Using the TIMSS results for improving mathematics learning Abstract Introduction

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1 Using the TIMSS results for improving mathematics learning Ariana-Stanca Văcăreţu, MA Mathematics teacher Romanian Reading and Writing for Critical Thinking Association Cluj-Napoca, Romania Abstract Trends in International Mathematics and Science Study (TIMSS) is a comparative study which measures trends in mathematics and science achievements of fourth and eighth graders. Romania has participated with the eighth graders in all five assessments (1995, 1999, 2003, 2007, 2011) and TIMSS reports have provided relevant information on both mathematics and science achievement trends and key curricular, instructional, and resource-related factors that can impact the teaching and learning process (Mullis et al., 2012). However, prior to 2011, Romanian policymakers, administrators, teachers and researchers didn t use the TIMSS reports for improving the Romanian educational system. As teachers have some freedom in designing their instructional approach, we consider that if they are aware of the TIMSS evaluation and results they can use these results for improving learning outcomes. This paper presents how mathematics teachers may use the results of the TIMSS evaluation(s) for improving their teaching practices and their students learning outcomes. We will analyze an eighth grade TIMSS mathematics item and percent correct statistics for the item, identify students related misconceptions and provide examples of learning activities for addressing students misconceptions by preventing or correcting them. Introduction TIMSS requires a significant commitment of resources (Mullis et al., 2012): institutional resources, human and financial resources. This is a good reason for expecting some benefits from the use of information provided by TIMSS. During 2011, extensive attention was paid to Romania s participation in TIMSS 2011, as the Romanian Ministry of National Education (RMNE) decided to design national assessments by using international evaluations as examples of good practices (Noveanu, Singer, 2012). RMNE s interest in TIMSS has been evidenced by the implementation of the European Social Funds project Effective education based on fundamental decisions Exploitation strategies of international evaluations for improving the learning outcomes ( ) which aimed to develop the capacity of using TIMSS and PIRLS results for improving the quality of the Romanian educational system. Within the above mentioned project, TIMSS-2007 released items were analyzed from the perspective of their cognitive approach and their relevance to the national curriculum, typical student misconceptions in learning mathematics and sciences were identified, experts developed methodological guides for learning mathematics and sciences and an in-service teacher training course was designed and delivered to mathematics and science teachers in order to improve instructional practices. Working as an expert in this project, I adapted the project s approach to a small scale teacher project which aimed to develop math teachers capacity of using TIMSS for improving mathematics learning.

2 How to use the results of the TIMSS evaluation(s) for improving my teaching practices and the learning outcomes of my students? For exemplifying the process, I chose one of the TIMSS-2011 released items. Figure 1.Item M05_04 SOURCE: TIMSS 2011 Assessment. Copyright 2013 International Association for the Evaluation of Educational Achievement (IEA). Publisher: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College, Chestnut Hill, MA and International Association for the Evaluation of Educational Achievement (IEA), IEA Secretariat, Amsterdam, the Netherlands. Some basic information about this item is provided below: Content domain: Algebra; Topic area: Algebraic Expressions; Cognitive Domain: Knowing; Topic (Romanian mathematics curriculum): Algebraic operations (grade 7); General competence (Romanian mathematics curriculum): Identification of data and mathematical relationships and their correlation depending on the context they have been defined; Specific competence (Romanian curriculum): Identification of algebraic operation rules for simplifying expressions.

3 Looking at the mathematics curricular achievement standards for the end of compulsory education (lower secondary education level) this item would target two framework objectives: 1. Knowing and using specific mathematical concepts, terminology, and computing procedures (curricular achievement standard: Perform mathematics operations with real numbers, possibly represented by letters); 2. Developing the capability to communicate using mathematical language (curricular achievement standard: Understand the overall significance of mathematical information from various sources). This type of item is not a common one for the Romanian 8 th grader as it can t be found in Romanian mathematics text books or other learning materials. The percent of Romanian students who answered the item correctly situated Romania on the 30 th position (out of 42 countries) (see table 1.) Country Percent correct Chinese Taipei 81 Singapore 73 International average 44 Romania 35 Syrian Arab Republic 28 Ghana 25 Table 1. Percent correct answers - item M05_04 Why did the Romanian students have such a bad performance? Before answering this question, I suggest one should look at the item below: Figure 2. Item M03_05 SOURCE: TIMSS 2011 Assessment. Copyright 2013 International Association for the Evaluation of Educational Achievement (IEA). Publisher: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College, Chestnut Hill, MA and International Association for the Evaluation of Educational Achievement (IEA), IEA Secretariat, Amsterdam, the Netherlands. This item has a similar description with the item M05_04. The only difference is that in order to solve this item, students only have to find similar monomials and do the addition. This item is a common one for the Romanian students, as in the mathematics text books there are numerous

4 similar exercises. The percentage of Romanian students who answered the item correctly situated Romania on the 16 th position out of 42 countries (see table 2.) Country Percent correct Singapore 93 Hong Kong SAR 88 Romania 60 International average 56 Chile 35 Saudi Arabia 26 Table 2. Percent correct answers - item M03_05 Table 2 shows that 60% of the Romanian students perform correctly addition of monomials/ operations with real numbers represented by letters. Analyzing the two items (M05_04 and M03_05) and the percent of Romanian students correct answers we conclude that more than half of the Romanian students apply rules of algebraic operations, but only about a third of the Romanian students understand the rules of the algebraic operations and conceptualize the monomial. Why do we have this result? There might be many reasons; we will mention some of them below: - we are not used to encouraging students to use different representations for the same mathematical object (e.g.: fractions represented in a geometric context); - mathematics concepts are not discussed with the students; a definition is considered easy stuff, as we do not look for understanding of concepts; students have to recall the definition of a concept, not to understand the concept; - we tend to provide rules and then have the students apply the rules in many exercises of the same type; this instructional practice does not help the students to understand the rules either. Starting from the reasons identified above, we developed some learning activities which targeted: - identification of the monomial elements; - understanding operations with monomials. Activity 1 Objectives: students will define and use specific key words related to monomials Task: working in groups of 3-4 students, complete the tasks on the worksheet. Worksheet Define the following terms: monomial, base, exponent, coefficient, variable. Then, use the textbook or a mathematics dictionary to check the validity of your definition and fill out the table below: Key word Your definition Formal definition (from the textbook/ mathematics dictionary) monomial Example and its geometric representation

5 coefficient of a monomial exponent base variable - Were your definitions correct? Discuss. - What is the coefficient of the monomial 5ab 2 x 4?.. - What are the variables of the monomial 5ab 2 x 4?.. - What is the exponent of a in the monomial 5ab 2 x 4?.. - What is the exponent of x in the monomial 5ab 2 x 4?.. - Write the monomial 5ab 2 x 4 without using exponents... - Identify the coefficient and the exponent of each variable in each of the monomials: 2m 2 x, 5.4x 3, abc 2. - What have you learnt by completing this worksheet? Activity 2 Aims: students will represent real numbers and real number operations by using different languages. Task: work in pairs to complete the worksheet. - Read the text below and notice how the rubrics of the table were filled out. I pick a number. I multiply the number by itself. I multiply the result by 6 and, then, I multiply the result by the initial number. The text in words I pick a number. I multiply the number by itself. The text numerical language The text in visual language The text in algebraic language 3 x 3 3 = 3 2 x x = x 2 I multiply the result by = x 2 6 = 6x 2 I multiply the result by the initial number. (6 3 2 ) 3 = = (6x 2 ) x = 6x 3 - Discuss with your peer how the word text is represented in numerical, visual and algebraic languages by answering the following questions: How is the text translated in

6 numerical language? How is the text translated in visual language? How is the text translated in algebraic language? What properties/ mathematical rules have been used when writing the text in the numerical language? What properties/ mathematical rules are used when writing the text in the algebraic language? Please explain. - Translate the following algebraic text: 3x + 5x in numerical language, visual language and a text with words. Share your translations with your classmates. Conclusions In this paper we have showed how the TIMSS evaluations might be used by mathematics teachers to improve the quality of their teaching. Of course, if the TIMSS items are also released in the national language, mathematics teachers might be interested in applying (some of the) TIMSS items in their classes. The advantage of using the TIMSS items for assessing student learning resides in the quality of this items their development is the result of a long process which includes collaboration, piloting, revision. Moreover, we believe that the process described in this paper might be modelled within in-service training for mathematics teachers especially in TIMSS countries. In this way, teachers learn how to use the TIMSS results for improving their teaching, which will implicitly enhance the chances of improved student learning. In Romania, where in mathematics the TIMSS high achievers represent 5% and the TIMSS low achievers represent 29%, we have to identify means to reduce the achievement gap between high and low achievers. As we have to start from somewhere, a small scale teacher project might be a good start. If this type of project is supported by other educational institutions and stakeholders (e.g. the Ministry of National Education, pre-service and in-service teacher training providers, schools, researchers, etc.) we can hope to improve mathematics teaching practices and student performance in mathematics. References 1, About TIMSS and PIRLS.(2013). Retrieved from 2. Ministerul Educației, Cercetării și Inovării. (2009). Programa școlară Matematică clasele a V- a, a VI-a, a VII-a și a VIII-a [National curriculum for grades 5, 6, 7 and 8. Mathematics]. Bucharest. 3. Mullis, I.V.S., Martin, M.O., Foy, P., Arora, A., (2012). TIMSS 2011 International Results in Mathematics. Publisher: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College, Chestnut Hill, MA and International Association for the Evaluation of Educational Achievement (IEA), IEA Secretariat, Amsterdam, the Netherlands. 4. Noveanu, G.N., Singer F.M. Chapter: Romania in TIMSS 2011 Encyclopedia: Education Policy and Curriculum in Mathematics and Science, Volumes 1 and 2. Edited by Mullis, I.V.S., Martin, M.O., Minnich, C.A., Stanco, G.M., Arora, A., Centurino, V.A.S., & Castle, C.E. (2012). Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College. Retrieved from 5. TIMSS 2011 User Guide for the International Database. Edited by Foy, P., Arora, A., Stanco, G.M. (2013). International Association for the Evaluation of Educational Achievement (IEA). Publisher: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College, Chestnut Hill, MA and International Association for the Evaluation of Educational Achievement (IEA), IEA Secretariat, Amsterdam, the Netherlands. Retrieved from