Algebra readiness for students with learning difficulties in grades 4–8: Support through the study of number

Ketterlin-Geller, Leanne R.; Chard, David J.

doi:10.1080/19404158.2011.563478

Cited by 21 publications

(22 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As in China, the use of algebraic strategy seems to be influenced by the way learners normally solve routine word problems (Jiang & Chua, 2010). This goes to show dominance of algebraic thinking that is routinely used in most mathematical problems albeit unaware (Ketterlin-Geller & Chard, 2011;Milgram, 2007;Vogel, 2008). The results also show that learners performed better in a question with a diagram because diagrams simplify complex situations and illustrate abstract concepts (Kidman, 2002) and make problems easier (Pantziara, Gagatsis, & Elia, 2009).…”

Section: Discussionmentioning

confidence: 99%

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Problem solving also plays significant role in the development of thinking skills (Carson, 2007) and reasoning skills (Ketterlin-Geller & Chard, 2011); promotes high-order thinking (Wu, An, King, Raminez, & Evans, 2009); and facilitates conceptual understanding and meaningful learning (Mabilangan, Limjap, & Belecina, 2011). Conceptual understanding is paramount in algebra learning (Ketterlin-Geller & Chard, 2011). Algebra learning entails integrating and extending prior learned skills (Ketterlin-Geller, Chard, & Fien, 2008); and manipulating symbols, isolating variables and constants and functions, plus decomposing and setting up word problems (Milgram, 2007).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

See 2 more Smart Citations

Mapping a Group of Northern Namibian Grade 12 Learners' Algebraic Non-routine Problem Solving Skills

Mogari

Lupahla

2013

African Journal of Research in Mathematics, Science and Technol

View full text Add to dashboard Cite

This article investigates the algebraic non-routine problem-solving skills of grade 12 learners of a high-achieving school in northern Namibia. The school was selected on the basis of its outstanding results and sound management style. The study followed a descriptive survey design that involved a written test to examine learners' problem-solving skills together with the solution strategies used, and structured learner interviews to get their views about the choice of strategies for solving non-routine problems. The assessment framework of the learners' problem-solving skills was based on the Trends in International Mathematics and Science Study (TIMSS) scales for Polya's problem-solving model. The results showed that learners were more successful in answering the question with a diagrammatic illustration, suggesting that the use of diagrams makes it easier to understand the problems. A significant number of learners' algebraic problemsolving skills function at or below level 2 of TIMSS scale. The algebraic strategy was the most preferred solution strategy and there were learners who encountered difficulties with the language used in the questions.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Theoretical Backgroundmentioning

confidence: 99%

See 1 more Smart Citation

Mapping a Group of Northern Namibian Grade 12 Learners' Algebraic Non-routine Problem Solving Skills

Mogari

Lupahla

2013

African Journal of Research in Mathematics, Science and Technol

View full text Add to dashboard Cite

show abstract

“…Mastering critical algebraic concepts, such as proportional reasoning and fractions, facilitates the learning of more advanced mathematical ideas. Many postsecondary degree programs require mastery of algebra content (Ketterlin-Geller & Chard, 2011).In recent years, nearly all states have established more rigorous mathematics requirements, including successful completion of Algebra 1, for high school graduation (American Diploma Project, 2004). Notably, students must learn mathematical topics, including fractions, prior to algebra instruction to be able to tackle the rigorous demands associated with this content area.Unfortunately, the National Assessment of Educational Progress (National Center for Education Statistics, 2013) indicated that about half of students in 8th and 12th grade lack the conceptual understanding and procedural knowledge that is critical for competence with fractions.…”

mentioning

confidence: 99%

Fraction Interventions for Students Struggling to Learn Mathematics

Shin

Bryant

2015

Remedial and Special Education

114

View full text Add to dashboard Cite

Success in algebra is considered to be the "gatekeeper" to postsecondary education and essential for many careers (National Mathematics Advisory Panel [NMAP], 2008). Mastering critical algebraic concepts, such as proportional reasoning and fractions, facilitates the learning of more advanced mathematical ideas. Many postsecondary degree programs require mastery of algebra content (Ketterlin-Geller & Chard, 2011).In recent years, nearly all states have established more rigorous mathematics requirements, including successful completion of Algebra 1, for high school graduation (American Diploma Project, 2004). Notably, students must learn mathematical topics, including fractions, prior to algebra instruction to be able to tackle the rigorous demands associated with this content area.Unfortunately, the National Assessment of Educational Progress (National Center for Education Statistics, 2013) indicated that about half of students in 8th and 12th grade lack the conceptual understanding and procedural knowledge that is critical for competence with fractions. Among fourth graders with and without disabilities, only about 31% could predict the first fraction in a pattern that was greater than 1, and only about 35% could solve a problem using operations with fractions. Among eighth graders, about 41% could solve a multistep problem involving fractions (National Center for Education Statistics, 2013). By comparison, according to the 2011 Trends in International Mathematics and Science Study, both fourth and eighth graders in East Asia countries outperformed those in the United States on mathematical reasoning, including fractions understanding and knowledge (Mullis, Martin, Foy, & Arora, 2012). Thus, for U.S. students, performance outcomes for fractions, including for students with academic difficulties, are alarming, given the importance of competence with fractions as part of the learning progression for algebra.As one of the critical foundations of algebra, conceptual understanding of fractions is considered an essential building block for successfully advancing in elementary and secondary mathematics. Conceptual understanding is defined as "implicit or explicit understanding of the principles that govern a domain and of the interrelations between units of knowledge in a domain" (pp. 346-347), whereas procedural understanding refers to "the ability to execute action sequences to solve problems" (Rittle-Johnson, Siegler, & Alibali, 2001, p. 346).

show abstract

“…Algebra requires students to further generalize these arithmetic principles to solve abstract problems involving symbolic notation. Building on our previous work defining the foundational components of algebra (Ketterlin-Geller & Chard, 2011), we hypothesize that students’ conceptual understanding of number systems, facility with basic number properties, and understanding and application of operations are the basis of students’ algebra readiness in middle school mathematics.…”

Section: Foundations For Algebramentioning

confidence: 99%

Measuring Middle School Students’ Algebra Readiness

Ketterlin-Geller

Gifford

Perry

2015

Assessment for Effective Intervention

Self Cite

View full text Add to dashboard Cite

Students’ understanding and proficiency with rational number concepts and operations is considered a key foundational skill for future success in algebra. As middle school students work with these concepts, teachers need timely data to determine whether students are making adequate progress. The purpose of this article is to document the content specifications and technical adequacy data of three experimental measures for Grades 6 to 8 that are intended to provide teachers with ongoing information about students’ development of algebra-readiness concepts and skills. Three experimental measures were administered to a total of 575 students in Grades 6 to 8 in two states. Results from a systematic content review indicate that the content assesses key algebra-readiness concepts and skills. Pilot study results suggest that the measures may provide teachers with technically adequate data.

show abstract

Algebra readiness for students with learning difficulties in grades 4–8: Support through the study of number

Cited by 21 publications

References 13 publications

Mapping a Group of Northern Namibian Grade 12 Learners' Algebraic Non-routine Problem Solving Skills

Mapping a Group of Northern Namibian Grade 12 Learners' Algebraic Non-routine Problem Solving Skills

Fraction Interventions for Students Struggling to Learn Mathematics

Measuring Middle School Students’ Algebra Readiness

Contact Info

Product

Resources

About