THE MATHEMATICS EDUCATOR

Determining the Multiplicative Reasoning of a High School Junior and Senior

2022-12-20T10:52:35-05:00

Our study was guided by the question, how does the multiplicative reasoning of upper high school students give insight to their performance on a grade-level standards-based assessment? After giving a group of high school students a sample ACT assessment, we identified students to make comparisons between low and high scoring students on the sample assessment. Through a written assessment targeted towards assessing students’ unit coordination schemes, and through semi-structured interviews with two students, we documented a correlation between students’ level of unit coordination and their performance on the sample assessment. The evidence that students showed of limited multiplicative reasoning skills help explain some of their challenges in responding to prompts on an assessment like the ACT. This study reflects the need to give more focused attention on the multiplicative reasoning skills of secondary students and to design interventions that might develop these students’ multiplicative reasoning.

Intellectual need, covariational reasoning, and function: Freeing the horse from the cart

2022-04-13T15:01:53-04:00

Authors (year) contended a quantitatively sophisticated image of a dynamic situation can provide students with the horse needed to pull the cart that is the mathematical properties important for the set-theoretic definition of function. In this paper, we extend our argument in two ways. First, we adopt Harel’s (2008, 2018) constructs of intellectual need and epistemological justification to describe how a student can develop a quantitatively sophisticated image of a dynamic situation. Second, we exemplify that constructing an epistemological justification can support a student in subsequently making determinations regarding ‘function’, yet there is an apparent lack of intellectual need for differentiating between functional and non-functional relationship. This latter factor leads us to call into question the value of focusing on the metaphorical cart that is the basis for the set-theoretic definition of function.

Why I Won't Teach Mathematics for Social Justice (Even though I Want to)

2023-05-05T14:50:03-04:00

This paper reports on a research study in which seven New York City high school mathematics teachers participated in a professional development opportunity around the teaching of mathematics for social justice. The teachers saw value in teaching math for social justice and were philosophically aligned with the pedagogy. Despite this and despite recognizing various benefits of its use, they all indicated that going forward they would implement the pedagogy infrequently if at all. This paper explores the reasons the teachers gave for why they would not implement the pedagogy fully as it explores barriers to teacher implementation of teaching mathematics for social justice.

Facilitating Mathematical Reasoning through Team-based Learning

2023-09-22T09:16:08-04:00

Team-based learning (TBL) is a flipped classroom model, where small group discussions and peer learning play a central role. Some of its features, such as scalability to large classes and a high degree of structure, together with a well documented success rate in other fields, could make TBL an attractive option for the mathematics educator wishing to transform their teaching. This article surveys available peer-reviewed literature to provide an overview of current use of TBL in mathematics, summarizes findings and based on these, discusses TBL’s potential to support mathematics learning. We pay particular attention to if and how TBL can be leveraged to shift student focus from procedural towards conceptual learning and more creative forms of mathematical reasoning.

Semantic Structure of Word Problems: A Content Analysis

2024-02-05T11:22:26-05:00

Solving word problems is a standard part of the mathematics classroom. However, many students struggle solving word problems due to the variety in types of problems. One word problem can require a different solution approach than another form with few semantic changes. The Common Core State Standards Initiative (CCSSI) released a taxonomy for classifying types of one-step addition and subtraction word problems. The present study is a content analysis of three widely distributed mathematics textbooks, one each from three separate textbook publishers. The researchers analyzed the textbooks to classify the types of word problems they contained according to the CCSSI taxonomy. The findings show that variation of semantic problem structure is not proportionate within a single textbook; however, problem category frequency is similar across textbooks.

Professional Noticing in the Context of Mathematical Modeling

2023-12-14T07:49:15-05:00

The purpose of this study is to examine how professional noticing evolves in the context of modeling and what is unique about the context of modeling for developing noticing. Eight middle and secondary school teachers participated in this one-semester long study and received three training sessions on professional noticing. The results support modeling as a desirable context for developing noticing. Teachers provided more substantial detail about the mathematical aspects of student strategies after participating in the training, and they benefited from conversations with colleagues scaffolded by the three phases of professional noticing: attending to, interpreting, and responding to student thinking. Teachers also identified some unique aspects of student thinking in the context of modeling, especially local conceptual development experienced by some students during the study.

The Mathematics Identity Bicycle

2024-01-08T15:36:06-05:00

In this conceptual paper, I trace the role of agency in mathematics learner identity development across several empirical studies to illuminate understanding of how researchers have conceptualized agency as it relates to identity in mathematics education research. Building on this line of research, I propose an adapted conceptual framework for examining the role of agency in mathematics learner identity development through attention to both micro and macro influences on mathematics learners. I argue that such a conceptual framework is needed to support novel research involving equity in mathematics education. Finally, I offer the metaphor of “the mathematics identity bicycle” to aid in understanding how this conceptual framework might be taken up by other researchers in the pursuit of equity in mathematics education.

Front Matter

2024-12-20T08:57:46-05:00

Editorial

A Note to Reviewers

2024-12-20T08:59:14-05:00

Reviewer note