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Papers by Tricia Strickland

Learning disabilities, 2013

The current study focuses on the effects of incorporating multiple visual representations on stud... more The current study focuses on the effects of incorporating multiple visual representations on students conceptual understanding of quadratic expressions embedded within area word problems and students procedural fluency of transforming quadratic expressions in standard form to factored-form and vice versa. The intervention included the concrete-representation-abstract integration (CRA I) strategy and the use of a graphic organizer called the Box Method to support student performance when transitioning to using abstract notation only. A multiple-probe design across two groups that included five participants was utilized. The participants were five high school students identified as having mathematics difficulties, including three students with an identified learning disability. Results indicated that participants significantly improved their algebraic accuracy and maintained their skills over time. Further, participants reported the intervention was worth their time and they would recommend it to others.

The current study examined the effect of an instructional package on the algebra performance of s... more The current study examined the effect of an instructional package on the algebra performance of secondary students with mathematics learning disabilities or difficulties (MD) when applied to the grade-appropriate algebra content of quadratic expressions.

Intervention In School And Clinic, Sep 1, 2010

To improve student success in mathematics, the use of research-based interventions is necessary t... more To improve student success in mathematics, the use of research-based interventions is necessary to help secondary students with learning disabilities (LD) access the algebra curriculum. The authors provide an overview of the following research-based approaches: explicit instruction, graduated instructional sequence, technology, and graphic organizers. For each approach, a summary of the research is provided along with suggestions for how the approach can be used by classroom teachers to support algebra instruction.

Learning Disability Quarterly, May 20, 2021

Single-case research design is a useful methodology for evaluating the presence of a functional r... more Single-case research design is a useful methodology for evaluating the presence of a functional relation between an intervention and the mathematical performance of students with a learning disability. However, a functional relation cannot be established with threats to internal validity of the design. External validity is impacted if researchers do not clearly describe their methods so that others may replicate them. Therefore, single-case researchers must maximize the internal and external validity of their investigations. We provide a commentary on investigations published in Learning Disability Quarterly that implemented a mathematics intervention for students with a mathematics learning disability. We will highlight specific features of single-case designs within the review and provide recommendations for the field.

Teaching Exceptional Children, Nov 1, 2016

and teacher educators-take a minute and take a gander. Browse by topic, keyword, or format to fin... more and teacher educators-take a minute and take a gander. Browse by topic, keyword, or format to find the latest evidence-based practices and strategies, reference and training materials, and more. Webinars n Books n Quick-reference guides Peruse the table of contents from a book, post product reviews, or check out the featured author, product, and eBook! New content is added every week, so don't miss out-stop by today! www.pubs.cec.sped.org

Focus on Exceptional Children, 2017

Both international and national assessments indicate that secondary students in the United States... more Both international and national assessments indicate that secondary students in the United States experience difficulty in learning mathematics and score below many of their international counterparts. In particular, data from two international educational assessments, the Trends in International Mathematics and Science Study (Gonzales et al., 2004) and the Program for International Student Assessment (Baldi, Jin, Skemer, Green, & Herget, 2007), show that students in the United States are performing below the level of many other industrialized countries in mathematics. Policy makers, educators, and parents use outcomes from TIMSS and PISA to determine the quality of the U.S. education system and to predict the success of the United States in the global economy (Bybee & Stage, 2005). The data from these assessments suggest that the U.S. education system is not providing students the conceptual knowledge and real-world problem-solving skills necessary to compete in the world market. The mathematics performance of secondary students within the United States raises additional concerns. For example, the National Assessment of Educational Progress (NAEP) showed that 30% of students in eighth grade scored below a basic achievement level, with "basic" defined as partial mastery of knowledge and skills. This result means that more than one quarter of the eighth-grade students did not demonstrate even partial mastery of the mathematics skills expected of them. Additionally, only 31 % of eighth graders scored at or above the "proficient" level, defined as solid academic performance and competency over challenging subject matter. Information on 12th-grade students is even more alarming, with 36% of 12th-graders scoring below the basic level and only 24% at or above the proficient level (Lee, Grigg, & Dion, 2007). These results suggest that secondary students are not attaining an acceptable level of mastery of the mathematics curriculum. Mathematics achievement of secondary students with disabilities deserves even closer attention. The Nation's Report Card indicated that, although some improvements in mathematics achievement have been documented for students with disabilities from 1996 to 2007, little progress has been made to close the gap between the achievement scores of

Focus on Exceptional Children, 2017

Ohio Journal of School Mathematics, Jan 9, 2018

In this article, the authors share research on the use of mnemonic devices in mathematics instruc... more In this article, the authors share research on the use of mnemonic devices in mathematics instruction. In particular, they address the following questions: What are mnemonic devices? What are their benefits? What should teachers be cautious about? How should mnemonic devices be used?

Journal of Nonprofit Education and Leadership, 2013

The current study focuses on the effects of incorporating multiple visual representations on stud... more The current study focuses on the effects of incorporating multiple visual representations on students conceptual understanding of quadratic expressions embedded within area word problems and students procedural fluency of transforming quadratic expressions in standard form to factored-form and vice versa. The intervention included the concrete-representation-abstract integration (CRA I) strategy and the use of a graphic organizer called the Box Method to support student performance when transitioning to using abstract notation only. A multiple-probe design across two groups that included five participants was utilized. The participants were five high school students identified as having mathematics difficulties, including three students with an identified learning disability. Results indicated that participants significantly improved their algebraic accuracy and maintained their skills over time. Further, participants reported the intervention was worth their time and they would recommend it to others.

Learning Disability Quarterly, 2021

Single-case research design is a useful methodology for evaluating the presence a functional rela... more Single-case research design is a useful methodology for evaluating the presence a functional relation between an intervention and the mathematical performance of students with a learning disability. However, a functional relation cannot be established with threats to internal validity of the design. External validity is impacted if researchers do not clearly describe their methods so that others may replicate them. Therefore, single-case researchers must maximize the internal and external validity of their investigations. We provide a commentary on investigations published in Learning Disability Quarterly that implemented a mathematics intervention for students with a mathematics learning disability. We will highlight specific features of single-case designs within the review and provide recommendations for the field.

Title of Document: THE EFFECTS OF BLENDED INSTRUCTION AND VISUAL REPRESENTATIONS ON AREA PROBLEMS... more Title of Document: THE EFFECTS OF BLENDED INSTRUCTION AND VISUAL REPRESENTATIONS ON AREA PROBLEMS INVOLVING QUADRATIC EXPRESSIONS FOR SECONDARY STUDENTS WITH MATHEMATICS LEARNING DIFFICULTIES Tricia Kay Strickland, PhD, 2011 Directed By: Associate Professor Paula Maccini Department of Special Education University of Maryland, College Park The current study examined the effect of an instructional package on the algebra performance of secondary students with mathematics learning disabilities or difficulties (MD) when applied to the grade-appropriate algebra content of quadratic expressions. The instructional package included a blend of research-based instructional practices for secondary students with LD (i.e., concrete-representation-abstract instruction, graphic organizers, and components of explicit instruction) and the process standards recommended by the National Council of Teachers of Mathematics process standards (i.e., problem solving, reasoning and proof, communication, conne...

This case study analyzed the impact of a concrete manipulative program on the understanding of qu... more This case study analyzed the impact of a concrete manipulative program on the understanding of quadratic expressions for a high school student with a learning disability. The manipulatives were utilized as part of the Concrete-Representational- Abstract Integration (CRA-I) intervention in which participants engaged in tasks requiring them to multiply linear expressions and factor quadratic expressions embedded within contextualized area problems. The case study focused on a representative participant, Marcia, who demonstrated significant gains from pre- to post-intervention assessments. The qualitative analysis provided descriptive data which offered insight into the reasons for these gains. Results indicated that the manipulatives supported metacognition through strategic planning and self- regulation.

Intervention in School and Clinic, 2021

The Common Core State Standards in Mathematics (CCSSM) were released more than 10 years ago. This... more The Common Core State Standards in Mathematics (CCSSM) were released more than 10 years ago. This set of standards outlines the mathematics that all students should know and be able to do to prepare them for post-secondary education and employment. Students with learning disabilities (LD) continue to underperform in relation to their peers without disabilities in secondary mathematics. As high school Algebra I is a required course for the majority of students, research-based instructional practices should be utilized to support students with LD in Algebra I. This article summarizes recent research on instructional practices for teaching algebra content that aligns to the CCSSM. Specifically, three types of instructional practices have been found to promote progress in the high school algebra content: (a) concrete-representational-abstract integration, (b) virtual manipulative instruction, and (c) gestures and diagrams.

TEACHING Exceptional Children

The current study examined the effect of an instructional package on the algebra performance of s... more The current study examined the effect of an instructional package on the algebra performance of secondary students with mathematics learning disabilities or difficulties (MD) when applied to the grade-appropriate algebra content of quadratic expressions.

Remedial and Special Education, 2013

We examined the effects of the Concrete–Representational– Integration strategy on the ability of ... more We examined the effects of the Concrete–Representational– Integration strategy on the ability of secondary students with learning disabilities to multiply linear algebraic expressions embedded within contextualized area problems. A multiple-probe design across three participants was used. Results indicated that the integration of the concrete manipulatives, sketches of manipulatives, and abstract notation with the support of a graphic organizer (i.e., expansion box) was an effective strategy to improve students’ conceptual understanding and procedural fluency of multiplying two linear expressions. Furthermore, participants generalized the algebraic material to novel problem tasks and maintained performance up to 6 weeks following intervention.

To improve student success in mathematics, the use of research-based interventions is necessary t... more To improve student success in mathematics, the use of research-based interventions is necessary to help secondary students with learning disabilities (LD) access the algebra curriculum. The authors provide an overview of the following research-based approaches: explicit instruction, graduated instructional sequence, technology, and graphic organizers. For each approach, a summary of the research is provided along with suggestions for how the approach can be used by classroom teachers to support algebra instruction.

Intervention in School and Clinic, 2010

To improve student success in mathematics, the use of research-based interventions is necessary t... more To improve student success in mathematics, the use of research-based interventions is necessary to help secondary students with learning disabilities (LD) access the algebra curriculum. The authors provide an overview of the following research-based approaches: explicit instruction, graduated instructional sequence, technology, and graphic organizers. For each approach, a summary of the research is provided along with suggestions for how the approach can be used by classroom teachers to support algebra instruction.

Learning disabilities, 2013

The current study focuses on the effects of incorporating multiple visual representations on stud... more The current study focuses on the effects of incorporating multiple visual representations on students conceptual understanding of quadratic expressions embedded within area word problems and students procedural fluency of transforming quadratic expressions in standard form to factored-form and vice versa. The intervention included the concrete-representation-abstract integration (CRA I) strategy and the use of a graphic organizer called the Box Method to support student performance when transitioning to using abstract notation only. A multiple-probe design across two groups that included five participants was utilized. The participants were five high school students identified as having mathematics difficulties, including three students with an identified learning disability. Results indicated that participants significantly improved their algebraic accuracy and maintained their skills over time. Further, participants reported the intervention was worth their time and they would recommend it to others.

The current study examined the effect of an instructional package on the algebra performance of s... more The current study examined the effect of an instructional package on the algebra performance of secondary students with mathematics learning disabilities or difficulties (MD) when applied to the grade-appropriate algebra content of quadratic expressions.

Intervention In School And Clinic, Sep 1, 2010

To improve student success in mathematics, the use of research-based interventions is necessary t... more To improve student success in mathematics, the use of research-based interventions is necessary to help secondary students with learning disabilities (LD) access the algebra curriculum. The authors provide an overview of the following research-based approaches: explicit instruction, graduated instructional sequence, technology, and graphic organizers. For each approach, a summary of the research is provided along with suggestions for how the approach can be used by classroom teachers to support algebra instruction.

Learning Disability Quarterly, May 20, 2021

Single-case research design is a useful methodology for evaluating the presence of a functional r... more Single-case research design is a useful methodology for evaluating the presence of a functional relation between an intervention and the mathematical performance of students with a learning disability. However, a functional relation cannot be established with threats to internal validity of the design. External validity is impacted if researchers do not clearly describe their methods so that others may replicate them. Therefore, single-case researchers must maximize the internal and external validity of their investigations. We provide a commentary on investigations published in Learning Disability Quarterly that implemented a mathematics intervention for students with a mathematics learning disability. We will highlight specific features of single-case designs within the review and provide recommendations for the field.

Teaching Exceptional Children, Nov 1, 2016

and teacher educators-take a minute and take a gander. Browse by topic, keyword, or format to fin... more and teacher educators-take a minute and take a gander. Browse by topic, keyword, or format to find the latest evidence-based practices and strategies, reference and training materials, and more. Webinars n Books n Quick-reference guides Peruse the table of contents from a book, post product reviews, or check out the featured author, product, and eBook! New content is added every week, so don't miss out-stop by today! www.pubs.cec.sped.org

Focus on Exceptional Children, 2017

Both international and national assessments indicate that secondary students in the United States... more Both international and national assessments indicate that secondary students in the United States experience difficulty in learning mathematics and score below many of their international counterparts. In particular, data from two international educational assessments, the Trends in International Mathematics and Science Study (Gonzales et al., 2004) and the Program for International Student Assessment (Baldi, Jin, Skemer, Green, & Herget, 2007), show that students in the United States are performing below the level of many other industrialized countries in mathematics. Policy makers, educators, and parents use outcomes from TIMSS and PISA to determine the quality of the U.S. education system and to predict the success of the United States in the global economy (Bybee & Stage, 2005). The data from these assessments suggest that the U.S. education system is not providing students the conceptual knowledge and real-world problem-solving skills necessary to compete in the world market. The mathematics performance of secondary students within the United States raises additional concerns. For example, the National Assessment of Educational Progress (NAEP) showed that 30% of students in eighth grade scored below a basic achievement level, with "basic" defined as partial mastery of knowledge and skills. This result means that more than one quarter of the eighth-grade students did not demonstrate even partial mastery of the mathematics skills expected of them. Additionally, only 31 % of eighth graders scored at or above the "proficient" level, defined as solid academic performance and competency over challenging subject matter. Information on 12th-grade students is even more alarming, with 36% of 12th-graders scoring below the basic level and only 24% at or above the proficient level (Lee, Grigg, & Dion, 2007). These results suggest that secondary students are not attaining an acceptable level of mastery of the mathematics curriculum. Mathematics achievement of secondary students with disabilities deserves even closer attention. The Nation's Report Card indicated that, although some improvements in mathematics achievement have been documented for students with disabilities from 1996 to 2007, little progress has been made to close the gap between the achievement scores of

Focus on Exceptional Children, 2017

Ohio Journal of School Mathematics, Jan 9, 2018

In this article, the authors share research on the use of mnemonic devices in mathematics instruc... more In this article, the authors share research on the use of mnemonic devices in mathematics instruction. In particular, they address the following questions: What are mnemonic devices? What are their benefits? What should teachers be cautious about? How should mnemonic devices be used?

Journal of Nonprofit Education and Leadership, 2013

The current study focuses on the effects of incorporating multiple visual representations on stud... more The current study focuses on the effects of incorporating multiple visual representations on students conceptual understanding of quadratic expressions embedded within area word problems and students procedural fluency of transforming quadratic expressions in standard form to factored-form and vice versa. The intervention included the concrete-representation-abstract integration (CRA I) strategy and the use of a graphic organizer called the Box Method to support student performance when transitioning to using abstract notation only. A multiple-probe design across two groups that included five participants was utilized. The participants were five high school students identified as having mathematics difficulties, including three students with an identified learning disability. Results indicated that participants significantly improved their algebraic accuracy and maintained their skills over time. Further, participants reported the intervention was worth their time and they would recommend it to others.

Learning Disability Quarterly, 2021

Single-case research design is a useful methodology for evaluating the presence a functional rela... more Single-case research design is a useful methodology for evaluating the presence a functional relation between an intervention and the mathematical performance of students with a learning disability. However, a functional relation cannot be established with threats to internal validity of the design. External validity is impacted if researchers do not clearly describe their methods so that others may replicate them. Therefore, single-case researchers must maximize the internal and external validity of their investigations. We provide a commentary on investigations published in Learning Disability Quarterly that implemented a mathematics intervention for students with a mathematics learning disability. We will highlight specific features of single-case designs within the review and provide recommendations for the field.

Title of Document: THE EFFECTS OF BLENDED INSTRUCTION AND VISUAL REPRESENTATIONS ON AREA PROBLEMS... more Title of Document: THE EFFECTS OF BLENDED INSTRUCTION AND VISUAL REPRESENTATIONS ON AREA PROBLEMS INVOLVING QUADRATIC EXPRESSIONS FOR SECONDARY STUDENTS WITH MATHEMATICS LEARNING DIFFICULTIES Tricia Kay Strickland, PhD, 2011 Directed By: Associate Professor Paula Maccini Department of Special Education University of Maryland, College Park The current study examined the effect of an instructional package on the algebra performance of secondary students with mathematics learning disabilities or difficulties (MD) when applied to the grade-appropriate algebra content of quadratic expressions. The instructional package included a blend of research-based instructional practices for secondary students with LD (i.e., concrete-representation-abstract instruction, graphic organizers, and components of explicit instruction) and the process standards recommended by the National Council of Teachers of Mathematics process standards (i.e., problem solving, reasoning and proof, communication, conne...

This case study analyzed the impact of a concrete manipulative program on the understanding of qu... more This case study analyzed the impact of a concrete manipulative program on the understanding of quadratic expressions for a high school student with a learning disability. The manipulatives were utilized as part of the Concrete-Representational- Abstract Integration (CRA-I) intervention in which participants engaged in tasks requiring them to multiply linear expressions and factor quadratic expressions embedded within contextualized area problems. The case study focused on a representative participant, Marcia, who demonstrated significant gains from pre- to post-intervention assessments. The qualitative analysis provided descriptive data which offered insight into the reasons for these gains. Results indicated that the manipulatives supported metacognition through strategic planning and self- regulation.

Intervention in School and Clinic, 2021

The Common Core State Standards in Mathematics (CCSSM) were released more than 10 years ago. This... more The Common Core State Standards in Mathematics (CCSSM) were released more than 10 years ago. This set of standards outlines the mathematics that all students should know and be able to do to prepare them for post-secondary education and employment. Students with learning disabilities (LD) continue to underperform in relation to their peers without disabilities in secondary mathematics. As high school Algebra I is a required course for the majority of students, research-based instructional practices should be utilized to support students with LD in Algebra I. This article summarizes recent research on instructional practices for teaching algebra content that aligns to the CCSSM. Specifically, three types of instructional practices have been found to promote progress in the high school algebra content: (a) concrete-representational-abstract integration, (b) virtual manipulative instruction, and (c) gestures and diagrams.

TEACHING Exceptional Children

The current study examined the effect of an instructional package on the algebra performance of s... more The current study examined the effect of an instructional package on the algebra performance of secondary students with mathematics learning disabilities or difficulties (MD) when applied to the grade-appropriate algebra content of quadratic expressions.

Remedial and Special Education, 2013

We examined the effects of the Concrete–Representational– Integration strategy on the ability of ... more We examined the effects of the Concrete–Representational– Integration strategy on the ability of secondary students with learning disabilities to multiply linear algebraic expressions embedded within contextualized area problems. A multiple-probe design across three participants was used. Results indicated that the integration of the concrete manipulatives, sketches of manipulatives, and abstract notation with the support of a graphic organizer (i.e., expansion box) was an effective strategy to improve students’ conceptual understanding and procedural fluency of multiplying two linear expressions. Furthermore, participants generalized the algebraic material to novel problem tasks and maintained performance up to 6 weeks following intervention.

To improve student success in mathematics, the use of research-based interventions is necessary t... more To improve student success in mathematics, the use of research-based interventions is necessary to help secondary students with learning disabilities (LD) access the algebra curriculum. The authors provide an overview of the following research-based approaches: explicit instruction, graduated instructional sequence, technology, and graphic organizers. For each approach, a summary of the research is provided along with suggestions for how the approach can be used by classroom teachers to support algebra instruction.

Intervention in School and Clinic, 2010

To improve student success in mathematics, the use of research-based interventions is necessary t... more To improve student success in mathematics, the use of research-based interventions is necessary to help secondary students with learning disabilities (LD) access the algebra curriculum. The authors provide an overview of the following research-based approaches: explicit instruction, graduated instructional sequence, technology, and graphic organizers. For each approach, a summary of the research is provided along with suggestions for how the approach can be used by classroom teachers to support algebra instruction.