University of Oregon

University of Oregon Team

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Accessible Algebra

Research Site:       University of Oregon, Eugene, Oregon
Researchers:         Patricia Almond and Mark Horney
Study Title            Oregon Accessible Middle School Algebra—2011 Spring Study

Study Description

This study investigates middle school algebra instruction for students in grades 6, 7, and 8 through a mixed methods case study exploring supported electronic text and students with learning disabilities (LD). The study seeks to identify and analyze key topics and lessons from Algebra 1 courses, in the light of the differing needs of students with learning disabilities.

We are seeking answers to the following questions regarding: 

(a) Could students use graphic organizers containing critical information from prior math lessons for use in current lessons to lower cognitive load requirements?  

(b) Could students' prior knowledge be activated by an image showing a concrete example of the concepts presented in a lesson to help the student better understand the mathematics?  

(c) What explanatory resources could assist in learning mathematics concepts, providing concrete descriptions and examples, e.g., video or animation to explain how a mathematical concept or process relates to students' personal experience?

(d) What about supplemental instruction? For example, could a short instructional video about fractions, with examples refresh student understanding of fractions so s/he could comprehend the Algebra, improve performance for students whose understanding of fractions is weak.

This initial exploratory study employs mixed research methods to gain an in-depth understanding of challenges and successes that students with learning disabilities (LD) encounter in learning algebraic concepts in middle school. During spring 2011, middle school students with LD were interviewed. The ultimate goal of the exploratory study is theory generation related to supported electronic text, students with LD, and algebra. Students were be observed both during their general education mathematics course and during a supplemental course designed to support their learning in mathematics and algebraic concepts. Observations began in February 2011 and continued till the end of the school year in June 2011.

Methods

This case study explores algebra and pre-algebra instruction with students in grades 6, 7, and 8 with a focus on the unique challenges students with LD encounter in learning algebra. The study includes classroom observations, teacher and student interviews, cognitive interviews, document analysis including textbooks, presentations, handouts, quizzes, assessments, analysis of student IEPs, and analysis of student achievement in reading and mathematics.

For the initial school investigation, participating teachers conducted typical classroom instruction in existing classes between February and June, 2011. In addition, teachers participated in the exploratory study in the following ways: (a) allowed study observers to observe classroom instruction, (b) provided copies of classroom handouts used during an observation period, (c) engaged in a brief orientation or clarification—3-5 minutes before or after the instructional period as time permits, and (d) completed interviews about their own observations.

Data were gathered from six sources: (a) course descriptions, (b) classroom observations, (c) teacher interviews, (d) student interviews, (e) primary documents, and (f) performance data from district and state measures of mathematics and reading.

Teacher interviews focused on (a) special education student performance on the statewide math assessment, (b) the read aloud accommodation for students in support classes, (c) strategies students use to solve word problems, and (d) coordination between the regular and support math classes.

Students provided think aloud comments about how they solved math problems and shared their views on having mathematics problems read aloud.

Table 1: Student Interview Protocol

Condition

Read Item: A Silently, B Aloud, C Teacher Aloud

Directions

Read both the question and the answer choices. After (you/I) finish reading, I will ask you some questions.

Questions

I am going to ask you some questions about the problem and I want you to tell me what you are thinking. You may reread the question if you want to.


Table 2: Sample Problems

2. Fencing is sold for id="mce_marker".50 per foot at the garden store. Shawn needs 24 feet of fence for his new puppy’s yard. How much will the fence cost?

  1. A.$9.00
  2. B.$22.50
  3. C.$25.50
  4. D.$36.00

12. Two packages of cookies cost $5.90.
How much do 6 packages cost?

  1. A.$35.40
  2. B.id="mce_marker"7.70
  3. C.id="mce_marker"1.90
  4. $2.95

In addition to observations and interviews, statewide assessment scores and scores from a progress monitoring system using curriculum based measures in mathematics and reading were obtained.

Sample

For spring 2011 data collection, both regular class sessions (n = 12) and support class sessions were observed (n = 14). Seven teachers participated in interviews focused on (a) special education student performance on the statewide math assessment, (b) the read aloud accommodation for students in support classes, (c) strategies students use to solve word problems, and (d) coordination between the regular and support math classes.

Ten students participated in interviews and responded to three math word problems. Students provided think aloud comments as they solved the problems and shared their views on having mathematics problems read aloud.

In addition to observations and interviews, statewide assessment scores and scores from a progress monitoring system using curriculum based measures in mathematics and reading were obtained. All data are being analyzed to consider ways in which supported electronic text can be used to support students with LD.

Findings

The first phase of the case study was completed in June 2011. Our purpose was to understand how students with learning disabilities and low performing students use text and are challenged by text and mathematical expressions when learning algebra. Components of algebraic content are targeted in the mathematics standards for the three middle school grades (6, 7, and 8) as follows:

  • Grade 6: Foundations of Algebra, order of operations, variables, & solutions to basic Algebraic equations
  • Grade 7: Understanding of operations on all rational numbers & greater fluency with linear equations
  • Grade 8: Refine understanding of Algebra, slope of a line, more on linear equations & functions, & solutions to systems of linear equations.

A review of mathematics scores on the statewide assessment for 2009-10 shows that a greater proportion of students with disabilities in the middle school obtain below proficient scores than other students in the district and the state. In addition, many of the below proficient scores were in the score range of “nearly meets” meaning the students were close to the “meets” or proficient score.

Table 3: Proficiency Scores

Gr. 6, 7, 8

School

District

State

Proficiency Level

Count

Percent

Count

Percent

Count

Percent

Exceeds

        6

        8.0

        71

     10.5

    1,475

       7.6

Meets

      20

      26.7

       233

     34.5

    6,029

     31.2

Nearly Meets

      33

      44.0

       192

     28.4

    4,651

     24.1

Low

      15

      20.0

       155

     22.9

    6,241

     32.3

Very Low

        1

        1.3

        25

       3.7

       941

       4.9

 Total

      75

    100.0

       676

     99.1

  19,358

     41.1

During observations of students taking the statewide mathematics assessment online for 2011, we learned that all students in the additional mathematics support classes received the “read aloud” accommodation on the state assessment. We wanted to know whether read aloud was an effective support. A second observation made during classroom observation sessions raised a question about student’s approach to mathematics word problems. Specifically, do students have a strategy for solving math word problems that involves a systematic process? For example, do students ask themselves questions like those below?

  • What is being asked?
  • What information is provided?
  • What do I need to do to solve the problem?
  • Did I show my work and check my answer?

Audio presentation is one aspect of supported electronic text. During spring 2011 the Oregon study observations revealed that reading mathematics text aloud was provided to students in support classes during the statewide mathematics assessments. As a follow-up, brief round of cognitive interviews was conducted with ten special education students enrolled in their general grade-level math class plus a supplemental math course to better understand student use and perceptions of “read aloud” as a support. In addition, the interview considered the process student used in solving word problems.

A set of three math word problems for each grade was selected from released Oregon items in Mathematics (2010-2013). Problems were selected from one grade below the students’ actual grade of enrollment (grade 5 sample test for 6th grade students, grade 6 sample test for 7th grade students, and so on). There were three conditions for reading the math word problems: a) student reads stem and response options silently, b) student reads stem and options aloud, and c) the interviewer reads the stem and options aloud. After the student selected their choice for the correct response, the interviewer asked a series of questions about the problem and prompted to “tell me what you are thinking.”

The students interviewed, i.e., students with IEPs and enrolled in supplemental math classes, preferred read aloud for the items in the interview. Four students indicated that they preferred to read aloud themselves and three indicated the interviewer read aloud. When asked if they found it helpful to have math items read aloud by the teacher for the state assessment six students indicated “sometimes” and two indicated “most/all of the time.” Teachers were also interviewed about the read aloud accommodation.

I kinda like you reading it and me reading. If I read it in my head it doesn’t really make sense but if someone reads it out loud it does.

They all believed that it helped the students. When asked in what way did read aloud help, teachers indicated that read aloud acted as a pacing device, that hearing the item read aloud improved comprehension, one teacher also asked students to explain how they determined the correct answer, although she did not give feedback during the accountability testing. 

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