Math Instruction for Students with Learning Difficulties

Susan Perry Gurganus

• Publisher: Routledge
• Year: 2021
• eBook ISBN: 9781000476033
• Topic: Pedagogía
• Subtopic: Educación general

This richly updated third edition of Math Instruction for Students with Learning Difficulties presents a research-based approach to mathematics instruction designed to build confidence and competence in preservice and inservice PreK- 12 teachers. Referencing benchmarks of both the National Council of Teachers of Mathematics and Common Core State Standards for Mathematics, this essential text addresses teacher and student attitudes towards mathematics as well as language issues, specific mathematics disabilities, prior experiences, and cognitive and metacognitive factors. Chapters on assessment and instruction precede strands that focus on critical concepts. Replete with suggestions for class activities and field extensions, the new edition features current research across topics and an innovative thread throughout chapters and strands: multi-tiered systems of support as they apply to mathematics instruction.

1Mathematics in Today’s SchoolsThe Context for Learning Challenges

DOI: 10.4324/9781003096733-1

Chapter Questions

1. How are teachers’ and students’ attitudes toward mathematics related to learning?
2. What mathematics reforms have influenced current mathematics standards?
3. What national standards have an effect on state and local mathematics curricula?
4. How do the mathematical practices relate to the content standards?
5. What mathematics topics are emphasized in PreK through Grade 12 classrooms?
6. How are multi-tiered systems of support (MTSS) models creating a new context for mathematics teaching and learning?

Schools in the 21st century are experiencing many forces for change in order to prepare students for college and career demands and to meet the needs of increasingly diverse students. National and state-wide curriculum standards have been adopted widely, with their high-stakes assessments. Technology offers new and challenging resources for teaching and learning. School-district initiatives offer students more options for study and concentration areas. Students with learning difficulties—those with disabilities, language differences, impoverished backgrounds, and others—find themselves in classrooms with high demands that offer varying degrees of learning support. This text addresses the variables that can assist students with learning difficulties in being successful in today’s mathematics learning settings: instructional, assessment, resource, interpersonal, and intrapersonal contexts. This first chapter sets the stage with discussions of teacher and student dispositions about mathematics, mathematics reform movements, current curricular standards, multi-tiered systems of support, and the need for collaboration among professionals.

Angela Smith was hired immediately after graduation as a special education teacher at Balsam Middle School. The principal informed her that she is to support regular mathematics classes for three periods of the day and will teach special pull-out mathematics classes two periods each day. Leaving the principal’s office, Angela feels panic as she struggles to recall the mathematics programs reviewed over only a two-week period in her special education methods course.

Joseph Lopez met with the assistant principal for instruction at Pine Road High School and was informed that a total of 20 students with learning, emotional, and communication disabilities will be in his Geometry, Algebra I, and Mathematics I classes. Joseph recalls accommodations for students with physical, visual, and hearing disabilities but cannot imagine what he should plan for students with other learning difficulties.

Chris Johnson feels fortunate to have a teaching position at Pinetops Elementary School after relocating to Pine Grove to be closer to her family. But the meeting with the principal has left her puzzled. What is a mathematics support teacher?

In a meeting of new teachers in the district, Angela expresses her anxiety about teaching a subject she is not very strong in herself. Joseph talks about his love of everything mathematical but uncertainty regarding individual student needs. Chris feels confident that her five years of elementary teaching will be beneficial for instructional planning but is not sure about how to work effectively with so many other teachers.

Angela, Joseph, and Chris are facing the challenges of new teaching positions that will involve mathematics instruction or the support of that instruction for students who are struggling to learn skills and concepts. In a fairly short period of time they must understand their instructional roles, get to know students, review the district mathematics curriculum, and develop long- and short-range instructional plans in cooperation with other teachers. All three teachers have doubts about their abilities to meet the needs of students with learning difficulties within the mathematics curriculum. However, they all have many strengths and demonstrate professional attitudes about developing new skills.

What teacher characteristics are most closely associated with student achievement in mathematics, especially for students who struggle to achieve? Multiple studies cite strong understanding of concepts in conjunction with skill in specific pedagogies for mathematics as requisite for student achievement (Baumert et al., 2010; Campbell et al., 2014; Hill et al., 2019). Mathematics knowledge alone is not enough. General pedagogical skill is not enough. Deep understanding of mathematics concepts and how to teach those concepts is critical for student learning. Additionally, teachers’ knowledge of students—knowing what their students know and don’t know—is related to student outcomes in mathematics (Hill & Chin, 2018). Teachers of students who struggle with mathematics must be skillful with a broader range of content, be able to trace learning pathways for individual students, demonstrate a wider array of pedagogical tools, and have expectations of students that will help build knowledge and positive attitudes towards mathematics. Unfortunately, in many states and districts, disadvantaged students tend to be served by less qualified teachers in mathematics (Goldhaber et al., 2016; Hill et al., 2019; Max & Glazerman, 2014).

Two of the most critical factors for increasing student achievement are the student’s self-efficacy beliefs in mathematics and the teacher’s high expectations for students (Campbell et al., 2014; Clark et al., 2014; Friedrich et al., 2015; Klehm, 2014; Tosto et al., 2016). These dispositions of students and teachers are among the strongest predictors of student achievement. The following sections introduce teacher and student dispositions toward mathematics, with strategies for building positive views, expectations, and aspirations.

Mathematical Dispositions

Many teachers and teacher candidates, especially in elementary and special education, are anxious about their responsibility for teaching mathematics. They may have had poor experiences themselves (Bekdemir, 2010; Gresham, 2009; Humphrey & Hourcade, 2010). They may have taken only one mathematics-education course, unlike their peers teaching middle- or high-school coursework. Special educators, often certified to teach K-12, may be dealing with higher levels of content than they feel prepared to teach. General educators may have had an exceptional children or diverse students overview course, but not a course specific to pedagogies for working with struggling students.

When asked about memories of their own math classes, teachers and teacher candidates cited indelible memories:

• My teacher lacked mathematics skills and could teach a lesson only by following the textbook and checking the solutions (Bekdemir, 2010, p. 320).
• My teacher asked me [to explain something in class and I said] I couldn’t do division and then all my classmates laughed at me (Bekdemir, 2010, p. 320).
• I took a computer class (in college) instead of a math course. I wouldn’t have passed a math course…because I was always doing badly in it (Humphrey & Hourcade, 2010, p. 28).
• I’ve never been a math person, but I can’t have my students ever know that. I’m really good at finding someone to explain the problem to me before I try and help my kids (Humphrey & Hourcade, 2010, p. 28).
• I had the best time in math class. I remember getting up every day during elementary school and couldn’t wait to get to school and do math (Gresham, 2009, p. 35).
• Ever since I was in elementary school I have hated math! I remember going home crying, not wanting to go to school, screaming at my mother for making me do my homework, … begging her to let me quit school,… all by fifth grade! (Gresham, 2009, p. 35).
• Math was always easy, fun, and something I always wanted to do. I would play math games instead of playing with dolls (Gresham, 2009, p. 35).
• As soon as the test was over, I forgot everything about math that day. I feel so bad for my students who are like me (Gresham, 2009, p. 28).

Teachers’ beliefs about their personal capabilities to help students learn is termed teacher (or instructional) self-efficacy (Klassen et al., 2011). There is evidence that teachers’ self-efficacy beliefs about teaching mathematics is strongly correlated with their past experiences in mathematics (Voss et al., 2013). Further, there appears to be a reciprocal relationship between teacher self-efficacy and the quality of their instruction (Holzberger et al., 2013). Other influences on these self-efficacy beliefs are level of mathematics anxiety (also correlated with past experiences), experiences in preservice coursework, and experiences in internships engaged in teaching mathematics. Field experiences, especially, give preservice teachers feedback on their performance, an important contributor to self-efficacy beliefs (Gresham, 2009). Higher levels of teachers’ self-efficacy and lower anxiety about teaching mathematics are also related to greater student achievement (Hadley & Dorward, 2011).

Teachers and teacher candidates should reflect on their own experiences with mathematics and beliefs about teaching mathematics if they are to be effective teachers. Since past experiences in school, which may not have represented the most effective teaching methods, have such a strong influence on future teachers, these candidates must understand their own beliefs about teaching mathematics and the sources of those beliefs (Clark et al., 2014).

To begin this exploration, locate the closest statement to your own on the following scale of views:

1. I avoid teaching math at all costs. I was not a good math student myself and I’d hate to teach my students the wrong way.
2. I really dislike math but if you give me a good textbook with lots of practice problems, I can muddle through.
3. Math is just another subject in school. I do (plan to do) the lessons and assign the work. I will spend extra time drilling what I know...

Table of contents

• Cover
• Half-Title Page
• Title Page
• Copyright Page
• Dedication Page
• Table of Contents
• Preface
• Acknowledgments
• 1 Mathematics in Today’s Schools: The Context for Learning Challenges
• 2 Foundations of Mathematics Learning
• 3 Mathematics Assessment
• 4 Effective Mathematics Instruction
• 5 Problem-Solving Instruction
• 6 Instruction and Collaboration for General Education Settings
• 7 Resources to Support Mathematics Instruction and Integration
• Introduction to Content Strands
• Appendix I: Mathematics Activities to Promote Positive Dispositions
• Appendix II: Resources
• Glossary of Select Terms
• Index