What is The 23+15+18+4 What is The 23+15+18+4 (Word) On Math?(Word) On Math?

Effects of Increased Levels in Readability on Mathematic

Performance for Special Needs Students

Do The MathDo The Math

6(4) ÷ 6 +7 Six times four, divided by six, added to

seven.The product of six and four divided by

six then increased by seven is equal to what value?

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Macro-ProblemsMacro-Problems

Conflicting Legislation:– IDEA - classified students do not need to

pass the HSPA as a graduation requirement

– NCLB- all student scores for statewide mandated test count toward a school, or school district’s rating

(NJDOE, 2006)(NJDOE, 2006)

Micro-ProblemsMicro-Problems

Freehold High School special needs students, as a group, continually under perform on mathematics HSPA / HSPA-like tests.

A large portion of these test rely heavily on a student’s ability to read the language and comprehend the task indicated.

Data to Support Micro-ProblemData to Support Micro-ProblemFreehold 9th and 10th grade students are

administered a Pre HSPA Assessment 90 special needs students took the PHA test. 90 Special Needs students: approximately

13% of the student population for both grades69% did not achieve a proficient grade.This means approximately 62 special needs

students are in danger of Failing HSPA.

DefinitionsDefinitions Readability Level:

– “…comprehensibility of the written text” (Hewitt and Homan 2004). .

***Higher readability levels indicate higher degree of difficulty in reading.

Translation:– Rewriting a mathematical problem from a ‘word’

representation to the numeric, symbolic, operational forms.

Mistranslation: – The translation from word to symbol was represented

incorrectly.

Literature ReviewLiterature ReviewLees (1974)

– Math vocabulary is difficult because of its specificity

– a word may have multiple meanings,

– it is not a part of a person’s general vocabulary

– or the vocabulary may generally relate a process

Literature ReviewLiterature Review Brian Bottge (2001)

– Mathematics must be meaningful to the student if they are to be successful

– How can Mathematics be meaningful if the student does not comprehend the language of Mathematics?

Crowley, Thomas, Tall (1994)– Students frequently make mistakes because they do not

view symbols as representing both a process and an answer (defined as a procept) but rather as one or the other.

– Students are rigid in their thinking and therefore more prone to mistakes.

Literature ReviewLiterature Review Helwig, Rozek-Tedesko, Heath and Almond (1996)

– Standardized tests often do not test a student’s mathematical ability, rather they test a student’s ability to read and comprehend.

– Students frequently gave incorrect answers because they misread a question or did not understand the directions.

– They indicate that slow processing of word meanings result in less capacity for other cognitive processes, making comprehension difficult.

Literature ReviewLiterature Review Noam Chomsky

– language may provide an opportunity to deepen thought and therefore generalize that thought to other

areas (Otero 1988, 2004) Benjamin Lee Worf

– Postulates that the language of different cultures has defined those cultures perception of reality. (Carroll, 1966)

Kelly and Mousley. (2001) – Due to the differences in perception caused by language

abilities deaf students have difficulty applying their strengths in basic computation to real world problems.

Research QuestionResearch QuestionWhat effect, if any, does readability have on

specific types of problems which are foundational to higher levels of mathematics?– Basic operations– Operations with integers– Solving single step equations

HypothesisHypothesisHigher levels of introduced readability will

negatively impact classified students’ test performance in mathematics.

Null hypothesis, comprehension of higher levels of language will not impact classified students’ test performance in mathematics

Any outcome is valuable in terms of its importance to understanding the instructional needs of classified students in math classes.

MethodologyMethodologyA quantitative approach

The study utilized a pretest, mid-test, and post test design by testing students in three separate phases.

All three tests were designed to explore the same level of mathematical difficulty but increase readability

SampleSample

76 High School Special Needs Students Participated in the study.

Ethnic Demographics of Ethnic Demographics of SampleSample

Ethnicity Number of Students

Percent of Sample

Caucasian 40 52.6%

African American

9 11.8%

Hispanic / Latino

22 28.9%

Other 5 6.7%

Total (N) 76 100%

(Chart A: Ethnicity of Participant) (Table A: Ethnicity of Sample)

Other

Hispanic / Latino

African American

Caucation

Ethnicity

Gender Demographics of SampleGender Demographics of Sample

Placement DemographicsPlacement Demographics Frequency Percent

INCLASS SUPPORT RESOURCE

43 56.6

RESOURCE 33 43.4

Total 76 100.0

Results Results

Special Education Teacher

Phase One Mean Test Score

Phase Two Mean Test Score

Phase Three Mean Test Score

Teacher 1 76.00 54.04 32.07

Teacher 2 66.48 73.20 50.33

Teacher 3 80.67 84.55 65.91

Teacher 4 80.56 73.75 67.78

Combined Mean Score

74.46 67.52 47.19

Results – Question by QuestionResults – Question by Question Correlations were found between nearly every

problem in the Phase I test and the corresponding Phase II problem.

For example: – Correlations indicate that students who answered a

problem correctly in Phase I are likely to answer correctly in Phase II.

These findings were all statistically significant at p < .05 with some being statistically significant at p < .001

Between corresponding questions in Phase II and Phase III there were nearly no statistically significant (p > .05) findings.– Frequency tests revealed this was caused by the increasing types of

mistakes students made when readability was increased.

Results Results

Results Results

Results Results

Analysis of ResultsAnalysis of Results Due to the design of the research causality can not be

explained by using tests such as Linear Regressions However, The only newly introduced variable was the

readability level of each successive phase.

Increasing readability levels coupled with higher level problems, multi-step problems, or abstract concepts– Missing, incorrect, and mistranslated responses become more

frequent to the point of surpassing correct responses

This seems to indicate that when grade appropriate readability levels are introduced with grade appropriate mathematical levels special needs students are very likely to under perform.

Analysis of ResultsAnalysis of ResultsThe extra cognitive processes involved in

translating an implicit direction to a set of actions may be cause for confusion and ultimately incorrect responses.

Special needs students at Freehold High School

may fail to recognize that the vocabulary indicates a process to derive an answer and not just a concept such as a type of answer.

This is in keeping with the findings of Crowley, Thomas, Tall (1994) – students mistake procepts

Limitations and Other ConfoundsLimitations and Other Confounds

Limited Control of Teachers – Time restrictions on students– Uniformity of Instructions

Sample Size is Limited– Only Represents the population of one high

SchoolTeacher EfficacyStudent Efficacy

Recommendations Recommendations Reading and writing of mathematics must become

an integrated part of Mathematics instruction. (Johanning, 2000).

The proper writing and speaking of mathematics must be modeled by teachers in all subject areas.

Professional Development programs such as ‘Math Across the Curriculum’ need to be more comprehensive in terms of the mathematic content covered.

Graphic organizers for vocabulary should be used in mathematics classes (Monroe, 1989).

Areas for Future ResearchAreas for Future ResearchThe use of commas in word problems and how it

impacts student translation, comprehension, and correct completion of mathematical problems.

Student acquisition of mathematical knowledge taught as it is impacted by teacher oral cadence may provide some understanding into the learning difficulties of special needs students.

The language level of teacher word choice during lectures as it impacts students’ acquisition of mathematics content being taught

This study should be conducted with a much larger sample size which is representative of multiple schools and age groups.

Acknowledgements Acknowledgements Freehold Regional High School District for granting

permission The teachers and students who participated The College of New Jersey and Dr. Seaton for the

challenges and their associated profits. Washington Township School District for allowing me

an opportunity to expand my professional horizons – I look forward to September.

Most importantly, My Wife without whom none of this would be possible.

– Now I can finish the house, and act like a husband again!

Questions, comments, Questions, comments, suggestions will now be gladly suggestions will now be gladly taken.taken.