Introducing Tables to Second-Grade Elementary Students in an Algebraic Thinking Context

In this study, we adopted a functional perspective on algebra. Our focus was on tables and how they were first used by second-grade elementary school students (7- and 8-year-olds) when working with functions. This qualitative, exploratory, and descriptive study consisted of five classroom sessions and two semi-structured interviews, one group and one individual, two weeks apart, focused on tasks involving different functions and uses of tables, with and without labels for headings. In this study, we ask the following research questions: How do children organise values in tables with or without (a priori) labels for headings? What are the regularities (structures) identified by students? Our data revealed that students were able to organise the values of variables by listing them in columns and labelling the headings (i.e., identifying the variables involved). The ways in which children organised the data in tables enabled us to identify the structures they identified as regularities between the variables involved in the functions. More structures were correctly identified in the second interview compared to the first.

THE EFFECTS OF USING BAR MODEL TOWARDS ALGEBRAIC THINKING SKILL IN ALGEBRAIC PROBLEM SOLVING AMONG STUDENTS

Algebraic thinking skills are one of the elements emphasized in the benchmarking of PISA (Program for International Student Assessment). However, the algebraic thinking skills among students were found to be still at a very weak level. The purpose of this study was to look at the effect of the bar model method on students’ algebraic thinking skills. Pre-test and post -test were used as research instruments. The study was an experimental study conducted on 90 Form One students from a school in Tuaran District, Sabah. This study used a quasi-experimental design of pre-and post-test. The sample was divided into 3 groups, namely the group of learning methods i) Bar Model (MB, n = 30), ii) Bar Model and Cooperative Learning (MBPK, n = 30), and conventional (TR, n = 30). Statistical inference test, One-way Analysis of Variances Test (ANOVA) was used to analyze the findings of this study. The results of one-way ANOVA analysis showed that there was a significant difference in the mean score of the post-test between the MB group, MBPK group, and TR group (F (2, 87) = 9.316, p <.05). Significant differences in mean scores for post-test could only be seen between TR group with MB group (P = 0.019) and between TR group with MBPK group (P = 0.000) while insignificant differences were shown between MB and MBPK group (P = 0.304). Therefore, it is suggested that mathematics teachers use the Bar Model as a teaching aid to improve students' algebraic thinking skills.

Integration of Ignatian values in the development of algebraic thinking via utilization of quasi-variables: A lesson study

<p dir="ltr"><span>This paper reflects on the outcome of lesson study in teaching the concept of algebraic equations utilizing quasi-variables. It also concurrently examines the integration of Ignatian values and social issues in learning the said concept. This study aimed to establish a culture of planning, collaboration, and reflection in developing the understanding and relevance of mathematical concepts in grade school through lesson study. The study showed how the process of lesson study was done given the following phases: planning phase, implementation phase, and post-lesson reflection and discussion phase. Emphasis on the planning phase was given on the details of the lesson design which aimed to integrate Ignatian values in the discussion while developing algebraic thinking from quasi-variable thinking delivered in the implementation phase. Findings highlighted on three statements: i) Collaborative lesson planning nurtures a deeper sense of scholarship and collegiality; ii) Building algebraic thinking from quasi-variable (arithmetic) thinking is a viable strategy for understanding the concept of algebraic equation; and iii) Looking into the “big picture” and responding to relevant social issues could strengthen meaning - integration of Ignatian values. Strong collaboration and communication among teachers in creating detailed lesson design enabled more meaningful learning among pupils. Research revealed the significant role of lesson study in creating meaningful strategies and activities which provided efficient structure in developing a chosen lesson topic. It does not only focus on the nature of the topic but also include making meaningful connections to the real world and integrate values.</span></p>

Learning Obstacle on Addition and Subtraction of Primary School Students: Analysis of Algebraic Thinking

This study aims at exploring learning obstacles about arithmetic operations, and problems of addition and subtraction of whole numbers in primary schools. This preliminary qualitative research used a didactic research design. The participants of this study were 50 second-grade students at primary schools in three regencies. The instruments used were test and nontest. The test technique was conducted by giving questions about algebra, whereas the nontest technique was in the form of interviews. The data were analyzed using interactive analysis by Miles & Huberman. The findings indicate that there are three types of learning obstacles, namely, (1) ontogenic obstacles with psychological and instrumental types (students feel afraid and do not understand the prerequisite material), (2) epistemological obstacles (students’ experience in working on story problems with the concept of algebraic thinking does not exist), and (3) didactical obstacle (the methods taught tend to focus on the counting process instead of understanding the concept). Learning barriers can be categorized into three types, namely, ontogenic, epistemological, and didactic barriers. With the discovery of these learning barriers, a solution is found in the form of making learning designs that are tailored to the learning obstacles found. One of them is by applying grading questions from story problems into mathematical sentences.

Preservice Teachers’ Mathematical Knowledge about Repeating Patterns and their Ability to Notice Preschoolers Algebraic Thinking

Background: Several studies have shown that many preservice teachers (PTs) who teach in the early years have a superficial knowledge about repeating patterns (RPs), which affects their knowledge about children’s algebraic thinking. Objective: This article aims to understand PTs’ algebraic thinking and their ability to notice preschoolers algebraic thinking and how these two domains articulate within a teacher education experiment. Design: The study follows a qualitative methodology based on participant observation, complemented by document collection. Setting and participants: The study stems from a teaching experiment carried out in a school module focused on patterns and algebra of a degree in basic education, with two pairs of PTs as participants. Data collection and analysis: The data come from the written productions and discussions between the elements of each pair of PTs within the scope of the tasks proposed in the teacher education course, adopting an original analysis framework. Results: The results reveal that the PTs successfully identify the structure of the RPs and the general position of each term; however, one of the pairs still find difficulties in fully understanding that mathematical object. The pairs attend to relevant aspects of children’s algebraic thinking, although sometimes with limited interpretation. Conclusions: This study highlights the importance of creating opportunities in initial teacher education for PTs to develop their algebraic thinking from an early algebra perspective and to analyse, in this context, the preschoolers’ work.

High School Students' Algebraic Thinking Ability in Solving Linear Program ProblemsHigh School Students' Algebraic Thinking Ability in Solving Linear Program Problems

Aljabar merupakan bagian matematika yang berperan penting dalam proses penyelesaian masalah pada bidang matematika maupun bidang ilmu lainnya. Mulai dari konsep-konsep hingga cara berpikir aljabar. Sehingga penting bagi siswa untuk menguasai kemampuan berpikir aljabar. Oleh karena itu penelitian ini akan memberikan gambaran terkait kemampuan berpikir aljabar dalam menyelesaikan masalah matematika. Model penelitian yang digunakan adalah kualitatif analisis deskriptif. Penelitian dilaksanakan pada salah satu SMA di kabupaten Karawang.

The Initial Algebraic Knowledge of Preservice Teachers

Early algebra proposes to incorporate algebra in primary school from the first years of schooling. The success of this incorporation depends, to a large extent, on the training of teachers, so the objective of this article is to study whether the degree of algebraic knowledge of student teachers at the beginning of their training. To conduct this, 106 preservice teachers were given a questionnaire. This survey is based on two daily life situations. They had to propose tasks to develop algebraic reasoning in primary school students. Most of the participants designed tasks in which they assigned specific values to the indeterminate ones and solved them arithmetically. In this way, they transformed open situations and numerous opportunities to promote algebraic thinking in students through the generalization and representation of relationships and functions into closed single-solution problems that do not promote algebraic thinking. We can see from the results that the participants’ algebraic knowledge is insufficient. Therefore, it is necessary to include in their training process the programs and experiences that will allow them to design tasks in order to detect and promote algebraic thinking in their future students. Sequences of tasks are presented to develop both situations by generalizing and representing relationships and functions, which can serve as a starting point for future training programs and experiences.