Targeted Support for Teachers Helps Students With Individualized Education Programs (IEPs) and Underachieving Students Learn Math

by Rebecca K. Shankland, Special Education Teacher Consultant, Forest Hills Central High School

All students can learn math, and the State Improvement Grant to Accomplish Adequate Yearly Progress Project (SIG-AYP Project) is helping math teachers learn how to help their students learn. The SIG-AYP Project focuses on enhancing student performance in mathematics by providing targeted support to teachers of students with individualized education programs (IEPs) and underachieving students who will take the Michigan Educational Assessment Program (MEAP) test with or without accommodations. The project helps teachers learn interventions that will benefit all students, linking special education and general education. Launched in the summer of 2004, the project held summer institutes at the Saginaw Intermediate School District (ISD) and the Wayne Regional Educational Service Agency (RESA). During the five-day workshops, lead facilitators included: Chuck Allan and Wayne Scott, retired mathematics consultants from the Michigan Department of Education (MDE), and Linda Patriarca, a retired Professor from the department of Counseling, Educational Psychology and Special Education at Michigan State University currently working with the special education program at University of Detroit-Mercy. As a facilitator collaborating with Allan, Patriarca, and Scott, we worked with teams of general and special educators from schools that failed to make AYP in the area of mathematics due to the special education subgroup*. The emphasis was on in-depth instruction in one mathematics strand—Number and Operations. The concepts and skills in the Number and Operations strand are foundational and essential for further learning in mathematics. A large percentage of items on the MEAP (at all grade levels) come from this strand.

Since that time, Allan, Patriarca, and Scott have developed three interrelated program components that support their work with school teams: instructional sequences, diagnostic inventories, and instructional planning.

Instructional Sequences

The instructional sequences provide coherence with the Michigan Grade Level Content Expectations (GLCEs). Each of the GLCEs are embedded within and aligned with the instructional sequences for a topic area. Instructional sequences have been developed for the following topic areas:

• Whole numbers
• Decimals
• Fractions

Diagnostic Inventories

The diagnostic inventories are designed to provide information to teachers about students’ thinking about mathematics, including what students know, what students do not know, and what students know that is incorrect and needs to be relearned. The nature of students’ errors tells more than the score on the inventory. By using the results of the diagnostic inventories and the instructional sequences, teachers can identify the content expectations on which each student needs to work. This information can be used to develop IEPs and to plan instruction. Diagnostic inventories have been developed for:

• Place value and numeration
• Whole number addition
• Whole number subtraction
• Whole number multiplication
• Whole number division
• Decimals (basic)
• Fractions (basic)

Instructional Planning

The instructional sequences and diagnostic inventories help teachers determine what to teach, while the instructional planning component helps teachers determine how to teach most effectively. Teachers often lament that curriculum is a mile wide and an inch deep, but the specificity of the grade-level content expectations provides teachers with much needed direction about what will be tested at each grade level. The instructional techniques and strategies are not tied to any commercially published curriculum but are techniques that can be used as a part of daily mathematics instruction.

The SIG-AYP Project also emphasizes developing connections between three types of representations used in mathematics. The three types of representations that students must work with in mathematics are symbolic (numbers), verbal (words), and concrete (both pictorial and manipulative) representations. In the SIG-AYP Project, base 10 blocks, straws, beans, money, and number lines are the manipulatives used to build concrete representations of each concept. For example, when learning place value, students may use straws, base 10 blocks, and money to illustrate “23” in addition to working with the numerals and the words. Later when they work on addition and subtraction, they will use these same manipulatives to build understanding of the process of addition. The instructional components highlight the way that multiple representations can be used to develop deep understanding of the number system and its operations. Students’ ability to move from one representation to another is evidence of students’ understanding of the concepts. The goal of this project is to develop depth of understanding rather than understanding that is a mile wide and an inch deep.

Tremendous Resources for Educators

The Michigan Council of Teachers of Mathematics (MCTM)—www.mictm.org—has posted many of the materials developed by Allan, Patriarca, and Scott on the MCTM Web site. This is a tremendous resource for educators. For a limited time, anyone can download these materials. From the MCTM home page, choose the “Publications” tab. These materials include:

• Updated versions of the mathematics GLCEs.
• Learning sequences.
• MEAP Classifications for the GLCEs. These documents are very useful tools for educators. Each of the GLCEs has been classified as core, extended core, future core, or not assessed at the state level. There are many GLCEs for each grade level, but only the core GLCEs will be tested in fall 2006. Because each core GLCE will be assessed using three items on the MEAP, it is critical that students become familiar with these GLCEs. As we work to fill in the gaps in our students’ understanding, we should focus on the core GLCEs; the task is not so great if we narrow our focus to these core concepts first.
• A file that includes information for each of the GLCEs in the Number and Operation, Algebra, and Measurement strands formatted for printing on 4 x 6 cards. Each card includes one GLCE, the MEAP Classification (core, extended core, future core, or not assessed by the state), MEAP restrictions to be used when writing MEAP test items, and a sample MEAP item for most of the core GLCEs. These cards are very useful in assessing student progress, determining what concepts need to be taught, and establishing a sequence of instruction.
• Alignment of various commercial textbooks with the GLCEs including Connected Mathematics, Investigations by Scott Foresman and Everyday Mathematics, Math Trailblazers published by McMillan McGraw Hill and Harcourt 2004.
• Addition fact strategies—A PowerPoint presentation of addition fact strategies.
• Multiplication fact strategies—A PowerPoint presentation of multiplication fact strategies.

A Web site that will have links to all these resources will soon be available.

The work of the SIG-AYP Project continues in 2006 with cohorts in several locations in Michigan. At Wayne RESA, two groups continue to work with the Project facilitators to improve mathematics instruction for their students; these groups include a number of dedicated educators from the original July 2004 cohort and others from a second cohort, which began work during the summer of 2005. Kelly Green, Special Education Consultant for Wayne RESA, coordinates the work of this group in collaboration with Project facilitators. In addition to building their skills in teaching mathematics, the educators in this group have previewed materials and provided invaluable feedback to Allan, Patriarca, and Scott during the process of developing materials for the Project. New cohorts have recently begun work in Genesee ISD (coordinated by LuAnn Murray), Macomb ISD (coordinated by Debbie Ferry), Clare-Gladwin RESD (coordinated by June Marsten), and Kent ISD (coordinated by Laurie VanderPloeg). In addition, Barbara Meier and Linda Fawcett have joined the project as facilitators. Barb is a doctoral student at Michigan State University and former special education teacher. Linda is a former teacher and most recently was the Director of the Mathematics and Science Center at Huron ISD.

Rebecca K. Shankland is a Special Education Teacher Consultant at Forest Hills Central High School in Grand Rapids, MI. She is also a doctoral student in literacy and special education at Michigan State University. Research interests include implementation of effective strategies for literacy and mathematics in the schools.

* To make AYP, the district must have at least 95% of its enrolled students participate in state assessment in both English language arts and in mathematics. School districts must make AYP for the district as a whole and for each student group of 30 or more students. The student groups measured for AYP are racial/ethnic groups (American Indian, Asian American, Hispanic, White, and Multicultural), students with disabilities, limited English proficient, and economically disadvantaged students. For more information about AYP, visit www.michigan.gov/mde.

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