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What is The 23+15+18+4 (Word) On Math?. Effects of Increased Levels in Readability on Mathematic Performance for Special Needs Students. Do The Math. 6(4) ÷ 6 +7 Six times four, divided by six, added to seven .
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What is The 23+15+18+4 (Word) On Math? Effects of Increased Levels in Readability on MathematicPerformance for Special Needs Students
Do 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? Λ
Macro-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)
Micro-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-Problem • Freehold 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 grades • 69% did not achieve a proficient grade. • This means approximately 62 special needs students are in danger of Failing HSPA.
Definitions • 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 Review • Lees (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 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 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 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 Question • What 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
Hypothesis • Higher 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.
Methodology • A 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
Sample • 76 High School Special Needs Students Participated in the study.
Ethnic Demographics of Sample (Chart A: Ethnicity of Participant) (Table A: Ethnicity of Sample)
Results – 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.
Analysis 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 Results • The 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 Confounds • Limited Control of Teachers • Time restrictions on students • Uniformity of Instructions • Sample Size is Limited • Only Represents the population of one high School • Teacher Efficacy • Student Efficacy
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 Research • The 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 • 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!
