A mathematics learning disability (MLD) affects about 5% of primary school students and impacts an individual's ability to perform math problems at their appropriate cognitive level despite having a normal IQ. Three subtypes of MLD have been proposed: procedural deficits characterized by difficulties with math procedures and concepts; semantic memory deficits involving problems retrieving math facts; and weak spatial representation of numbers causing issues with number alignment and interpretation. Effective classroom accommodations for students with MLDs include explicit instruction using visual representations and examples, encouraging student verbalization, and providing ongoing feedback. Standardized tests can help identify MLDs while teachers should implement progress monitoring to track student strengths and weaknesses.
The Effect of the Concrete-Representational-Abstract Mathematical Sequence o...Janet Van Heck
This document describes a study that examined the effects of using the concrete-representational-abstract (CRA) teaching sequence with explicit instruction to teach addition skills from 0 to 9 to kindergarten students struggling in math. The CRA sequence begins by using manipulatives, then representations like pictures, before moving to abstract problems. Three kindergarten students identified as needing math support through RTI screening were given scripted CRA lessons and their test scores were measured. The study found the CRA sequence improved students' conceptual understanding and performance on addition facts from 0 to 9 when delivered with explicit instruction.
This document provides an overview of the 5th grade mathematics standards for North Carolina related to the Common Core. It is intended to help educators understand what students are expected to know and be able to do under the new standards. The document explains that the standards describe the essential knowledge and skills students should master in order to be prepared for 6th grade. It also provides examples for how the standards can be unpacked to clarify their meaning and intent. Educators are encouraged to provide feedback to help improve the usefulness of the document.
- The document discusses research on mathematics education in the United States, finding that only about a third of students are proficient in math based on national assessments. It also discusses research showing US students performing poorly compared to other nations.
- The research emphasizes the need for a well-designed curriculum, quality teacher preparation, and explicitly teaching concepts and making connections to help students succeed in algebra and beyond. It discusses characteristics of students with learning difficulties in math.
- The document provides an overview of effective teaching practices informed by research, including concrete-representational-abstract instruction, explicit teaching, sequencing skills appropriately, and providing cumulative practice and review.
This document summarizes a study that investigated how students' learning progresses through five levels of activity for multiplying fractions with natural numbers based on a Realistic Mathematics Education approach. The study used a Hypothetical Learning Trajectory to guide activities centered around measuring lengths on a running route. Results showed students were able to develop informal strategies into more formal mathematical understanding by using tools like number lines. The five levels of activity were found to support progressive learning from concrete to abstract concepts.
There are several methods for assessing students' math skills, including formal and informal assessments. Formal assessments include achievement tests which measure overall math achievement and diagnostic tests which identify specific strengths and weaknesses. Informal assessments involve examining student work samples, using curriculum-based measurements, and teacher-constructed tests. Assessments should be given at the concrete, semiconcrete, and abstract levels to evaluate students' understanding. Periodic and continuous assessments are also important to monitor progress.
1) The purpose of this study was to examine the relationship between visual static models and students' written solutions to fraction problems using a large sample of student work.
2) The results indicate that common student errors relate to how students interpret the given model or their own model of the situation. Students' flexibility with visual models is related to successful written solutions.
3) Researchers hypothesize that exposure to varied mathematical representations influences students' ability to flexibly use static visual representations. Students need a solid understanding of real-world situations to successfully create and interpret visual models.
These are the unpacking documents to better help you understand the expectations for 1st grade students under the Common Core State Standards for Math. The example problems are great.
The Effect of the Concrete-Representational-Abstract Mathematical Sequence o...Janet Van Heck
This document describes a study that examined the effects of using the concrete-representational-abstract (CRA) teaching sequence with explicit instruction to teach addition skills from 0 to 9 to kindergarten students struggling in math. The CRA sequence begins by using manipulatives, then representations like pictures, before moving to abstract problems. Three kindergarten students identified as needing math support through RTI screening were given scripted CRA lessons and their test scores were measured. The study found the CRA sequence improved students' conceptual understanding and performance on addition facts from 0 to 9 when delivered with explicit instruction.
This document provides an overview of the 5th grade mathematics standards for North Carolina related to the Common Core. It is intended to help educators understand what students are expected to know and be able to do under the new standards. The document explains that the standards describe the essential knowledge and skills students should master in order to be prepared for 6th grade. It also provides examples for how the standards can be unpacked to clarify their meaning and intent. Educators are encouraged to provide feedback to help improve the usefulness of the document.
- The document discusses research on mathematics education in the United States, finding that only about a third of students are proficient in math based on national assessments. It also discusses research showing US students performing poorly compared to other nations.
- The research emphasizes the need for a well-designed curriculum, quality teacher preparation, and explicitly teaching concepts and making connections to help students succeed in algebra and beyond. It discusses characteristics of students with learning difficulties in math.
- The document provides an overview of effective teaching practices informed by research, including concrete-representational-abstract instruction, explicit teaching, sequencing skills appropriately, and providing cumulative practice and review.
This document summarizes a study that investigated how students' learning progresses through five levels of activity for multiplying fractions with natural numbers based on a Realistic Mathematics Education approach. The study used a Hypothetical Learning Trajectory to guide activities centered around measuring lengths on a running route. Results showed students were able to develop informal strategies into more formal mathematical understanding by using tools like number lines. The five levels of activity were found to support progressive learning from concrete to abstract concepts.
There are several methods for assessing students' math skills, including formal and informal assessments. Formal assessments include achievement tests which measure overall math achievement and diagnostic tests which identify specific strengths and weaknesses. Informal assessments involve examining student work samples, using curriculum-based measurements, and teacher-constructed tests. Assessments should be given at the concrete, semiconcrete, and abstract levels to evaluate students' understanding. Periodic and continuous assessments are also important to monitor progress.
1) The purpose of this study was to examine the relationship between visual static models and students' written solutions to fraction problems using a large sample of student work.
2) The results indicate that common student errors relate to how students interpret the given model or their own model of the situation. Students' flexibility with visual models is related to successful written solutions.
3) Researchers hypothesize that exposure to varied mathematical representations influences students' ability to flexibly use static visual representations. Students need a solid understanding of real-world situations to successfully create and interpret visual models.
These are the unpacking documents to better help you understand the expectations for 1st grade students under the Common Core State Standards for Math. The example problems are great.
Are Remedial courses Effective for Engineering Incoming Students?Raúl Martínez López
1) A remedial math course was offered to incoming engineering students to address high dropout rates.
2) Students who took the course (the studio group) had significantly higher average marks and success rates compared to students who did not take the course (the control group).
3) A statistical analysis found the studio group outperformed the control group across compulsory subjects, demonstrating the effectiveness of the remedial course.
This document provides guidance for teachers on effective instructional practices for teaching mathematics to students with learning disabilities or difficulties learning mathematics. It identifies seven effective practices supported by research: 1) using explicit instruction regularly, 2) teaching with multiple instructional examples, 3) having students verbalize decisions and solutions, 4) teaching step-by-step problem solving strategies, 5) using visual representations, 6) providing students with opportunities for guided practice, and 7) conducting frequent reviews of content. The document summarizes evidence from a meta-analysis and the National Mathematics Advisory Panel report supporting the use of these practices.
This document provides an overview and unpacking of the 4th grade mathematics Common Core State Standards that will be implemented in North Carolina schools in 2012-2013. It is intended to help educators understand what students need to know and be able to do to meet the standards. New concepts for 4th grade include factors and multiples, multiplying fractions by whole numbers, and angle measurement. The document also discusses the Standards for Mathematical Practice and the two critical areas of focus for 4th grade: multi-digit multiplication and division.
The document provides the curriculum guide for mathematics from grades 7 to 10 in the Philippines. It outlines the conceptual framework, content standards, performance standards, and learning competencies for patterns and algebra in grade 8. Specifically, it covers factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, and systems of linear equations and inequalities in two variables. It also provides the time allotment and describes the expectations for student understanding and demonstration of key concepts in this strand.
The document discusses the relationship between the cognitive demand of math tasks and student achievement. It finds that maintaining high cognitive demand throughout the setup and implementation of math tasks is linked to higher achievement. When tasks involve memorization or procedures without meaning, learning gains are lower. However, tasks requiring procedures with understanding or doing mathematics fully lead to greater gains. The document recommends further research on how the cognitive demand of math instruction changes from K-12 and how teachers' perceptions of task demands may also change.
This document provides an overview of a course on techniques of correlation and multiple regression. The course aims to familiarize students with correlation and regression techniques for analyzing research data. Topics include measures of correlation for different variable types, multiple regression, and tests of significance. The course consists of 12 units covering these topics through lectures, assignments, and projects. Students will learn to calculate correlations, conduct regression analyses, and interpret results.
This document outlines the K to 12 mathematics curriculum guide for the Philippines from Kindergarten to Grade 10. It discusses the conceptual framework, course description, learning area and grade level standards, time allotment, and sample content for Grade 1. The goals are critical thinking and problem solving. Key concepts covered include numbers, measurement, geometry, patterns and algebra, and statistics. The curriculum is supported by theories of experiential learning and constructivism.
The document is the K to 12 Curriculum Guide for Mathematics from Kindergarten to Grade 10 in the Philippines. It outlines the conceptual framework, brief course description, learning area standards, key stage standards, grade level standards, and sample grade level content for Grade 1. The goals of mathematics education are developing critical thinking and problem solving skills. Key concepts include numbers, measurement, geometry, patterns and algebra, and probability and statistics. The curriculum is based on theories of experiential learning, constructivism, and inquiry-based learning.
This document outlines the K to 12 Mathematics Curriculum Guide for the Philippines, which aims to develop critical thinking and problem solving skills. It covers 5 content areas from K to 10: Numbers and Number Sense, Measurement, Geometry, Patterns and Algebra, and Probability and Statistics. The curriculum is supported by experiential learning theories and focuses on developing skills like problem solving while fostering attitudes like accuracy and perseverance. Grade level standards are provided for each grade from K to 10.
This document outlines the conceptual framework and curriculum guide for mathematics education in the Philippines from Kindergarten to Grade 10. The goals of mathematics education are developing critical thinking and problem solving skills. The curriculum covers 5 content areas - numbers, measurement, geometry, patterns and algebra, and probability and statistics. It is grounded in theories of experiential learning, reflective learning, constructivism, cooperative learning, and discovery learning. The curriculum guide describes the learning standards and expectations for each key stage of learning.
The document is a curriculum guide for mathematics education in the Philippines from grades K-10. It outlines the conceptual framework, course description, learning area standards, and grade level standards for mathematics. The goals of mathematics education are developing critical thinking and problem solving skills. The curriculum covers 5 content areas: numbers and number sense, measurement, geometry, patterns and algebra, and probability and statistics. It is based on theories of experiential learning, situated learning, reflective learning, constructivism, cooperative learning, and discovery learning. The guide describes the key concepts and skills students should demonstrate at different grade levels.
This document outlines the K to 12 mathematics curriculum for grades 1 to 10 in the Philippines. It discusses the goals of critical thinking and problem solving. It describes the content areas of numbers and number sense, measurement, geometry, patterns and algebra, and probability and statistics. It provides the standards and competencies for each grade level, with a focus on applying mathematical concepts to real-life problem solving. Time allotment for mathematics is 4 hours per week for grades 1 to 6 and 50 minutes daily for grades 7 to 10.
This document outlines the K to 12 mathematics curriculum guide for the Philippines from Kindergarten to Grade 10. It discusses the conceptual framework, course description, learning area and grade level standards, time allotment, and sample content for Grade 1. The goals are critical thinking and problem solving. Key concepts covered include numbers, measurement, geometry, patterns and algebra, and statistics. The curriculum is supported by theories of experiential learning and aims to develop skills like problem solving while considering students' contexts.
1) The document summarizes literature on students' strategies, episodes and metacognitions during mathematical problem solving. It discusses problem solving strategies, cognitive and metacognitive problem solving episodes, and components of metacognition.
2) The study aims to investigate the problem solving strategies, episodes and metacognition of 5 Turkish students and how these factors influence their problem solving success. Insights could help improve mathematics education.
3) The conclusions confirm the students' academic success levels matched their problem solving behaviors. Choosing correct strategies and efficiently changing strategies when needed relates to higher success. Metacognition, like recognizing mistakes, relates strongly to reaching correct answers.
The document discusses Maryland's Voluntary State Curriculum for high school mathematics. It aims to ensure students are mathematically competent and confident problem solvers by preparing them for college-level mathematics courses or high-performance jobs. The curriculum is divided into sections on Algebra/Data Analysis, Geometry, and Algebra II. It outlines the core learning goals and prerequisites for each section to guide instruction and connect topics between middle and high school mathematics. Technology is emphasized as a tool to enhance understanding of mathematical concepts. The goal is for students to communicate mathematically and apply their skills to real-world problems.
This study applied a content analysis method to compare how the algebraic topic of using symbols for unknown quantities is presented in elementary school mathematics textbooks from Taiwan (Nani), Singapore (My Pals Are Here!), and Finland (Laskutaito). Specifically, differences in question types (purely mathematical, verbal, visual, or combined representation), contextual versus noncontextual presentation, and pedagogical content design were compared. The findings showed that (1) fewer visual representations are found in Nani compared with the other textbooks; (2) Taiwan uses more contextual problems than the other countries; and (3) the content design in Taiwan focuses on applying the equivalent axiom to solve for unknown quantities, whereas Singapore and Finland use line segments or divide concepts in geometry graphs. In addition, the Singaporean textbooks teach algebraic simplification, providing this topic earlier than the other countries and enabling students to form connections with junior high school learning. Other implications of this study are discussed, and suggestions for future research are provided.
Dr. M.THIRUNAVUKKARASU
Research Associate
Department of Education
Bharathidasan University,
Tiruchirappalli - 620 024, Tamil Nadu, India
E-mail: edutechthiru@gmail.com
Dr. S. SENTHILNATHAN
Director (FAC),
UGC - Human Resource Development Centre
(HRDC)
Bharathidasan University
Khajamalai Campus
Tiruchirappalli - 620 023
E-mail: edutechsenthil@gmail.com
This document outlines the Philippine Elementary Learning Competencies for Mathematics for grades 1 through 6. It provides the standards and expectations for student understanding of key mathematical concepts like whole numbers, operations, fractions, decimals, measurement, and data analysis at each grade level. The goal is for students to demonstrate understanding, speed and accuracy in computations, estimating, problem solving, analytical thinking, and applying mathematics to daily life.
Mathematics instruction for secondary students with learning disabilitiespschlein
This document discusses effective mathematics instruction techniques for secondary students with learning disabilities. It notes that these students generally have low achievement in math due to prior difficulties, low expectations, and inadequate instruction. The article examines research on practices shown to improve math achievement for these students. It identifies six factors that can hinder effective instruction: prior achievement, self-efficacy perceptions, content and presentation of instruction, instruction management, efforts to evaluate and improve teaching, and beliefs about effective instruction. The document focuses on how addressing these factors, such as through well-organized content and examples, can enhance math learning for secondary students with learning disabilities.
Chapter 8 math strategies and techniques by sheena bernalEdi sa puso mo :">
This document discusses strategies and techniques for improving mathematics instruction for students with mild disabilities. It covers foundational math concepts like number sense, calculation, and problem solving. Some key instructional approaches mentioned include explicit instruction, peer tutoring, drill and practice, and ongoing progress monitoring. The document emphasizes teaching math concepts in a logical sequence and ensuring students have mastered foundational skills before moving on.
Are Remedial courses Effective for Engineering Incoming Students?Raúl Martínez López
1) A remedial math course was offered to incoming engineering students to address high dropout rates.
2) Students who took the course (the studio group) had significantly higher average marks and success rates compared to students who did not take the course (the control group).
3) A statistical analysis found the studio group outperformed the control group across compulsory subjects, demonstrating the effectiveness of the remedial course.
This document provides guidance for teachers on effective instructional practices for teaching mathematics to students with learning disabilities or difficulties learning mathematics. It identifies seven effective practices supported by research: 1) using explicit instruction regularly, 2) teaching with multiple instructional examples, 3) having students verbalize decisions and solutions, 4) teaching step-by-step problem solving strategies, 5) using visual representations, 6) providing students with opportunities for guided practice, and 7) conducting frequent reviews of content. The document summarizes evidence from a meta-analysis and the National Mathematics Advisory Panel report supporting the use of these practices.
This document provides an overview and unpacking of the 4th grade mathematics Common Core State Standards that will be implemented in North Carolina schools in 2012-2013. It is intended to help educators understand what students need to know and be able to do to meet the standards. New concepts for 4th grade include factors and multiples, multiplying fractions by whole numbers, and angle measurement. The document also discusses the Standards for Mathematical Practice and the two critical areas of focus for 4th grade: multi-digit multiplication and division.
The document provides the curriculum guide for mathematics from grades 7 to 10 in the Philippines. It outlines the conceptual framework, content standards, performance standards, and learning competencies for patterns and algebra in grade 8. Specifically, it covers factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, and systems of linear equations and inequalities in two variables. It also provides the time allotment and describes the expectations for student understanding and demonstration of key concepts in this strand.
The document discusses the relationship between the cognitive demand of math tasks and student achievement. It finds that maintaining high cognitive demand throughout the setup and implementation of math tasks is linked to higher achievement. When tasks involve memorization or procedures without meaning, learning gains are lower. However, tasks requiring procedures with understanding or doing mathematics fully lead to greater gains. The document recommends further research on how the cognitive demand of math instruction changes from K-12 and how teachers' perceptions of task demands may also change.
This document provides an overview of a course on techniques of correlation and multiple regression. The course aims to familiarize students with correlation and regression techniques for analyzing research data. Topics include measures of correlation for different variable types, multiple regression, and tests of significance. The course consists of 12 units covering these topics through lectures, assignments, and projects. Students will learn to calculate correlations, conduct regression analyses, and interpret results.
This document outlines the K to 12 mathematics curriculum guide for the Philippines from Kindergarten to Grade 10. It discusses the conceptual framework, course description, learning area and grade level standards, time allotment, and sample content for Grade 1. The goals are critical thinking and problem solving. Key concepts covered include numbers, measurement, geometry, patterns and algebra, and statistics. The curriculum is supported by theories of experiential learning and constructivism.
The document is the K to 12 Curriculum Guide for Mathematics from Kindergarten to Grade 10 in the Philippines. It outlines the conceptual framework, brief course description, learning area standards, key stage standards, grade level standards, and sample grade level content for Grade 1. The goals of mathematics education are developing critical thinking and problem solving skills. Key concepts include numbers, measurement, geometry, patterns and algebra, and probability and statistics. The curriculum is based on theories of experiential learning, constructivism, and inquiry-based learning.
This document outlines the K to 12 Mathematics Curriculum Guide for the Philippines, which aims to develop critical thinking and problem solving skills. It covers 5 content areas from K to 10: Numbers and Number Sense, Measurement, Geometry, Patterns and Algebra, and Probability and Statistics. The curriculum is supported by experiential learning theories and focuses on developing skills like problem solving while fostering attitudes like accuracy and perseverance. Grade level standards are provided for each grade from K to 10.
This document outlines the conceptual framework and curriculum guide for mathematics education in the Philippines from Kindergarten to Grade 10. The goals of mathematics education are developing critical thinking and problem solving skills. The curriculum covers 5 content areas - numbers, measurement, geometry, patterns and algebra, and probability and statistics. It is grounded in theories of experiential learning, reflective learning, constructivism, cooperative learning, and discovery learning. The curriculum guide describes the learning standards and expectations for each key stage of learning.
The document is a curriculum guide for mathematics education in the Philippines from grades K-10. It outlines the conceptual framework, course description, learning area standards, and grade level standards for mathematics. The goals of mathematics education are developing critical thinking and problem solving skills. The curriculum covers 5 content areas: numbers and number sense, measurement, geometry, patterns and algebra, and probability and statistics. It is based on theories of experiential learning, situated learning, reflective learning, constructivism, cooperative learning, and discovery learning. The guide describes the key concepts and skills students should demonstrate at different grade levels.
This document outlines the K to 12 mathematics curriculum for grades 1 to 10 in the Philippines. It discusses the goals of critical thinking and problem solving. It describes the content areas of numbers and number sense, measurement, geometry, patterns and algebra, and probability and statistics. It provides the standards and competencies for each grade level, with a focus on applying mathematical concepts to real-life problem solving. Time allotment for mathematics is 4 hours per week for grades 1 to 6 and 50 minutes daily for grades 7 to 10.
This document outlines the K to 12 mathematics curriculum guide for the Philippines from Kindergarten to Grade 10. It discusses the conceptual framework, course description, learning area and grade level standards, time allotment, and sample content for Grade 1. The goals are critical thinking and problem solving. Key concepts covered include numbers, measurement, geometry, patterns and algebra, and statistics. The curriculum is supported by theories of experiential learning and aims to develop skills like problem solving while considering students' contexts.
1) The document summarizes literature on students' strategies, episodes and metacognitions during mathematical problem solving. It discusses problem solving strategies, cognitive and metacognitive problem solving episodes, and components of metacognition.
2) The study aims to investigate the problem solving strategies, episodes and metacognition of 5 Turkish students and how these factors influence their problem solving success. Insights could help improve mathematics education.
3) The conclusions confirm the students' academic success levels matched their problem solving behaviors. Choosing correct strategies and efficiently changing strategies when needed relates to higher success. Metacognition, like recognizing mistakes, relates strongly to reaching correct answers.
The document discusses Maryland's Voluntary State Curriculum for high school mathematics. It aims to ensure students are mathematically competent and confident problem solvers by preparing them for college-level mathematics courses or high-performance jobs. The curriculum is divided into sections on Algebra/Data Analysis, Geometry, and Algebra II. It outlines the core learning goals and prerequisites for each section to guide instruction and connect topics between middle and high school mathematics. Technology is emphasized as a tool to enhance understanding of mathematical concepts. The goal is for students to communicate mathematically and apply their skills to real-world problems.
This study applied a content analysis method to compare how the algebraic topic of using symbols for unknown quantities is presented in elementary school mathematics textbooks from Taiwan (Nani), Singapore (My Pals Are Here!), and Finland (Laskutaito). Specifically, differences in question types (purely mathematical, verbal, visual, or combined representation), contextual versus noncontextual presentation, and pedagogical content design were compared. The findings showed that (1) fewer visual representations are found in Nani compared with the other textbooks; (2) Taiwan uses more contextual problems than the other countries; and (3) the content design in Taiwan focuses on applying the equivalent axiom to solve for unknown quantities, whereas Singapore and Finland use line segments or divide concepts in geometry graphs. In addition, the Singaporean textbooks teach algebraic simplification, providing this topic earlier than the other countries and enabling students to form connections with junior high school learning. Other implications of this study are discussed, and suggestions for future research are provided.
Dr. M.THIRUNAVUKKARASU
Research Associate
Department of Education
Bharathidasan University,
Tiruchirappalli - 620 024, Tamil Nadu, India
E-mail: edutechthiru@gmail.com
Dr. S. SENTHILNATHAN
Director (FAC),
UGC - Human Resource Development Centre
(HRDC)
Bharathidasan University
Khajamalai Campus
Tiruchirappalli - 620 023
E-mail: edutechsenthil@gmail.com
This document outlines the Philippine Elementary Learning Competencies for Mathematics for grades 1 through 6. It provides the standards and expectations for student understanding of key mathematical concepts like whole numbers, operations, fractions, decimals, measurement, and data analysis at each grade level. The goal is for students to demonstrate understanding, speed and accuracy in computations, estimating, problem solving, analytical thinking, and applying mathematics to daily life.
Mathematics instruction for secondary students with learning disabilitiespschlein
This document discusses effective mathematics instruction techniques for secondary students with learning disabilities. It notes that these students generally have low achievement in math due to prior difficulties, low expectations, and inadequate instruction. The article examines research on practices shown to improve math achievement for these students. It identifies six factors that can hinder effective instruction: prior achievement, self-efficacy perceptions, content and presentation of instruction, instruction management, efforts to evaluate and improve teaching, and beliefs about effective instruction. The document focuses on how addressing these factors, such as through well-organized content and examples, can enhance math learning for secondary students with learning disabilities.
Chapter 8 math strategies and techniques by sheena bernalEdi sa puso mo :">
This document discusses strategies and techniques for improving mathematics instruction for students with mild disabilities. It covers foundational math concepts like number sense, calculation, and problem solving. Some key instructional approaches mentioned include explicit instruction, peer tutoring, drill and practice, and ongoing progress monitoring. The document emphasizes teaching math concepts in a logical sequence and ensuring students have mastered foundational skills before moving on.
This document discusses mathematical disabilities and approaches to teaching mathematics to students with special needs. It covers the following key points in 3 sentences:
Mathematical disabilities can include difficulties with number concepts, arithmetic skills, memory of facts, and visual-spatial processing. Effective teaching strategies include using manipulatives, building on student strengths, focusing on mastery of key concepts, and assessing students' prerequisite skills and learning styles. The document also discusses considerations for teaching mathematics to English language learners and strategies for diagnosing learning difficulties in mathematics.
The document discusses using a multi-dimensional approach called SPUR (Skills, Properties, Uses, and Representations) to assess students' mathematical knowledge. It provides examples of assessment items in each dimension for topics like fractions and solving linear equations. Assessment data from the US and Singapore showed that looking at overall scores masks important differences in how students perform in each dimension. Analyzing assessments according to SPUR can provide insights to guide instruction.
READING COMPREHENSION AND PROBLEM SOLVING SKILLS OF GRADE SEVENSTUDENTS: A MI...AJHSSR Journal
ABSTRACT: The purpose of this study was to determine the relationship between the extent of students‟
reading comprehension and problem solving skills and identify teaching strategies that would address the
problem in teaching problem solving in Mathematics. The research utilized mixed explanatory design. The
subject consists of 189 grade 7 students who were part of the general section enrolled at Davao City National
High School. Purposive sampling was used in identifying the respondents taking the reading comprehension test
and problem solving test while random sampling was used in identifying participants for the key informant
interview. The result of the study revealed that students reading comprehension and problem solving skills were
at developing level. Moreover, reading comprehension skill was a predictor of problem solving skill. This
means that students‟ problem solving skill is dependent on their reading skills. Results also showed from the
conducted focus group discussion that students gave importance to vocabulary and main idea in learning
problem solving. Furthermore, using differentiated instruction was the identified best teaching strategy to
understand problem solving.
Adaptive computer assisted instruction (cai) for students with dyscalculiadaegrupo1
The document describes an adaptive computer-assisted instruction tool to help students with dyscalculia, or a learning disability in mathematics. The tool presents numerical problems adapted to each student's performance level using a multidimensional learning algorithm. This allows the tool to constantly adjust difficulty based on three dimensions: distance between numbers, speed required to respond, and conceptual complexity of problems. The goal is to provide intensive, individualized training to improve students' number sense and mastery of basic arithmetic skills through an entertaining e-learning experience.
An Investigation Of The Look-Ask-Pick Mnemonic To Improve Fraction SkillsSarah Morrow
The document describes a study that evaluated the effects of the Look-Ask-Pick (LAP) mnemonic on the fraction addition and subtraction skills of 3 sixth-grade students in general education. The LAP mnemonic teaches students to categorize fraction problems into 3 types and solve them accordingly. The study used a multiple baseline design to teach students the LAP strategy and measure its impact on their percentage of fraction problems solved correctly and digits correct per minute. Results showed increases in both measures for all students, and gains were maintained after 3 weeks. The study extends previous research on the LAP strategy by targeting general education students and including a fluency measure.
Students struggle with mathematics for several reasons:
- Difficulty recalling basic computational skills if early skills were not fully mastered
- Trouble connecting mathematical concepts like numbers and quantities
- Not understanding mathematical language and symbols
- Issues with attention span, memory, and inconsistent computing skills
To help struggling students, teachers need to use explicit instruction, guided practice, discussion, and real-world examples to build skills over time in a supportive environment. Small chunks of new concepts and learning aids can also help students experience success in mathematics.
This document discusses teaching mathematical problem solving. It begins by defining what constitutes a problem versus a routine exercise, noting that problems are unfamiliar, unstructured, and complex. It then discusses how teaching problem solving requires going beyond memorization and standard techniques to focus on conceptual understanding. Several examples of complex, unfamiliar problems are provided. The document emphasizes the importance of supporting student engagement through scaffolding, modeling, and valuing explanation over just obtaining answers. Finally, it discusses the critical role of metacognition in problem solving, providing examples of metacognitive questioning techniques and heuristics students can use to monitor and regulate their problem solving activity.
complete a correlation matrix of the four Interpersonal Strategies a.pdfFootageetoffe16
complete a correlation matrix of the four Interpersonal Strategies above with the eight CCSSM
practices:
1.Make sense of problems and persevere in solving them.
2.Reason abstractly and quantitatively.
3.Construct viable arguments and critique the reasoning of others.
4.Model with mathematics.
5.Use appropriate tools strategically.
6.Look for and make use of structure.
7.Look for and express regularity in repeated
Solution
Make sense of problems and persevere in solving them.
Mathematically proficient students start by explaining to themselves the meaning of a problem
and looking for entry points to its solution. They analyze givens, constraints, relationships, and
goals. They make conjectures about the form and meaning of the solution and plan a solution
pathway rather than simply jumping into a solution attempt. They consider analogous problems,
and try special cases and simpler forms of the original problem in order to gain insight into its
solution. They monitor and evaluate their progress and change course if necessary. Older
students might, depending on the context of the problem, transform algebraic expressions or
change the viewing window on their graphing calculator to get the information they need.
Mathematically proficient students can explain correspondences between equations, verbal
descriptions, tables, and graphs or draw diagrams of important features and relationships, graph
data, and search for regularity or trends. Younger students might rely on using concrete objects
or pictures to help conceptualize and solve a problem. Mathematically proficient students check
their answers to problems using a different method, and they continually ask themselves, \"Does
this make sense?\" They can understand the approaches of others to solving complex problems
and identify correspondences between different approaches.
MP2 Reason abstractly and quantitatively.
Mathematically proficient students make sense of quantities and their relationships in problem
situations. They bring two complementary abilities to bear on problems involving quantitative
relationships: the ability to decontextualize—to abstract a given situation and represent it
symbolically and manipulate the representing symbols as if they have a life of their own, without
necessarily attending to their referents—and the ability to contextualize, to pause as needed
during the manipulation process in order to probe into the referents for the symbols involved.
Quantitative reasoning entails habits of creating a coherent representation of the problem at
hand; considering the units involved; attending to the meaning of quantities, not just how to
compute them; and knowing and flexibly using different properties of operations and objects.
MP3 Construct viable arguments and critique the reasoning of others.
Mathematically proficient students understand and use stated assumptions, definitions, and
previously established results in constructing arguments. They make conjectures and build a.
This document discusses barriers to mathematics fluency for students and potential tools and strategies to help overcome these barriers. It identifies several common barriers, including problems with visual and language processing, conceptual understanding, memory, writing skills, and independence. To build fluency, the document stresses the importance of conceptual understanding, procedural fluency, and automatic recall of facts. It suggests teachers consider each student's specific barriers and how tools or instructional strategies could help students strengthen skills outlined in the mathematical practice domains like problem-solving, reasoning, modeling, and precision.
The document describes a lesson where fourth grade students are introduced to decimals through measuring objects in the classroom using a meter stick divided into tenths. Students work in groups to measure and record lengths, then create bar graphs on computers and the board to display their results. The teacher facilitates discussion by asking open-ended questions to help students make sense of decimals and develop their reasoning and understanding of measurement. Students demonstrate their understanding of decimals by recording measurements correctly using decimal notation.
- The document discusses the need for high school curriculum and instruction to focus on meaning making and transfer of learning rather than just content coverage and acquisition of facts.
- It presents three categories of goals for learning: acquisition, meaning making, and transfer. High schools currently focus too much on acquisition at the expense of meaning and transfer.
- Examples are provided of how to restructure instructional sequences, lessons, and assessments to better support all three goals by incorporating more activities focused on meaning making and transfer before, during, and after content acquisition.
The document summarizes a study that investigated the views of primary teachers and pre-service teachers on the misconceptions primary school students have about fractions. The teachers stated that students most often had difficulties representing fractions with models, understanding the concepts of the numerator and denominator, ranking fractions, solving problems, reading and writing fractions, distinguishing fraction types and converting between them, and placing fractions on a number line. They reported misconceptions with these concepts, such as thinking the numerator and denominator are separate numbers rather than parts of a whole. The study aimed to help teachers address common student misconceptions to improve fractional understanding.
This document provides an overview of the Year 7 mathematics curriculum and teaching approaches at the school. It outlines the key units covered in each term including topics like integers, fractions, geometry, statistics, and algebra. It emphasizes developing students' problem solving, reasoning, and communication skills. Teachers guide students through multi-step problem solving processes involving understanding problems, making connections, investigating possibilities, getting feedback, and reflecting on strategies. The curriculum aims to develop students' mathematical understanding and skills as outlined in the Australian National Curriculum.
ActionResearch - Strategies FOR PRACTICE.pptx300272
This document discusses instructional strategies that can be used in action research, including active learning, cooperative learning, experimental inquiry, and graphic organizers. It also provides examples of problems identified in past action research studies, such as students having low scores in problem solving, mathematics, and difficulty comprehending science concepts. The document outlines identifying problems, analyzing problems, considering alternative courses of action, and selecting a probable action, such as using activity cards, assignment sheets, or cooperative learning, to address the issues identified.
1. The document provides an overview of a new developmental math course called Mathematical Literacy for College Students (MLCS).
2. MLCS aims to provide an alternative pathway to college-level math for non-STEM majors by integrating numeracy, proportional reasoning, algebraic reasoning, and functions.
3. The course is designed to develop students' mathematical maturity through problem solving, critical thinking, writing, and communication while covering topics over four units in a semester.
The document summarizes a study that aims to identify the least mastered mathematics skills of grade 9 students at Lawaan National High School. It discusses the study's rationale, theoretical background, objectives, scope, methodology and research instruments. The study will administer a questionnaire to 346 grade 9 students to determine their proficiency in algebra, geometry, trigonometry and radical expressions. It seeks to identify weaknesses and inform interventions to improve student performance in mathematics.
1. Learning Disabilities in Mathematics 1
Learning Disabilities in Mathematics –
What High School Math Teachers Need to Know
William E. Engler
American International College
2. Learning Disabilities in Mathematics 2
A mathematics learning disability (MLD) is a specific type of learning disability that
affects about 5% of primary school students (Kaufmann, 2012). If diagnosed with a MLD, a
student is eligible for special education as per IDEA 2004. While no universally accepted
definition of a mathematics learning disability (MLD) exists, it is important to ground our
analysis with a definition that is both meaningful and helpful. At the risk of oversimplification, a
person with a MLD has a normal IQ but is unable to do math at the appropriate cognitive level,
based on his or her age and schooling. A learning disability can result from deficits in the ability
to represent or process information in one or all of the many mathematical domains, e.g.
geometry, or in one or a set of individual competencies within each domain. The most widely
used term for disabilities in arithmetic and mathematics is dyscalculia (Mazzocco, 2003).
Three subtypes of MLD have been proposed by Geary (1993). The first subtype is
characterized by procedural deficits. These individuals tend to use developmentally
unsophisticated procedures, make frequent errors, do not fully grasp the basic underlying
concepts, and exhibit sequencing difficulties. Persons with a procedural deficit have some form
of working memory deficiency. The overall performance of these individuals can be
summarized as developmentally delayed, as their performance in similar to that of younger
children. For example, individuals with procedural deficits may exhibit the following symptoms:
Relatively frequent use of developmentally immature procedures.
Frequent errors in the execution of procedures, e.g. does not distribute the negative
sign across a binomial; difficulty adding, subtracting, multiplying, dividing positive
and negative numbers; difficulty adding, subtracting, multiplying, dividing fractions;
difficulty applying rules for exponents; difficulty solving an equation with one or
more variables.
3. Learning Disabilities in Mathematics 3
Poor understanding of the concepts underlying procedural use, e.g. does not relate a
negative number to the concept of a number line.
Difficulties sequencing the multiple steps in complex procedures.
The second subtype is characterized by semantic memory deficits. These individuals have
difficulty retrieving math facts from long-term memory and there are often errors in the facts that
they are able to recall, suggesting that retrieval deficits resistant to instructional intervention
might be an indicator of mathematics learning disability. This usually coexists with a reading
disability. In contrast to a developmental delay, this second subtype is believed to represent a
qualitative difference in the cognitive processes underlying math aptitude. For example,
individuals with semantic memory deficits may exhibit the following symptoms:
Difficulties retrieving mathematical facts, e.g., a high-school student may not have
memorized basic multiplication facts, how to convert a decimal number to a fraction
or percentage, how to interpret inequalities.
For facts that are retrieved, there is a high error rate.
For arithmetic, retrieval errors are often associates of numbers in the problem, e.g. a
student may say the square root of 16 is 8 (because 8 + 8 = 16) or 9 squared is 18
(because 9 + 9 = 18).
Reaction times for correct retrieval are unsystematic.
The final subtype is characterized by poor spatial representation of numbers and other
mathematic information. These individuals have difficulty with properly aligning numeric
information, sign confusion, number omission or rotation, and general misinterpretation of
spatially relevant numerical information (e.g. place value). When writing, reading and recalling
numbers, these common mistakes occur: number additions, substitutions, transpositions,
omissions, and reversals.
4. Learning Disabilities in Mathematics 4
Difficulties in spatially representing numerical and other forms of mathematical
information and relationships.
Frequent misinterpretation or misunderstanding of spatially represented information.
For example, a student may have problems with textbook illustrations; with geometric
constructions; with diagrams of segments, planes, parallel lines, and vertical and
horizontal lines; confusion with graphs of functions; confusion with illustrations of
three-dimensional figures.
How do you know if a student has a MLD? Many professionals rely on standardized
achievement tests in combination with measures of IQ. Typical criteria for diagnosing a MLD
are scores lower than 20th
or 25th
percentile on math achievement tests combined with a low
average or higher IQ. Be aware that standardized achievement tests sample a broad range of
arithmetical and mathematical topics, whereas children with MLD often have severe deficits is
some areas and average or better competencies in others (Geary 1993).
Feifer (2007) provides a comprehensive list of purchasable assessments, categorized by
cognitive mechanisms. For example, assessments of working memory include Wechsler
Intelligence Scale for Children Fourth Edition Integrated (WISC IV Integrated), Stanford-Binet
Intelligence Scale Fifth Edition (SB5), Test of Memory and Learning; assessments of visual-
spatial functioning include WISC IV Integrated, SB5, Differential Ability Scales (DAS);
assessments of executive functions include Wisconsin Card Sort Test, NEPSY II, Behavior
Rating Inventory of Executive Functions; assessments of attention measures include Test of
Everyday Attention for Children (Tea-CH), NEPSY II, Cognitive Assessment System (CAS);
assessments of mathematical skills and number sense include Wechsler Individual Achievement
Test, Woodcock Johnson III Achievement Test, Test of Early Mathematics Ability; assessments
of math anxiety scales include Math Anxiety Rating Scale, State-Trait Anxiety Inventory;
5. Learning Disabilities in Mathematics 5
Achenbach Child Behavior Checklist. If you suspect a student has a math learning disability,
inform the appropriate special education professional at your school and discuss the possibility
of having the student evaluated.
As a classroom teacher, how can you accommodate students with math learning
disabilities? Baker et al (2009) synthesized findings from 42 interventions on instructional
approaches that improve the mathematics proficiency of students with learning disabilities. The
following instructional components resulted in significant mean effects: Explicit instruction,
visual representations, ranges of examples, student verbalizations, and providing ongoing
feedback.
In the most effective form of explicit instruction, the teacher demonstrated a step by step
plan (strategy) for solving the problem. The plan was problem specific (not a generic, heuristic
guide) and students were actively encouraged to use the same procedure/steps demonstrated by
the teacher.
Visual representations of problems that illustrate solution strategies should be used
frequently. For example, use number lines, color-coded graphs, three-dimensional figures, and
any visual context for word problems.
The teacher should thoughtfully plan the lesson by carefully selecting and sequencing
instructional examples. For example, for a lesson on inverse functions, the following
instructional examples could be presented in this order:
Review the differences between a function and a relation.
Review the vertical line test.
Demonstrate how to find the inverse of a set of coordinate points by interchanging
the entries in each ordered pair.
Define a one-to-one function.
6. Learning Disabilities in Mathematics 6
Explain the horizontal line test.
Explain how the domain and range of a function and its inverse are related.
Have students graph a function and its inverse.
Demonstrate how to find the inverse function f-1
(x) with an easy function.
Demonstrate how to find the inverse function f-1
(x) with a hard function.
Explain how to find the inverse of a domain-restricted function.
Teachers should encourage students to verbalize their thinking or their strategies, even if
the students were explicitly taught one specific way to solve a problem. Verbalization may help
to anchor skills and strategies both behaviorally and mathematically. While not a primary
instructional component, some heuristics trial and error could be explored with students with
MLDs.
Student math achievement is enhanced when teachers are provided with precise
information on student progress and specific areas of students’ strengths and weaknesses.
Schools should develop and implement progress monitoring systems in mathematics that include
graphs of student performance as well as specific instructional guidelines and curricular
materials for teachers or other relevant personnel to use with particular students.
It is still unclear whether or not the use of heuristics and peer-assisted instruction are
effective forms of instruction. When scaffolded to discover solutions on their own, students with
a MLD appear to arrive at a higher level of understanding. But the success of this approach may
be at odds with the notion that students with a MLD have difficulty with cognitively demanding
routines. The flexible use of heuristic strategies would seem to place a cognitive load on
students with a MLD that would make learning difficult. Also, within class peer-assisted
learning has not been as successful as it has with other populations.
7. Learning Disabilities in Mathematics 7
In summary, MLDs are recognized by IDEA 2004. MLD categories include procedural
deficits, semantic memory deficits, and weak spatial representation of numbers. Numerous
standardized tests have been developed that help teachers determine whether or not a student has
a MLD. Baker et al (2009) provides a list of effective accommodations that classroom teachers
can use immediately to help students with MLDs.
8. Learning Disabilities in Mathematics 8
References
Baker, S. K., Chard, D. J., Flojo, J., Gersten, R., Jayanthi, M., Morphy, P. (2009). Mathematics
Instruction for Students with Learning Disabilities: A Meta-Analysis of Instructional
Components. Review of Educational Research 79(3), 1202-1242.
Feifer, Steven G. (2007). The Neuropsychology of Math Disorders: Diagnosis and Intervention.
School Neuropsych Press.
Geary, David C. (2004). Mathematics and Learning Disabilities. Journal of Learning
Disabilities 37(1), 4-15.
Mazzocco, Michele M., Myers, Gwen F (2003). Complexities in Identifying and Defining
Mathematics Learning Disability in the Primary School-Age Years. Ann Dyslexia 53(1),
218-253.