Contextualizing Mathematical Problem-Solving Instruction for Secondary Students with Extensive Support Needs: A Systematic Replication

2020 ◽  
Vol 45 (4) ◽  
pp. 241-255
Author(s):  
Jenny R. Root ◽  
Sarah K. Cox ◽  
Kat Davis ◽  
Nanette Hammons
Keyword(s):  
Problem Solving ◽  
Secondary Students ◽  
Real World ◽  
Instructional Strategy ◽  
Mathematical Problem ◽  
Functional Relation ◽  
Future Research ◽  
Support Needs ◽  
School Students ◽  
Systematic Replication

Replication research provides evidence to establish, refute, or support evidence-based practices. Systematic replications are also necessary to determine “what works for whom when.” The purpose of this study was to conduct a conceptual systematic replication to evaluate the effectiveness of a multicomponent treatment package on multiplicative problem solving for middle school students with extensive support needs. Using a modified schema-based instructional strategy, three participants were taught to solve percent of change problems contextualized in real-world scenarios and a purchasing strategy (i.e., next-dollar strategy) to help them determine how much money was needed to pay for services/products. In addition, goal-setting and self-graphing activities supported development of self-determination skills. Findings from the multiple probe across participant design demonstrate a functional relation between the intervention and independent problem-solving behaviors of all three participants. Students also generalized problem-solving behaviors when presented with real-world stimuli of coupons and receipts. Implications for practice and future research are discussed.

Teaching Personal Finance Mathematical Problem Solving to Individuals With Moderate Intellectual Disability

2016 ◽  
Vol 40 (1) ◽  
pp. 5-14 ◽  
Author(s):  
Jenny Root ◽  
Alicia Saunders ◽  
Fred Spooner ◽  
Chelsi Brosh
Keyword(s):  
Problem Solving ◽  
Mathematical Problem ◽  
Functional Relation ◽  
Personal Finance ◽  
Future Research ◽  
School Students ◽  
Problem Solving Skills ◽  
Mathematical Problems ◽  
Based Instruction ◽  
Multiple Probe

The ability to solve mathematical problems related to purchasing and personal finance is important in promoting skill generalization and increasing independence for individuals with moderate intellectual disabilities (IDs). Using a multiple probe across participant design, this study investigated the effects of modified schema-based instruction (MSBI) on personal finance problem solving skills, purchasing an item on sale or leaving a tip, and using a calculator or iDevice (i.e., iPhone or iPad) for three middle school students diagnosed with a moderate ID. The results showed a functional relation between MSBI using a calculator on the participant’s ability to solve addition and subtraction personal finance word problems and generalize to iDevices. The findings of this study provide several implications for practice and offer suggestions for future research.

Contextualizing Mathematics: Teaching Problem Solving to Secondary Students With Intellectual and Developmental Disabilities

2018 ◽  
Vol 56 (6) ◽  
pp. 442-457 ◽  
Author(s):  
Jenny R. Root ◽  
Sarah K. Cox ◽  
Nannette Hammons ◽  
Alicia F. Saunders ◽  
Deidre Gilley
Keyword(s):  
Problem Solving ◽  
Developmental Disabilities ◽  
Secondary Students ◽  
Word Problems ◽  
Mathematical Problem ◽  
Functional Relation ◽  
Future Research ◽  
Intellectual And Developmental Disabilities ◽  
Mathematics Intervention ◽  
Problem Solving Skills

Abstract The purpose of this study was to evaluate the effect of a multicomponent mathematics intervention (modified schema-based instruction, video anchors, and goal setting with self-graphing) on mathematical problem-solving skills of secondary students with intellectual and developmental disabilities. Three participants were taught to solve percent of change word problems, which involved calculating the discounted price of an item or activity after using a coupon and then determining whether they had enough money to make the purchase. Results of the multiple probe across participant design indicate a functional relation between the intervention and problem solving, and all participants were able to generalize skills from word problems to real-world stimuli (i.e., coupons, receipts, menus). Implications for practice and future research are discussed.

Development of Mathematics and Self-Determination Skills for Young Adults With Extensive Support Needs

2020 ◽  
pp. 002246692090276
Author(s):  
Deidre P. Gilley ◽  
Jenny R. Root ◽  
Sarah K. Cox
Keyword(s):  
Young Adults ◽  
Problem Solving ◽  
Task Analysis ◽  
Mathematical Problem ◽  
Functional Relation ◽  
Self Determination ◽  
Support Needs ◽  
Self Monitoring ◽  
Instructional Supports ◽  
Based Instruction

The purpose of this study was to support the development of mathematics and self-determination skills of young adults with extensive support needs. Mathematical problem solving is a natural context for teaching two component skills of self-determination: self-monitoring and goal setting. Three young adults with extensive support needs (i.e., autism and intellectual disability) were taught to solve real-world thematic word problems using modified schema-based instruction (MSBI). To build self-determination skills, participants self-monitored completion of problem-solving steps using a task analysis, self-graphed steps completed independently correct and then set goals for subsequent sessions. Generalization was measured within the context of scaling ingredients from a recipe without instructional supports of a task analysis or graphic organizer. Results of the multiple probe across participants design indicate a functional relation between MSBI and steps of problem solving completed independently correct. Implications for practice and research are discussed.

Teaching Equivalent Fractions to Secondary Students With Disabilities via the Virtual–Representational–Abstract Instructional Sequence

2017 ◽  
Vol 32 (4) ◽  
pp. 220-231 ◽  
Author(s):  
Emily C. Bouck ◽  
Laura Bassette ◽  
Jordan Shurr ◽  
Jiyoon Park ◽  
Jackie Kerr ◽  
...  
Keyword(s):  
Students With Disabilities ◽  
Secondary Students ◽  
Single Case ◽  
Functional Relation ◽  
Mathematical Concept ◽  
Future Research ◽  
School Students ◽  
Mathematics Intervention ◽  
Equivalent Fractions ◽  
Mathematical Problems

Fractions are an important mathematical concept; however, fractions are also a struggle for many students with disabilities. This study explored a new framework adapted from the evidence-based concrete–representational–abstract framework: the virtual–representational–abstract (VRA) framework. The VRA framework involves teaching students to solve mathematical problems with virtual manipulative, then representations or drawings, and finally abstractly. A multiple probe across-students single-case design was used to investigate the effectiveness of the VRA framework for finding equivalent fractions for three middle-school students with disabilities. A functional relation was found between the VRA framework and students’ ability to solve equivalent fractions. Implications related to the use of the VRA framework as a mathematics intervention for secondary students with disabilities as well as directions for future research are discussed.

scholarly journals Students’ reflective thinking based on their levels of emotional intelligence in mathematical problem-solving

2021 ◽  
Vol 14 (1) ◽  
pp. 69-84
Author(s):  
Dwi Priyo Utomo ◽  
Erentrudis Junirestu ◽  
Arif Hidayatul Khusna
Keyword(s):  
Emotional Intelligence ◽  
Problem Solving ◽  
Secondary School ◽  
Secondary Students ◽  
Reflective Thinking ◽  
Mathematical Problem ◽  
School Students ◽  
Mathematical Problems ◽  
High Level ◽  
Available Information

[English]: This qualitative research aims to analyze secondary students’ reflective thinking in solving mathematical problems based on their emotional intelligence (EI). It involved four secondary school students selected from twenty-nine students who were given the EI questionnaire. The research instrument was a test and an interview guideline. Data analysis was referred to as Polya's four problem-solving stages integrated with the indicators of reflective thinking. The findings reveal that students with a high level of emotional intelligence can fulfill the whole indicators of reflective thinking. In this case, the students can react to a given situation or problem by carefully understanding the available information, making comparisons between elements to formulate strategies, explaining in detail the steps to solve problems, and doing contemplation in checking step by step and correcting mistakes. Meanwhile, students with mid-levels of emotional intelligence are less reflective in making comparisons between elements to formulate strategies for problem-solving. [Bahasa]: Penelitian kualitatif ini bertujuan untuk menganalisis pemikiran reflektif siswa sekolah menengah pertama dalam menyelesaikan masalah matematika berbasis kecerdasan emosional. Subjek penelitian adalah empat siswa, dipilih dari 29 siswa yang mengisi kuesioner. Data dikumpulkan melalui tes dan wawancara kemudian dianalisis dengan merujuk pada empat langkah pemecahan masalah Polya yang diintegrasikan dengan indikator berpikir reflektif. Hasil penelitian ini menunjukkan bahwa siswa dengan tingkat kecerdasan emosional tinggi memenuhi semua indikator berpikir reflektif dalam pemecahan masalah. Dalam hal ini, siswa mampu memberikan reaksi pada situasi atau permasalahan yang diberikan dengan memahami secara cermat informasi yang ada, melakukan komparasi antar elemen untuk menyusun strategi, menjelaskan secara rinci langkah memecahkan masalah, melakukan kontemplasi dalam memeriksa langkah demi langkah dan memperbaiki kesalahan. Sedangkan siswa dengan tingkat kecerdasan emosional sedang kurang reflektif dalam melakukan komparasi antar elemen untuk menyusun strategi pemecahan masalah.

Using Modified Schema-Based Instruction with Technology-Based Supports to Teach Data Analysis

2019 ◽  
Vol 44 (1) ◽  
pp. 53-68 ◽  
Author(s):  
Jenny R. Root ◽  
Sarah K. Cox ◽  
Stephanie Gonzalez
Keyword(s):  
Data Analysis ◽  
Problem Solving ◽  
Visual Analysis ◽  
Single Case ◽  
Functional Relation ◽  
Future Research ◽  
Support Needs ◽  
Problem Solving Skills ◽  
Social Studies Textbooks ◽  
Based Instruction

Data analysis inherently requires problem solving, yet it is the most understudied mathematical skill for individuals with extensive support needs. The current study taught elementary students with extensive support needs (i.e., autism and intellectual disability) to solve math word problems requiring analysis of scaled pictographs through modified schema-based instruction on an iPad. Results of the single-case multiple probe across participants design found a functional relation between the iPad-based math intervention and math problem solving, with a large effect size (Tau-U = .96) confirming visual analysis. In addition, participants were able to generalize problem-solving skills when they were presented with data analysis problems from grade-level social studies textbooks and visual supports were faded. Implications for practice and future research in teaching mathematics to learners with extensive support needs are discussed.

Modifying a Research-Based Problem-Solving Intervention to Improve the Problem-Solving Performance of Fifth and Sixth Graders With and Without Learning Disabilities

2016 ◽  
Vol 50 (4) ◽  
pp. 468-480
Author(s):  
Jennifer Krawec ◽  
Jia Huang
Keyword(s):  
Learning Disabilities ◽  
High School Students ◽  
Problem Solving ◽  
General Education ◽  
Repeated Measures ◽  
Mathematical Problem ◽  
Intervention Group ◽  
Future Research ◽  
Second Phase ◽  
School Students

The purpose of the present study was to test the efficacy of a modified cognitive strategy instructional intervention originally developed to improve the mathematical problem solving of middle and high school students with learning disabilities (LD). Fifth and sixth grade general education mathematics teachers and their students of varying ability (i.e., average-achieving [AA] students, low-achieving [LA] students, and students with LD) participated in the research study. Several features of the intervention were modified, including (a) explicitness of instruction, (b) emphasis on meta-cognition, (c) focus on problem-solving prerequisites, (d) extended duration of initial intervention, and (e) addition of visual supports. General education math teachers taught all instructional sessions to their inclusive classrooms. Curriculum-based measures (CBMs) of math problem solving were administered five times over the course of the year. A multilevel model (repeated measures nested within students and students nested within schools) was used to analyze student progress on CBMs. Though CBM scores in the intervention group were initially lower than that of the comparison group, intervention students improved significantly more in the first phase, with no differences in the second phase. Implications for instruction are discussed as well as directions for future research.

Schema-Based Instruction Implemented Under Routine Conditions

2019 ◽  
Author(s):  
Corey Peltier ◽  
Mindy E Lingo ◽  
Faye Autry-Schreffler ◽  
Malarie Deardorff ◽  
Leslie Mathews ◽  
...  
Keyword(s):  
Problem Solving ◽  
Word Problems ◽  
Mathematical Problem ◽  
Functional Relation ◽  
Probe Design ◽  
Resource Room ◽  
Group Settings ◽  
Intervention Protocol ◽  
Prior Literature ◽  
Based Instruction

Students identified with a specific learning disability (SLD) experience difficulty with mathematical problem solving. One specific intervention identified as a promising practice for students with a SLD is schema-based instruction (SBI). The current projects aimed to tests the efficacy of SBI under routine conditions. This extends prior literature by (a) using a teacher as the implementer, (b) allowing flexibility in the intervention protocol, (c) condensing the duration of intervention sessions, and (d) providing instruction in small group settings. In addition, we examined student problem solving performance on word problems requiring two-steps and combined schema structures. We used a multiple-probe design across three groups of fifth-grade participants (n = 7) receiving supplemental instruction in a resource room setting. Results indicated a functional relation between SBI and problem-solving performance for all students on simple structure word problems, with the magnitude of effects varying across cases. The NAP, Tau, and BC-SMD effect sizes were used to quantify effects. Implications were discussed in regard to systematic replication and conditions that may impact fidelity.

The Interplay Between Mathematical and Computational Thinking in Primary School Students’ Mathematical Problem-Solving Within a Programming Environment

2021 ◽  
pp. 073563312097993
Author(s):  
Zhihao Cui ◽  
Oi-Lam Ng
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Mathematical Problem ◽  
Computational Thinking ◽  
Programming Environment ◽  
Primary School Students ◽  
School Students ◽  
Mathematical Concepts ◽  
Block Based

In this paper, we explore the challenges experienced by a group of Primary 5 to 6 (age 12–14) students as they engaged in a series of problem-solving tasks through block-based programming. The challenges were analysed according to a taxonomy focusing on the presence of computational thinking (CT) elements in mathematics contexts: preparing problems, programming, create computational abstractions, as well as troubleshooting and debugging. Our results suggested that the challenges experienced by students were compounded by both having to learn the CT-based environment as well as to apply mathematical concepts and problem solving in that environment. Possible explanations for the observed challenges stemming from differences between CT and mathematical thinking are discussed in detail, along with suggestions towards improving the effectiveness of integrating CT into mathematics learning. This study provides evidence-based directions towards enriching mathematics education with computation.

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