of educational performance.

#### **2. Burundi's Education System**

The report issued by PASEC after the first collection of test score data (PASEC 2010) lists many constraints and deficiencies in Burundi's education system, including the small tax base to finance educational expenses as a result of the high level of poverty in the country, the high birth rate that puts pressure on the educational system, the lack of adequate infrastructure and educational material, and the low qualification of teachers. As a result of the presidential decision to abolish school fees in primary school a major step towards realizing universal access as stipulated in SDG 4—the school population increased from 1,000,000 pupils in 2004 to 1,800,000 in 2008 (PASEC 2010, p. 29), a massive increase for which the school system was unprepared and under resourced. Nevertheless, the number of teachers and schools in that period also increased by 50%, keeping pace with the increase in pupils.

In Burundi, the first four years (out of six) of primary school are taught in Kirundi, the national language, a policy that has positively affected the retention and promotion of children in those grades. This can also be witnessed in the results of the PASEC tests run for literacy in Kirundi in the second grade. In fifth and sixth grade, however, all teaching is done in French, posing a strong hurdle for pupils and resulting in very high repetition and dropout rates.

On top of nationwide deficiencies in the education sector, Burundi is plagued by ethno-regional favoritism. At the end of the sixth grade, the Ministry of Education organizes a national test, the Concours National. Each year, the Ministry of Education

sets a threshold depending on the number of seats available in the country's secondary school system. Even before the start of the civil war, much fewer seats were available annually than pupils competing for a seat in the Concours National. This was a very competitive and merit-based system in which only a select few would attend secondary school. Dunlop (2015), who interviewed Hutu and Tutsi adults on their school career for her MA thesis, writes that the Concours National favored Tutsi pupils because the latter were better prepared for the exam in better-funded schools. The 'objective' outcome of the exam made Tutsi pupils believe that Hutu were not interested in pursuing secondary education and preferred to stay on farms. When he came into power, president Nkurunziza was determined to change this.

While the Ministry uses the Concours National to regulate access to secondary school, it can be usefully employed to monitor deficiencies in learning and to follow-up policies that improve the quality of education. The test measures the abilities of pupils in 4 domains: mathematics, French, Kirundi and environmental science. The maximum one could obtain was 200 points, with 80 for the math part, 70 for French, 30 for Kirundi and 20 for environmental science. The latter was conceived as a combination of biology and geography. As Ntwari (2016, p. 19) points out in his doctoral dissertation there is no separate training offered in Burundi for science teachers, in contrast to math. This may limit adequate teaching and curriculum development in the domain of sustainable development.

#### **3. Data**

We are using two PASEC data collection efforts in this chapter,<sup>1</sup> the first PASEC wave we use was implemented in more than 10 countries in the first decade of the new millennium (in Burundi in 2009). The PASEC is an international program that measures the academic performance of children attending primary school in French speaking Sub-Saharan African countries. In each country, PASEC surveys a nationally representative sample of schools randomly selected from active primary schools. To represent the variety of schooling environments available in the country, each sample is stratified by regions and types of school (e.g., private and public schools). Once a school is sampled, one class of second grade and one class of fifth grade students are randomly selected, and 15 students are randomly drawn from each class to take the test. Since primary school across sub-Saharan Africa are organized around six grades, surveying pupils from the second and fifth grades is expected

<sup>1</sup> PASEC. Available online: http://www.pasec.confemen.org/ (accessed on 29 April 2020).

to yield a balanced image of numeracy and literacy skills near the entry and exit of primary education, while avoiding the peculiarities of the first and last grades.

Each student is assessed in language, arts and numeracy at the beginning and at the end of the academic year, using standardized tests made of multiple items in line with official curricula. At the end of the academic year, a teacher questionnaire provides further information on classroom organization and infrastructure, teacher characteristics, training, remuneration and literacy skills for each teacher. Similarly, the headmaster of each school is interviewed and provides detailed information on his/her characteristics, training, school infrastructure, pedagogical practices, and human resource practices.

The second PASEC test was done for all countries a few years later (in 2014). Three major modifications were applied. First, students were not sampled at the beginning of the school year anymore, but only at the end of the year instead. Second, students were tested in grade 6 instead of grade 5. Finally, the nature of the test itself changed: following the PISA methodology, the tests were designed to assess pupils' ability to achieve general objectives. For literacy, for instance, a general understanding of text and reading are tested. The methodology used to measure proficiency is based on Item Response Theory and uses plausible values. Consequently, PASEC 2014 tests are not directly comparable to PASEC 2009.

For the sake of comparability, we only used the end-of-the-year test in the first wave of PASEC. In the following, we refer to the tests implemented in grade 2 as "early primary" and those implemented in grade 5 (first wave) or grade 6 (second wave) as "late primary". Since the results of the two waves are not directly comparable, we first compare the relative performance of countries. Later in this chapter, we will use standardized test scores to compare different regions within Burundi.

In our analysis, we compare the following countries between the two waves: Burundi (2009 and 2014), Benin (2005 and 2014), Cameroon (2005 and 2014), Côte d'Ivoire (2009 and 2014), Senegal (2007 and 2014) and Tchad (2009 and 2014).

#### **4. Descriptive Statistics**

We start by plotting the results for the language and mathematics scores for PASEC 2009 in the second and fifth grades in Burundi and the other countries (Figure 1). In grade 2, compared to the other countries, Burundi has a low mean and low standard deviation on the French language test, meaning that practically everyone performs badly in the test. This comes as no surprise as the language of instruction in Burundi is Kirundi, the national language. French is not on the curriculum in grade 2. When we look at scores for the Kirundi test in grade 2,

the mean improves but the standard deviation is much larger, meaning that some pupils do well and other do not. For the mathematics test, the mean is high and the standard deviation low, a situation that we term "Scandinavian type", as it means that everyone is doing well. The fact that mathematics is taught in Kirundi in the second grade may be the main explanation, as pupils are better able to understand the teacher.

**Figure 1.** Mean and standard deviation for mathematics and language Program for the Analysis of Education Systems (PASEC) tests (2000s). Source: PASEC data for Burundi (2009), Benin (2005), Cameroon (2005), Côte d'Ivoire (2009), Senegal (2007) and Tchad (2009).

In grade 5, the mean and the standard deviation are both high, for mathematics as well as for language (which is solely French here), meaning that some but not all students do well. Importantly, we believe, in regard to the PASEC 2009 results for other countries, that the scores for Burundi cannot be considered outliers, neither for grade 2 nor for grade 5. In both grades, the combination of the mean and standard deviation for Burundi is in the proximity of the linear fitted line, albeit more obvious in grade 5 compared to grade 2, with the caveat that the linear fit is performed only on a very small sample of countries.

Turning our attention to PASEC 2014 (Figure 2), we notice the extremely positive scores for Burundi compared to other countries, meaning a very high mean and a low standard deviation. This is the most obvious in grade 6, but also in grade 2, as can be witnessed in Figure 2, for language as well for mathematics. The scores for Burundi are so exceptional that the country is situated far from the linear fit—an outlier, in other words.

**Figure 2.** Mean and standard deviation for mathematics and language PASEC tests (2014)<sup>2</sup> . Source: PASEC 2015.

<sup>2</sup> The linear prediction lines does not include Burundi.

When we compare test scores for grade 5 in PASEC 2009 with those for grade 6 in PASEC 2014 for those countries which took part in the test in both years, we notice that Cameroun, Benin and the Ivory Coast do not change much (meaning they demonstrate the same combination of mean and standard deviation), whereas the test scores for Chad deteriorate along the 45-degree axis (meaning that all students do worse in 2014 compared to 2009) and Senegal improves along the 45-degree axis. Burundi stands out as the only country that improves outside the 45-degree axis, meaning the mean score increases and the standard deviation decreases. For the language test, Burundi has the highest mean score combined with the lowest standard deviation of all countries. Since the test is testing the knowledge of French, and since French is the language of instruction only in the final two years of Burundi's primary school, this is an extraordinary performance. This is also the case for mathematics: the mean score for Burundi is also the highest of all countries, by a large margin, and Burundi also has the lowest standard deviation.

#### **5. Di**ff**erence in Di**ff**erences Analysis**

Upon disaggregating the test scores for Burundi for northern provinces versus southern provinces, we notice that the strong improvements for Burundi (higher mean and lower standard deviation in 2014 compared to 2009 compared to other countries) are mainly driven by the outstanding performance in the northern provinces. This can be witnessed in Figure 3.

Taking the analysis a step further, we perform a difference in differences analysis whereby the PASEC test score results for 2009 serve as the baseline, where we compute the changes with 2014 in the north and in the south of the country. Later, we discuss the parallel trends assumption that we are making here and demonstrate that both parts of the country were indeed on a parallel trend prior to 2009.

The results in Table 1 show that pupils in the northern provinces of Burundi, in general, perform worse compared to the southern provinces and that the test scores in 2014 were lower compared to 2009. However, compared to the south, northern test scores improve much more in 2014, which we demonstrate with the statistical significance of the interaction effect (even if the proportion of the variance described by this model, represented by the R-squared statistics, is very low).

**Figure 3.** Mean and standard deviation in PASEC tests in late primary (for the 2014 results, the linear prediction line does not include Burundi). Source: PASEC data for Burundi (2009 and 2014), Benin (2005 and 2014), Cameroon (2005 and 2014), Côte d'Ivoire (2009 and 2014), Senegal (2007 and 2014) and Tchad (2009 and 2014).


**Table 1.** Difference in difference estimation, late primary (standardized scores). Source: PASEC data for Burundi (2009 and 2014).

Note: regression of PASEC test scores on a constant, a dummy variable equal to 1 if the school of the student is located in the North region, a dummy equal to 1 if the student was studied in 2014 and a variable for the interaction of those 2 dummies. \* *p* < 0.1, \*\* *p* < 0.05, \*\*\* *p* < 0.01.

#### **6. Parallel Trends before 2009**

Figure 3 depicts the evolution of test scores between 2009 and 2014 in Burundi, separated between northern and southern provinces. Before discussing the mechanisms behind this reversal of fortune, we want to point out that this is a particularity of this period, meaning that, before 2009, both parts were on a parallel trend and there was no sign of reversal. We demonstrate this in two graphs, depicted in Figure 4 where panel (b) depicts the PASEC scores for the north and south and panel (a) depicts the success rate in the Concours National for the years 2006, 2007 and 2008 in the schools sampled by PASEC during the 2009 test. Indeed, part of the data collection in 2009 by PASEC included the success rate of pupils in each sampled school in the three years prior to the test. The Concours National is a nationwide test, consisting of mathematics, French, Kirundi and environmental science that each pupil has to take if she/he wants to continue into secondary school. Hence, this constitutes an administrative source of information that is independent of PASEC and which allows us to corroborate the parallel trend in the north and the south before 2009.

**Figure 4.** (**a**) Success rate in the Concours National, Burundi; (**b**) PASEC scores (2009 and 2014) in Burundi. Sources: PASEC data for Burundi (2009 and 2014) and results of the Concours National (Ministry of Education).

#### **7. Potential Mechanisms**

north

A number of reasons can explain the reversal of fortune of northern versus southern schools in Burundi's education system. As mentioned in the introduction, the north has been disadvantaged for several decades under the Tutsi-led regimes who favored their own southern region. By ending advantage and disadvantage, we could thus witness a return to long-term mean performance on both regions. Searching for variables that capture potential advantages and disadvantages, the PASEC data allows us to test several potential pathways. We introduce them one by one in the subsequent analysis. In Table 2, we first add school budgets, in nominal terms as well as on a per pupil basis. As expected, we find a small and statistically significant effect (at the 10% level) of this variable, meaning that increases in school budgets play a role in test score performance. However, after controlling for this, neither the magnitude nor the statistical significance of our variable of interest (the interaction between the north and the 2014 test year) changes. This pattern is repeated when we control for two other variables which can be leveraged by educational policymakers in Burundi: the size of classes (again in nominal terms and per teacher), as well as school and class infrastructure. Both variables have the expected effect on test score performance (meaning negative for the effect of size and positive for the effect of infrastructure), but their inclusion does not change the effect of our variable of interest.



Note: regression of PASEC test scores on a constant, a dummy variable equal to 1 if the school of the student is located in the North region, a dummy equal to 1 if the student was studied in 2014, a variable for the interaction of those 2 dummies and a series of possible mediators. \* *p* < 0.1, \*\* *p* < 0.05, \*\*\* *p* < 0.01.

#### **8. Political Economy**

In Table 2, the interaction effect thus remains unexplained after the inclusion of a number of policy variables. We know, however, that the northern region is the area

of origin of president Nkurunziza. As discussed in Verwimp (2019), an explanation of this reversal of fortune may also be found in the political arena. He showed that success rates in the Concours National changed dramatically from one year to the next in northern schools, after the landslide victory of the president's party in the parliamentary elections in 2010. Schools in Nkurunziza's municipality, a very poor area, score as good in the Concours National in 2010, 2011 and 2012 (period under investigation in Verwimp's paper) as the best performing schools in well-off neighborhoods in the capital Bujumbura, whereas, before 2010, this was not the case.

Since the second test run by PASEC took place in 2014 and since this test is run by an independent, international body running these tests in dozens of African countries, it may be that school quality and pupil performance in the north indeed improved between PASEC 2009 and PASEC 2014, in which case the improvements in the north can be the result of large investments over the last few years, and these improvements need not be the result of tinkering or political manipulation.

We are not able to determine the exact mechanisms that explain Burundi's very favorable scoring in the PASEC in 2014. It may be that the investment policies directed to the school system in the north under president Nkurunziza (more classrooms, more teachers, etc.) started paying off, as is also witnessed in our analysis. This may not explain the favorable test scores in the north one year later (2010, as in Verwimp (2019)), but may offer a plausible explanation 5 years later, in PASEC 2014. The unexplained part (the interaction effect in our analysis) may be caused by a motivational component compared to baseline observations in 2009—the combination of material improvements and immaterial ones (proudness, motivation, etc.) in the northern population, given that their plight is finally being answered by the president's policies.

#### **9. Discussion and Conclusions**

In the context of the learning crisis observed in many developing countries, Burundi stands as an outlier. When it comes to international skills assessments, Burundi students perform far better than other sub-Saharan African students, in both mathematics and language. Quite surprisingly, this is only the case for the 2014 PASEC survey. In this chapter, we studied potential explanations for this evolution. We suggest that this outstanding performance may be driven by a reversal of fortune within Burundi between northern and southern provinces, whereby the northern provinces did exceptionally well in PASEC 2014. The northern provinces, home turf of President Nkurunziza, have received a lot of public goods since his ascent to power. School budgets, class sizes and teachers per student have the expected effect

in explaining the change in performance between PASEC 2009 and 2014. However, these elements do not seem to explain everything, as the northern dummy's interaction with the year 2014 dummy remains statistically significant after the inclusion of the above variables. This leaves the door open for other explanations of this progress, possibly related to the political economy or a motivational component.

As for the curriculum is concerned we recommend that Burundi builds on its experience with the inclusion of environmental science as a (small) part of the Concours Nationale. This offers a pathway to include sustainable development goals in the curriculum. It will require a strong effort on behalf of the teacher training institutes to educate future teachers who can build effective learning environments, another key element in SDG 4.

**Author Contributions:** Both authors contributed equally to this work.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
