Examining Two Middle School Mathematics Teachers’ Knowledge for Teaching Manipulation of Algebraic Expressions during Lesson Planning and Instruction (original) (raw)

An Investigation of Middle School Mathematics Teachers ’ Knowledge for Teaching Algebra

2016

The purpose of this study was to investigate middle school mathematics teachers’ knowledge for teaching algebra. The participants of the study were 48 mathematics teachers from various middle schools. A questionnaire was conducted in order to collect data about the teachers’ knowledge related to teaching of algebra. The results showed that the participant teachers were competent in making transitions among different algebraic representations. However, they had difficulties in explaining the conceptual bases of some of the algebraic concepts and procedures. In addition, results indicated that some of the teachers had similar difficulties and misconceptions with students as they were depicted in the scenarios in the questionnaire.

Knowledge for Teaching School Algebra: Challenges in Developing an Analytic Framework

The problem of knowledge for teaching mathematics is of growing concern to practitioners and researchers in ongoing efforts to improve mathematics education. Algebra is of particular importance since it functions as a gatekeeper for later mathematics courses. In this paper we describe our developing framework for understanding and assessing teachers' knowledge for teaching algebra. Using literature on teacher knowledge and student learning along with empirical evidence from our own research, we propose a two dimensional framework (tasks of teaching x categories of knowledge) with three additional overarching categories (decompressing, trimming, and bridging) to conceptualize knowledge for algebra teaching.

A MULTI-SITE CASE STUDY: ALGEBRAIC CONTENT AND PEDAGOGICAL KNOWLEDGE OF SIXTH GRADE MATHEMATICS TEACHERS.

Algebra is a fundamental topic in mathematics and lays the foundation for mathematical reasoning and complex problem-solving. A baseline study conducted in the Maldives showed that algebra test scores were the lowest compared to any other area of mathematics. Research shows that strengthening algebra instruction could improve student achievement. This concurrent mixed methods study examined the algebraic content and pedagogical knowledge of five sixth grade mathematics teachers who teach in five different schools across the Maldives. This study is guided by Shulman’s major categories of teacher knowledge and Ball, Thames, and Phelps’ domains of mathematical knowledge for teaching. The research questions examined the relationship between teachers’ perceptions of their mastery of algebraic content and pedagogical knowledge, and what teachers actually know about algebraic content and pedagogy. Purposive sampling was used to select the 5 participants. Quantitative data were collected using the Diagnostic Teacher Assessments of Mathematics and Science – Middle Mathematics Teacher Assessments and qualitative data were gathered through lesson observations, interviews, and analysis of teachers’ lesson plans and notes. All participants believed that they were proficient in both algebraic content and pedagogical knowledge. However, the results of this study showed that all participants lacked both algebraic content and pedagogical knowledge. Moreover, in-depth analysis of the textbooks and resource materials used by these teachers revealed that algebraic concepts were explained incorrectly in the prescribed textbooks, and resource materials.

Knowledge for teaching school algebra

2015

The problem of knowledge for teaching mathematics is of growing concern to practitioners and researchers in ongoing efforts to improve mathematics education. Algebra is of particular importance since it functions as a gatekeeper for later mathematics courses. In this paper we describe our developing framework for understanding and assessing teachers' knowledge for teaching algebra. Using literature on teacher knowledge and student learning along with empirical evidence from our own research, we propose a two dimensional framework (tasks of teaching x categories of knowledge) with three additional overarching categories (decompressing, trimming, and bridging) to conceptualize knowledge for algebra teaching.

Elementary teachers’ mathematical knowledge for teaching prerequisite algebra concepts

Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal, 1: Content Knowledge, 1-16, 2011

The current study investigated the effects of an undergraduate mathematics content course for pre-service elementary teachers. The participants’ content knowledge was quantitatively measured using an instrument comprised of items from the Mathematical Knowledge for Teaching Measures (Hill, Schilling, & Ball, 2004). Using a one-group pretest-posttest design, matched pairs t-tests showed significant gains (p = .000) in both common and specialized content knowledge and in two areas of prerequisite algebra concepts (numbers and equations/functions). Results provide evidence of pre-service teachers developing mathematical understanding beyond common content knowledge within collegiate course settings.

Understanding the characteristics of mathematical knowledge for teaching algebra in high schools and community colleges

International Journal of Mathematical Education in Science and Technology, 2021

In this paper we present an exploratory analysis of differences in the performance of two different samples of teachers-high school practicing teachers and community college faculty-on an instrument that assesses mathematical knowledge for teaching algebra 1. To better understand the variance in the performance within and between the two groups of teachers, we examine the relationships between the measured knowledge and teachers' educational and teaching background. Highlighting the positive effect of algebra-based teaching experience on the knowledge, we discuss the implications regarding the extent to which the instrument captures the construct it seeks to assess.

THE DEVELOPMENT OF CONTENT KNOWLEDGE OF PROSPECTIVE MIDDLE SCHOOL MATHEMATICS TEACHERS ON ALGEBRA

Explanatory-confirmatory research design, one of the mixed methods research designs, was used in this study to investigate content knowledge (CK) developments of prospective teachers regarding algebra. Cross-sectional study method, as a type of descriptive research and one of the non-experimental research designs, was used to collect quantitative data in the study. In the qualitative part of the study, case study was used. The participants of the study were composed of 176 prospective teachers studying in the elementary mathematics education department of a university in Turkey, who were first, second, third, and fourth year students with equal numbers. Interview, observation and knowledge test for algebra were used as the instruments for the purpose of study. One way ANOVA test was used to compare the means of the total scores of the prospective teachers obtained from Algebra Content Knowledge Test (ACKT) since ACKT score are normally distributed. According to the results of the study, it was observed that knowledge levels of the prospective teachers have developed as directly proportional depending on the class level. This development continued during the passing from second year to third year while it decelerates. In spite of this, it was observed that the development of CK accelerated again in the fourth year. In addition, it was also observed that the knowledge of prospective teachers in terms of CK was not at the desired level.

Teaching algebra conceptually: Preliminary findings

This paper reports some preliminary findings from a two-year TLRI study designed to develop approaches to teaching in Years 9 and 10 that will assist students to acquire a conceptual understanding of algebra. The aim of the research is to explore and develop teaching approaches and to document the impact of these approaches on student outcomes. Previous work (Linsell, 2010) has detailed the strategies that students use to solve equations and the prerequisite knowledge required for implementing these strategies. However there has been no research to date on teaching approaches that make use of these recent findings. The two main components of this action research study are a qualitative description of teaching approaches based on videos, teachers' diaries and meeting notes, and a quantitative analysis of student outcomes based on results from a previously developed assessment tool . Approaches to teaching were not uniform, but all made extensive use of the diagnostic assessment information and recognised that algebraic thinking pervades the entire mathematics curriculum. Assessment of the Year 9 students' algebraic strategies and knowledge at baseline and end of the first year of the study demonstrated that all but one of the six measures showed significant improvements. All the measures of student outcomes displayed significantly higher values in this study compared to a previous study on Year 9 students in Secondary Numeracy Project (SNP) schools, which was carried out at the same time of year.

Middle School Mathematics Teachers' Knowledge of Students' Understanding of Core Algebraic Concepts: Equal Sign and Variable

Mathematical Thinking and Learning, 2007

This article reports results from a study focused on teachers' knowledge of students' understanding of core algebraic concepts. In particular, the study examined middle school mathematics teachers' knowledge of students' understanding of the equal sign and variable, and students' success applying their understanding of these concepts. Interview data were collected from 20 middle school teachers regarding their predictions of student responses to written assessment items focusing on the equal sign and variable. Teachers' predictions of students' understanding of variable aligned to a large extent with students' actual responses to corresponding items. In contrast, teachers' predictions of students' understanding of the equal sign did not correspond with actual student responses. Further, teachers rarely identified misconceptions about either variable or the equal sign as an obstacle to solving problems that required application of these concepts. Implications for teacher professional development are discussed.