Date of Award

2017

Document Type

Dissertation

Degree Name

Doctor of Philosophy

College

College of Education and International Services

Program

Leadership PhD

First Advisor

Shirley Freed

Second Advisor

Janet Ledesma

Third Advisor

Bordes Henry Saturne

Abstract

The Problem

Teaching mathematics can be a difficult task. United States students on comparative international mathematics assessments consistently rank near the test averages. On a national assessment, commonly called the Nation’s Report Card, more than half of American students rank as ‘not proficient’ in mathematics. The purpose of this study was to describe the strategies used by teachers with at least average mathematical knowledge for teaching. This was evidenced by their scores on the Mathematical Knowledge Test for Teaching (MKT). In addition to teacher knowledge, the study sample was selected from among schools where the five-year average was above the average curve equivalent mean. The research question was “In what ways do teachers of high achieving mathematics students deliver mathematics instruction?”

Method

The methodology employed was a case study. The research analyzed videos of eight mathematics teachers using the Mathematics Quality of Instruction (MQI), to analyze the quality and the usage of the instructional strategies. The MQI provided a framework to view and analyze instruction in 14 mathematics lessons in grades 1 – 8. The MQI is divided into four dimensions: Richness of the Mathematics, Working with Students and Mathematics, Teacher Error and Imprecisions, and Common Core-Aligned Student Practices. Each dimension is further divided into instructional strategies. The Richness of the Mathematics dimension has six instructional strategies: Linking Between Representations, Teacher Provided Explanations, Mathematical Sense-Making, Multiple Procedures or Solutions, Patterns and Generalizations, and Mathematical Language. Working with Students and Mathematics has two strategies: Remediation of Student Errors and Difficulties and Teacher Uses Student Mathematical Contributions. Teacher Errors and Imprecisions has three parts: Mathematical Imprecision in Language or Notation, Content Errors, and Lack of Clarity in Presentations of Mathematical Content. Common Core-Aligned Student Practices has five strategies: Students Provide Explanations, Student Mathematical Questioning and Reasoning, Students Communicate about the Mathematics of the Segment, Task Cognitive Demand, and Students Work with Contextualized Problems. The lessons were videotaped and then 7.5-minute segments were coded using the MQI framework.

Results

These teachers know their mathematics. Of the 80 segments analyzed only 3% contained any errors and all instruction was clear. Of the four MQI dimensions, the teachers excelled in the Richness of the Mathematics dimension. Most of the strategies in this section were used a large majority of the time. When utilizing Working with Students and the Mathematics, the teachers used student comments and provided correction to student errors when needed. Common Core-Aligned Student Practices was the least used dimension. While students did communicate mathematically, the level of their communication tended to be procedural. There were a few instances of students making conjectures or conclusions based on patterns or mathematical reasoning.

The five strategies that were used more than 80% of the time were Mathematical Language (90%), Teacher Uses Student Mathematical Contributions (90%), Students Communicate about the Mathematics (85%), Mathematical Sense-Making (83%), and Teacher Provided Explanations (80%). The least used strategies were Multiple Procedures or Solutions (45%) and Student Mathematical Questioning (45%). Remediation of Student Errors was used in 51% of the segments, likely because students made few errors. Linking Between Representations, Patterns and Generalizations, Students Provide Explanations, and Students Work with Contextualized Problems were found in 61% of the segments.

There was higher quality of usage in grades one and two for the Richness of the Mathematics dimension. Teachers in grades three-five used both Working with Students and Mathematics strategies more often than the other grades. The quality of strategy usage by grade showed that in all strategies, grades one and two had a higher quality of usage than the other grades.

Conclusions

This study was conducted to identify the strategies used by effective math teachers in the Florida Conference of Seventh-day Adventists. These teachers have evident knowledge and are skillful in explaining and providing examples of the mathematical content. Their instruction was clear and precise. A relative weakness of the study teachers was their ability to guide students to generalize and reason mathematically. The ability to express oneself mathematically will increase student understanding and develop students who are successful in elementary school mathematics and beyond.

Subject Area

Mathematics--Study and teaching (Elementary)--Florida; Mathematics teachers--Florida; Seventh-day Adventist elementary schools--Florida; Seventh-day Adventist teachers--Florida; Florida Conference of Seventh-day Adventists

DOI

https://dx.doi.org/10.32597/dissertations/1641

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