Selecting Tools to Model Integer and Binomial Multiplication (original) (raw)

Effects Of Algebra Tiles In The Teaching And Learning Of Algebraic Expressions

IOSR JRME, 2023

This study is aimed at using algebra tiles to assist students at the basic level to understand the concept of addition and subtraction of algebraic expressions in East Mamprusi Municipality of the North East Region of Ghana. The study also aims at providing practical ways by which teachers can use them to handle the topic effectively. A good grasp of algebraic expressions will help improve pupils' performance in exponents, polynomials, quadratic equations among others. Action research design was adopted for this study. Two research questions were formulated to guide the study. Achievement pre-test and post-test were developed and administered to the pupils and they were analyzed using simple frequency distribution tables. Percentages and average scores of the students were also calculated. In all, twenty-five (25) pupils were selected from form one junior high school (JHS) using stratified random sampling technique. The results of the study indicated a very significant difference between the pre-test and post-test which implied that the intervention yielded positive results on the pupils in the introduction of addition and subtraction of algebraic expressions. The study recommended among others that teachers should resort to the use of algebra tiles as teaching and learning materials when teaching algebraic expressions. More emphasis must be placed on the use of child centered method of teaching to ensure pupils participation during lesson delivery.

Teaching multidigit multiplication: combining multiple frameworks to analyse a class episode

Educational Studies in Mathematics, 2017

This paper provides an analysis of a teaching episode of the multidigit multiplication algorithm, with a focus on the influence of teacher's mathematical knowledge on his teaching. The theoretical framework uses Mathematical Knowledge for Teaching, mathematical pertinence of the teacher and structuration of the milieu in a downward and upward a priori analysis and an a posteriori analysis. This analysis shows a development of different didactical situations and some links between mathematical knowledge and pertinence. In the conclusion, the contribution of the two traditions originated frameworks is briefly addressed. This paper originated in a doctoral research project (Clivaz, 2011) that aimed to describe the influence of the mathematical knowledge of primary school teachers on their management of school mathematical tasks. The origin of that question partly came from U.S. mathematics education research and partly from the French didactique des mathématiques. Ball's categories of Mathematical Knowledge for Teaching (Ball, Thames, & Phelps, 2008) were used to describe the teacher's knowledge, while I described the effect on teaching through mathematical pertinence of the teacher (Bloch, 2009). I analysed the teacher's knowledge and the effect of this knowledge in ordinary classroom situations with the model of structuration of the milieu (Margolinas, Coulange, & Bessot, 2005) to take into account the complexity of the teacher's activity. After a brief explanation of these three frameworks, their interaction will be shown through an episode about the teaching of the algorithm of multidigit multiplication. Finally, I will discuss the interaction of these frameworks for analysing the teacher's knowledge and teaching. FRAMEWORK CATEGORIES OF MATHEMATICAL KNOWLEDGE FOR TEACHING Refining Shulman's (1986, 1987) categories of teacher knowledge for mathematics, Ball, Thames, and Phelps (2008) provide a practice-based division of Mathematical Knowledge for Teaching (MKT) (Figure 1).

Dynamic models for multiplication and division offered by

2016

Abstract: One of the most important features of GeoGebra is the coordination of the geometric and algebraic representations, easily observed in GeoGebra window. Using GeoGebra software the teacher can geometrically and fruitfully teach the concepts and algorithms of arithmetic operations in the elementary school. Our paper focuses on two important operations: multiplication and division in the set of natural numbers. Using GeoGebra features we visually demonstrate the concepts of these two operations and help the students to develop the process of mastering multiplication and division facts. Our paper aims to achieve three objectives: Firstly, teach multiplication and division using an area model with base and height of 10 squares. The table designed for this special purpose can be considered as a platform where the arrangements of objects, pictures or numbers in columns and rows is done. Secondly, teach division by using the concept of sharing or partitioning. We have designed a pa...

The Effect of Structured Game Using Algebra Tiles in Learning Multiplication of Binomials

Psychology and Education: A Multidisciplinary Journal , 2023

This study was conducted among the Grade 9 students at Kidapawan City National High School to find empirical evidence that the use of Structured Games using Algebra Tiles in Learning Binomials is more effective than the traditional teaching method. A quasi-experimental research design was used in the study. The respondent's scores on the pretest showed that there were no significant differences in their scores, which indicates that at the beginning of the study, the comparative groups, namely the experimental and the control group, have the same level of understanding on the Multiplication of Binomials. The result of the post-test indicated that the scores of the experimental are higher than the control group. The gain scores of the experimental group were greater compared to the control group. The gain score of the experimental group and control group had significant difference. It was further concluded that the utilization of game and Algebra tiles in learning Multiplication of Binomials improved students learning. Thus, manipulative games help students visualize and solve the problem.

Explanations, illusion of explanations, and resistance: Pre-service teachers’ thoughts on models for integer operations

This article reports the experience of a group of pre-service teachers when they discussed effective models for integer operations. While the participants proposed various models, analogies, and metaphors, it was difficult to find effective models that explain all the cases of integer operations and that were acceptable to all of them. This experience of discussing the rules for integer operations provided the participants with an opportunity to refine their prior knowledge and rediscover extant findings regarding effective mathematical models. However, their experience also revealed uncertainties about the mathematical and pedagogical nature of integer operations. Those uncertainties include the issues of convention versus understanding, the unnecessary complexity of the models, and the possibility of using models in a rote manner. The opportunity to discuss these models of integer operations helped the pre-service teachers to unpack their perceptions and understanding. For teacher educators, this work emphasizes the value of offering this type of activity in their mathematics teacher preparation courses.

Implementing alternative models for introducing multiplication

2019

The research literature provides plenty of examples of epistemological analyses of multiplication and descriptions of the complexity of the conceptual field of multiplication. Nevertheless, multiplication is often introduced as repeated addition, although decades of research have identified this pedagogical choice as leading to persistent problems in students’ conceptualisation of multiplication. In this paper, we describe a teaching design that aims to implement theoretical and empirical research results regarding multiplication in classroom practice. Within our design, models in the form of iconic representations serve as a means for creating patterns that make multiplicative invariants and structures visible. The teaching we have designed is currently tested in a mid-scale randomized controlled trial and in a large-scale professional development project.

Using The Jar Model To Improve Students’ Understanding of Operations on Integers

2008

The purpose of this ICME-11 Topic Study Group 10 (TSG-10), Research and Development in the Teaching and Learning of Number Systems and Arithmetic, is to gather congress participants who are interested in research and development in the teaching and learning of number systems and arithmetic, including operations in the number systems, ratio and proportion, and rational numbers. The focus of the group is broad and includes issues such as the development of number sense in students, the role of contexts and models in teaching and learning about numbers and arithmetic, and the development of teaching/learning units that connect basic arithmetic skills with higher order thinking skills. From an international perspective, we will study and discuss advances in research and practice, new trends, and the state-of-the-art. We also hope that putting together this Proceeding will make it possible to make the congress participants' experience available to people not able to attend ICME-11 or this specific TSG.

Building Opportunities for Learning Multiplication

2020

This chapter seeks to illustrate a comprehension-based learning approach focused on multiplication. We use episodes to show the potential of a teaching design of multiplication focused on the development of mental calculation based on tasks with appropriate contexts and calculations anchored in the use of benchmark numbers and operation properties, with examples to explain the ideas that are introduced. They are based on a collaborative work experience between a third-grade primary teacher and a researcher (the first author of this chapter). Using these specific examples, we discuss mathematical ideas and didactic options that can guide the actions of teachers when teaching multiplication. Finally, we discuss some points of convergence between the approach introduced here and the lesson study approach.

Knowing, Doing, and Teaching Multiplication

Cognition and Instruction, 1986

This investigation analyzes the structure and process of multidigit multiplication. It includes a review of recent theories of mathematical knowledge and a description of several fourth-grade math lessons conducted in a regular classroom setting. Four types of mathematical knowledge are identified: intuitive, concrete, computational, and principled knowledge. The author considers each type in terms of its relation to instructional issues and suggests that instruction should focus on strengthening the connections among the four types. Illustrations from instructional sessions show children generating and testing hypotheses when salient connections are made between concrete materials and principled, computational practices. Implications for teaching are discussed along with suggestions for future research.