**Math Topics**- Common Core
- Initiatives
- Methodology
- Resources
- Projects
- Manipulatives
- Software

**Learning Support**- Standardized Test Prep
- Technology Integration
- Assisting Readers

Instruction Resources

Math Methodology is a three part series on instruction, assessment, and curriculum. Sections contains relevant essays and resources.

This page continues part 1 on Instruction, providing Instruction Resources, including for special needs students (e.g., deaf, visually impaired, learning disabilities, English language learners).

Part 1:

**Math Methodology: Instruction**The Instruction Essay An Introduction to Teaching Challenges, Bloom's Taxonomy and Levels of Understanding; Teaching Mathematics Right the First Time: Learning for Understanding; and Addressing the Needs of Students with Math Difficulties

**Instruction Resources**on this page are grouped into sections:

Part 2: Math Methodology: Assessment essay and resources

Part 3: Curriculum: Content and Mapping and resources

Jordan School District in Utah has made available colorful Common Core math posters that visually describe each mathematical practice with pictures, words, and examples. Within each of the eight standards are posters applicable to grade bands K-1, 2-3, 4-5, and 6. Display these in your classroom.

Achievethecore.org provides valuable Common Core resources:

- Where To Focus: Math Shifts, Key Fluencies, and Major Work of Grade is of particular relevance for K-8 mathematics as it provides guidance for focusing instruction at each grade level for implementing the Common Core State Standards in Mathematics. Content emphases are identified by major clusters, supporting clusters, and additional clusters.
- The mathematics section includes Common Core exemplar tasks and assessments with explanations and supporting resources, and Common Core aligned exemplar lessons and units with supporting resources. There are also tools for planning, additional materials for understanding the math, and ready-to-use modules for professional development.
- The Aligned Instructional Practice Suite (AIP) "includes coaching and lesson planning tools to help teachers and those who support teachers to make the Shifts in instructional practice required by the Common Core and other college- and career-ready standards" (AIP description, para. 1).

**Common Core Math Book Bundle**: Leslie Texas and Tammy Jones (2013) have a series of three books, each explaining the eight
mathematical practices for the grade band and providing specific
instructional strategies that align with the Common Core State Standards
for Mathematics:

Strategies for Common Core Mathematics: Implementing the Standards for Mathematical Practice, K-5

Strategies for Common Core Mathematics: Implementing the Standards for Mathematical Practice, 6-8

Strategies for Common Core Mathematics: Implementing the Standards for Mathematical Practice, 9-12

**HOT!**: Inside Mathematics at
The Dana Center, University of Texas, grew out of the Noyce Foundation's Silicon Valley Mathematics Initiative.
It is exemplary as a professional resource for educators "passionate about improving
students' mathematics learning and performance." This site features multiple
tools for educators such as non-routine math problems organized by five levels
of difficulty, formative re-engaging lessons, performance assessment tasks
aligned to the Common Core standards (grades 2-8, algebra 1, geometry, and algebra 2),
classroom videos of innovative teaching methods and insights into student learning, and
social and emotional resources for math classrooms. Inside Mathematics also has
a section devoted to
Common Core
Resources with videos, tasks, and problems aligned to each math
standard in K-8 and high school organized by strands.

PBS LearningMedia includes free media resources searchable by grade level, standards, media type, and subject. Resources include video and audio segments, interactives, images, documents, lesson plans, productivity tools for teachers, self-paced lessons,and student-oriented activities. You'll find media from NOVA, Frontline, American Experience, and other public broadcasting and content partners. The mathematics section features K-8 mathematics strands, and high school number and quantity, algebra, geometry, functions, statistics and probability. Highly recommended.

PowerUp WHAT WORKS provides "customizable resources for teachers, school leaders, PD facilitators, and teacher educators to improve teaching and learning for struggling students and those with disabilities." You'll find "teaching strategies supported by technology, technology use in schools and classrooms, Universal Design for Learning (UDL) and differentiated instruction, [and] guidance on meeting Common Core Standards" (About Us section). The Resource Library contains numerous articles on math teaching strategies.

Teaching Channel offers free videos "on the Internet and TV—of inspiring and effective teaching practices in America's schools." Further, the "video library offers educators a wide range of subjects for grades K-12. The videos also include information on alignment with Common Core State Standards and ancillary material for teachers to use in their own classrooms" (About Us section). Videos are searchable by topic, subject, and grade level.

Understanding Language: Supporting ELL in Mathematics is an initiative at Stanford University to develop materials that illustrate how Common Core aligned math tasks can be used to support math instruction and language development for English language learners in elementary, middle, and high school. You'll find adapted tasks from the publicly accessible curriculum projects Inside Mathematics and the Mathematics Assessment Project, principles for teaching mathematics to ELLs, and "Language of Math" Task Templates that can be used by teachers to design and write their own language-focused activities, and more.

Judit Moschkovich (2012) provided the following recommendations for connecting mathematical content to language:

- Focus on students’ mathematical reasoning, not accuracy in using language.
- Shift to a focus on mathematical discourse practices, move away from simplified views of language.
- Recognize and support students to engage with the complexity of language in math classrooms.
- Treat everyday language and experiences as resources, not as obstacles.
- Uncover the mathematics in what students say and do. (pp. 21-23)

Reference:

Moschkovich, J. (2012). *Mathematics, the Common Core, and
language: Recommendations for mathematics instruction for ELs aligned
with the Common Core*.
https://ell.stanford.edu/publication/mathematics-common-core-and-language
Also available at
https://eric.ed.gov/?id=ED584919

**
**Hung-Hsi Wu (University of California at Berkeley) has a
series of articles on the Common Core Math Standards and other
articles and books related to
teaching mathematics. The following are among those:

- In Teaching Fractions According to the Common Core Standards, Wu (2014) presents an expanded view on how CCSS fraction standards may be taught in grades 3-7. Discussion at each grade level begins with the fraction standard. "As of 2014, it may be unique in that it is written for the classroom teachers by someone who has been teaching fractions to elementary and middle school teachers since year 2000 in a way that is in almost complete agreement with the Common Core Standards" (Preface section).
- In Teaching Geometry According to the Common Core Standards, Wu (2013) presents grade-by-grade commentaries on teaching the geometry standards for grades 4-8 and high school. He emphasizes the progression of the mathematical ideas through the grades. The companion article to this is Teaching Geometry in Grade 8 and High School According to the Common Core Standards.

**HOT:** High-Quality
Mathematics Instruction: What Teachers Should Know from the IRIS Center
(2017) at Vanderbilt University is a professional development module (completion in about 1.5 hours).
Such instruction includes a standards-based curriculum and use of evidence-based
strategies, which the module addresses. These include explicit, systematic
instruction, visual representations, schema instruction, and metacognitive
strategies. The module also highlights several effective practices that teachers
can use to teach mathematics. Effective classroom practices include
encouraging student discussion, presenting and comparing multiple solutions, and
assessing student understanding. The research base for strategies and
practices is included.

**HOT:**
Practice Guides
from the What Works Clearinghouse (WWC), and its special section for
What Works in Math, are intended to help educators make evidence-based decisions.
The WWC is managed by the Institute of Education Sciences (IES) on behalf of the
U.S. Department of Education. Practice guides "consist of actionable
recommendations, strategies for overcoming potential roadblocks, and an
indication of the strength of evidence supporting each recommendation. IES
practice guides are subjected to rigorous external peer review," according to the WWC.
The following examples are among those:

Developing Effective Fractions Instruction for Kindergarten Through 8th Grade (2010, September). "This practice guide presents five recommendations intended to help educators improve students’ understanding of fractions. Recommendations include strategies to develop young children’s understanding of early fraction concepts and ideas for helping older children understand the meaning of fractions and the computations involved. The guide also highlights ways to build on students’ existing strategies to solve problems involving ratios, rates, and proportions" (Summary section). Recommendations include:

- Build on students’ informal understanding of sharing and proportionality to develop initial fraction concepts.
- Help students recognize that fractions are numbers and that they expand the number system beyond whole numbers. Use number lines as a central representational tool in teaching this and other fraction concepts from the early grades onward.
- Help students understand why procedures for computations with fractions make sense.
- Develop students’ conceptual understanding of strategies for solving ratio, rate, and proportion problems before exposing them to cross-multiplication as a procedure to use to solve such problems.
- Professional development programs should place a high priority on improving teachers’ understanding of fractions and of how to teach them.

Improving Mathematical Problem Solving in Grades 4 Through 8 (2018, October). "This practice guide provides five recommendations for improving students’ mathematical problem solving in grades 4 through 8. This guide is geared toward teachers, math coaches, other educators, and curriculum developers who want to improve the mathematical problem solving of students" (Summary section). A video accompanies each recommendation. Recommendations 2 and 3 are supported by "strong" evidence, according to research reviewed for this practice guide. They include:

- Prepare problems and use them in whole-class instruction.
- Assist students in monitoring and reflecting on the problem-solving process.
- Teach students how to use visual representations.
- Expose students to multiple problem-solving strategies.
- Help students recognize and articulate mathematical concepts and notation.

Teaching Math to Young Children: A Practice Guide (2013, November). This guide elaborates on five evidence-based recommendations principally for educators who teach mathematics to children ages 3 to 6:

- Teach number and operations using a developmental progression.
- Teach geometry, patterns, measurement, and data analysis using a developmental progression.
- Use progress monitoring to ensure that math instruction builds on what each child knows.
- Teach children to view and describe their world mathematically.
- Dedicate time each day to teaching math, and integrate math instruction throughout the school day.

Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students (2019, January). "This practice guide presents evidenced-based suggestions for how to improve algebra skills and knowledge for students in grades 6–12. The guide offers three recommendations that provide teachers with specific, actionable guidance for implementing these practices in their classrooms. It also provides a level of supporting evidence for each recommendation, examples to use in class, and solutions to potential implementation challenges" (p. 1). Recommendations include:

- Use solved problems to engage students in analyzing algebraic reasoning and strategies.
- Teach students to utilize the structure of algebraic representations.
- Teach students to intentionally choose from alternative algebraic strategies when solving problems. (p. 2)

Math Wonders to Inspire Teachers and Students by Alfred S. Posamentier (2003) is an ASCD publication. Chapter 1, for example, is an amazing discussion of some surprising number patterns, power relationships, beautiful number relationships, strange equalities, perfect numbers, friendly numbers (Yes, there is a definition of friendly numbers), palindromic numbers (e.g., 12321), number associations with geometric figures, Fibonacci numbers (i.e., 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,...) and more.

As examples:

Note the digits of these special numbers and the consecutive exponents (p. 12)

598 = 5

^{1}+9^{2}+8^{3}1,676 = 1

^{1}+6^{2}+7^{3}+6^{4}

A palindrome, which is a number that can be read the same in both directions, can be generated from any number by making successive additions of the number with its reversal (p. 27). This might take a few such additions.

67 + 76 = 143; 143 + 341 = 484, a palindrome

There are only five numbers (i.e., 1, 153, 370, 371, and 407) in which the number is the sum of the cubes of its digits as in 153 = 1

^{3}+5^{3}+3^{3}(p. 36).

Adding It Up: Helping Children Learn Mathematics (2001) is a longer book (over 400 pages), available online, by the Mathematics Learning Study Committee and editors Jeremy Kilpatrick, Jane Swafford, and Bradford Findell of the Center for Education at the National Research Council. Its focus is school mathematics from pre-kindergarten to eighth grade. Much of this report attends to the learning and teaching of number, but authors emphasize that their perspective is considerably broader than just computation. Authors say, "Three kinds of knowledge are crucial for teaching school mathematics: knowledge of mathematics, knowledge of students, and knowledge of instructional practices" (p. 370).

Adolescent Literacy in the Content Areas posted at Brown University
contains a section devoted to *Supporting the Math Classroom through Literacy Development,
* originally posted at the Knowledge Loom web site. Note: the Knowledge
Loom was archived in 2013. Strategies that support literacy development and understanding of math
concepts include "Think Alouds, graphic organizers, word problems, brainteasers,
math journals, Inquiry Models, Quick Writes, Word Walls, concept maps, flow
charts, computer or graphic programming, creation of texts, Socratic
Questioning, and WebQuests" (p. 174).

The Art of Teaching Resources from TeacherVision.com.

Centre for Innovation in
Mathematics Teaching (CIMT) was established in 1986 at the University of
Exeter in the UK and is now housed at the University of Plymouth. Content
is focused on research and curriculum development for mathematics teaching and
learning. K-12 educators will be particularly interested in the CIMT
curriculum resources, such as "pupil texts, lesson plans, classroom resources,
assessment materials and on-line interactive resources." Resources
also include a section for math misconceptions and the project, *The Mathematics Enhancement Programme*, which offers school curriculum and
teaching material (posted online) for mathematics for all grade levels with
lesson plans, copymasters, and tests. Read articles from the
International
Journal for Mathematics Teaching and Learning.

In
the first edition of *Classroom Instruction That Works* (2001), Robert Marzano, Debra Pickering, and Jane Pollock presented nine research-based instructional strategies that have
a high probability of enhancing student achievement for all students in all
subject areas at all grade levels. The authors cautioned, however, that instructional strategies are
only tools and they should not be expected to work equally well in all
situations. In the second edition of Classroom
Instruction That Works (2012), Ceri Dean, Elizabeth Ross Hubbell, Howard Pitler,
and Bj Stone organized those nine strategies within a framework with three components
geared toward instructional planning (p. xvi). The framework with the
strategies and some suggestions for classroom practices includes:

1. Creating the Environment for Learning

*Setting objectives and providing feedback*--set a unit goal and help students personalize that goal; use contracts to outline specific goals students should attain and grade they will receive if they meet those goals; use rubrics to help with feedback; provide timely, specific, and corrective feedback; consider letting students lead some feedback sessions.*Reinforcing effort and providing recognition*--you might have students keep a weekly log of efforts and achievements with periodic reflections of those. They might even mathematically analyze their data. Find ways to personalize recognition, such as giving individualized awards for accomplishments.*Cooperative learning*--consider common experiences or interests; vary group sizes and objectives. Core components include positive interdependence, group processing, appropriate use of social skills, face-to-face interaction, and individual and group accountability.

2. Helping Students Develop Understanding

*Cues, questions, and advance organizers*--these should be highly analytical, should focus on what is important, and are most effective when used before a learning experience.*Nonlinguistic representations*--incorporate words and images using symbols to show relationships; use physical models and physical movement to represent information.*Summarizing and note taking*--provide guidelines for creating a summary; give time to students to review and revise notes; use a consistent format when note taking.-
*Assigning homework and providing practice*--vary homework by grade level; keep parent involvement to a minimum; provide feedback on all homework; establish a homework policy; be sure students know the purpose of the homework.

3. Helping Students Extend and Apply Knowledge

*Identifying similarities and differences*(e.g., comparing, contrasting, classifying, analogies, and metaphors)-- graphic forms, such as Venn diagrams or charts, are useful.*Generating and testing hypotheses*--a deductive (e.g. predict what might happen if ...), rather than an inductive, approach works best.

As in the first edition, Dean, Hubbell, Pitler, and Stone (2012) "do not claim that these strategies are "silver bullets" or that they will be effective in all circumstances. Rather they are "best bets" if teachers incorporate them systematically and intentionally as they plan and deliver instruction" (p. xiii).

*The New Classroom Instruction That Works* by Bryan Goodwin and Kristin
Rouleau (2023) is the third edition in the series. What makes the
book "New," per the authors, is that they used review criteria from the
What Works Clearinghouse to ensure the studies selected for their
"research base employed true scientific research designs and were
peer-reviewed" (p. 5). Their methodology yielded a different shorter set
of teaching strategies than in previous editions, but they "do not
advocate for teachers to abandon strategies highlighted in previous
editions" if they have found them to be beneficial (p. 7). They do claim that the strategies in this
edition "have been shown, scientifically, to support better learning for
diverse students" (p. 7). The list includes 14 instructional
strategies:

- Cognitive interest cues
- Student goal setting and monitoring
- Vocabulary instruction
- Strategy instruction and modeling
- Visualizations and concrete examples
- High-level questions and student explanations
- Guided initial application with formative feedback
- Peer-assisted consolidation of learning
- Retrieval practice
- Spaced and mixed independent practice
- Targeted support
- Cognitive writing
- Guided investigations
- Structured problem solving

For an introduction (12 pages) to those 14 strategies, see Unleashing the Power of Best First Instruction (2022) by Bryan Goodwin of McREL in which he discussed those "14 high-impact Tier 1 instructional strategies that are directly linked to higher levels of student learning."

The Critical Thinking Community comprises The Center for Critical Thinking and Moral Critique and the Foundation For Critical Thinking. "The work of the Foundation is to integrate the Center’s research and theoretical developments, and to create events and resources designed to help educators improve their instruction. Materials developed through the Foundation for Critical Thinking include books, Thinker's Guides, videos, and other teaching and learning resources" (Mission section). There's an extensive Library of Critical Thinking Resources.

Digital Promise Research Map:
Math Learning includes over 1500 research articles on teaching and learning math.
Per the description: "The Math Learning topic includes research on how the brain
develops the ability to understand and do math. Studies in this topic also
explore math learning differences and the effects of math interventions."
There are eight additional focused subtopics of interest, including math learning
disabilities and math interventions. **HOT!**:
Also see the Learner Variability
Navigator from Digital Promise, which is a free tool to help find
research-based strategies that support the whole learner. Three models are
available for math: grades preK-2, 3-6, and 7-10. Each model "identifies
the factors that are critical to learner success and the strategies to help you
purposely support each learner." Additional resources are included.

Everyday Mathematics: Algorithms, developed by the authors of Everyday Mathematics at the University of Chicago, contains "examples that demonstrate how to use a variety of algorithms included in Everyday Mathematics. It also includes the research basis and explanations of and information and advice about basic facts and algorithm development." The algorithms address addition, subtraction, multiplication, and division. These are also good for family use.

Get Ready to Read: Early Math from the National Center for Learning Disabilities. This section has tips for teachers of preschool math, including for building an effective preschool math program, tips for screening for math awareness and skills in early learners, activities to help preschoolers gain math literacy, tips for partnering with parents, and more.

Helping Children Learn Mathematics (2002) is a short book (52 pages), available online, by the Mathematics Learning Study Committee and editors J. Kilpatrick and J. Swafford of the Center for Education at the National Research Council. The authors stress that mathematics proficiency involves five intertwined strands: understanding mathematics, computing fluency, applying concepts to solve problems, reasoning logically, and engaging with mathematics, seeing it as sensible, useful, and doable. Mathematics in grades K-8 should be taught for an hour a day. Time should be divided so that all of the strands receive adequate attention--the key being that instructional materials should integrate the five strands. All students can and should be proficient in mathematics.

Images: A Resource Guide for Improving Measurement and Geometry in Elementary Schools was a K-5 professional development initiative of the Pennsylvania State Team of the Mid-Atlantic Eisenhower Consortium for Mathematics and Science Education at Research for Better Schools. You'll find information and resources to help teachers develop a deeper understanding of geometry and measurement concepts and to assist in designing meaningful instruction for elementary students. Instructional activities and lesson plans are included that address five strands: visual and spatial reasoning, two and three dimensional geometry, coordinate geometry, transformational geometry, and measurement. However, math teachers throughout K-12 will benefit from the content. Of particular interest are the Van Hiele Levels of Geometric Reasoning. Teaching strategies and assessment issues are addressed with how-to's, lesson plans and activities:

Strategies

- Have high expectations for all students
- Base practice on educational research
- Integrate content areas
- Incorporate standards
- Collaborate with others
- Promote cooperative learning
- Use technology as a tool
- Use inquiry-based learning
- Promote mathematical reasoning and problem solving
- Use hands-on activities to model topics
- Integrate assessment and instruction
- Reflect on teaching and learning
- Include strong academic content
- Cluster concepts

Assessments

- Observation, questioning, interviewing
- Performance tasks, self-assessment and peer-assessment
- Work samples, portfolios, writings
- Teacher-designed written tests, achievement tests

Instructional Methods Information by Dr. Bob Kizlik includes advantages, disadvantages, and required preparation related to using direct teaching, cooperative learning, lecture, lecture with discussion, a panel of experts, brainstorming, video tapes/slides, discussion, small group discussion, role playing, worksheets/surveys, guest speakers, and values clarification.

Kindergarten-lessons.com provides information for parents who home school, early childhood or primary educators, education students, beginning teachers, seasoned teachers changing grade, and parents wondering what their children should be learning in school. General tips for teaching and how to teach math, science, social studies, with themes, art, and ideas for holidays are provided.

Knowing and Teaching Elementary Mathematics (2020) by Liping Ma is the anniversary edition of his book, which was first published in 1999. It includes examples from teachers explaining what it means to know and be able to teach elementary school mathematics.

The Most Common Errors in Undergraduate Mathematics is a list of common errors found in math (communication, algebra, notation, reasoning, generalizations, and some calculus), possible causes, and remedies. These are posted at Vanderbilt University.

Mathwire.com has a section on instructional strategies addressing active participation, cooperative learning, assessment, classroom management, and differentiation.

Pedagogy in Action from the Science Education Resource Center (SERC) at Carleton College includes a library of pedagogic methods and related activities exemplifying each method. You can begin by exploring sections on Engaged Pedagogies, Teaching with Data, Quantitative Reasoning, and Assessment.

Promoting Reading Strategies for Developmental Mathematics Textbooks by Anne E. Campbell, Ann Schlumberger, and Lou Ann Pate (1997) presented three reading and study strategies designed to facilitate student comprehension of and learning from developmental mathematics textbooks. The discussion includes a preview, predict, read, and review reading strategy; concept cards; and a Question Answer Relationship technique. For example, concepts cards can include definitions, characteristics, examples, and nonexamples. Common kinds of concept cards in math include: (a) strategy cards for solving problems; (b) fact cards that include rules, laws, or theorems; and (c) cards for symbols and specialized vocabulary.

Teachersnetwork.org has a series of articles on how to teach math. Among resources are lesson plans, podcasts, and curriculum units for elementary, middle, and high school math.

Teaching Calculus by Lin McMullin is a blog for high school teachers and students, especially Advanced Placement Calculus teachers and students. You'll find comments, suggestions, hints, and observations on the topics for the course, and a video collection. Of particular value is the Blog Guide section, which includes 10 units with calculus topics in an order that they are typically taught.

Teaching Math to Young Children by Rick Garlikov is "one of a series of Web pages to help students understand math, and to help parents teach their children math -- especially to help children have a good foundation." Some other essays in this series include:

- "The Concept and Teaching of Place-Value"
- "The Socratic Method: Teaching by Asking Instead of by Telling"
- "A Supplemental Introduction to Algebra" and a separate webpage "The Way Algebra Works"
- "Understanding 'Rate' Word Problems"

Teaching Strategies for Multiple Course Modalities from the State University of New York at Albany's Institute for Teaching, Learning, and Academic Leadership (ITLAL) address six modalities, principally those involving online learning. You'll find strategies for fully remote synchronous courses, fully remote asynchronous courses, hybrid-synchronous simulcast courses, hybrid-blended/reduced classroom meetings courses, hybrid-alternating attendance courses, and in-person courses involving online components.

The Problem with Math Is English by Concepcion Molina (2012) is "A Language-Focused Approach to Helping All Students Develop a Deeper Understanding of Mathematics." All math teachers, particularly those who teach grades 3-9, will benefit as Molina delves into the language and symbolism of mathematics and the importance of integrating English language comprehension lessons into math instruction. He provides tips for doing so. All students, including English language learners, benefit from explicit language instruction integrated into the math curriculum. The focus is on building conceptual understanding of key concepts "primarily in the algebra and number and operation strands of the mathematics content standards. At the same time, the text explores the relationships between and connections among key mathematical topics to illustrate how a basic understanding of more complex concepts can be developed while teaching fundamental ideas" (p. xvii) .

An Introduction to Teaching Mathematics at the College Level (pdf) by Suzanne Kelton (Assumption College) is intended primarily for those new to teaching math at the college level. The subject-matter content relates to teaching algebra, precalculus and calculus with excellent tips for introducing concepts. As those subjects are also in the high-school curriculum, this guide should prove helpful for high school teachers.

TouchMath, a product that is designed to teach mathematics to struggling students, provided the following on dyscalculia:

"Dyscalculia is a learning disability that affects one’s ability to learn mathematics, as compared to same age peers who receive identical instruction. It may cause difficulty with counting, working memory for numbers, ability to recognize patterns, time, sense of direction, estimation of distance and volume, math facts, and procedures. Dyscalculia is a lifelong condition that can impact academic and economic progress as well as self-esteem."

"Dyscalculia can be classified as a disability under both the Individuals with Disabilities Education Act (IDEA) and the Americans with Disabilities Act (ADA), which may qualify them to receive accommodations in school via an IEP."

Prominent learning disabilities among school-age children include dyscalculia, dysgraphia, dyspraxia, dyslexia, ADHD, and Gerstmann's Syndrome. You can learn more about these and their symptoms, possible causes, and common issues from the Learning Disabilities Infographic posted at special-education-degree.net.

Understood.org provides infomation on dyscalculia including what it is, signs and symptoms, possible causes, and how it is diagnosed.

Assistive Technology: an Overview is a five-part module from Vanderbilt University, which provides classroom teachers with information and videos on working with students with disabilities. In addition to providing the basics, it "explores ways to expand students' access to [assistive technology] in the classroom."

National Center for Learning Disabilities has several research documents of interest. Among those is an online LD Checklist designed to help detect potential signs of LDs or an attention issue in a child or student and decide what to do next. You'll also find Promising Practices to Accelerate Learning for Students with Disabilities (2021).

The Family Educational Rights and Privacy Act (FERPA) (20 U.S.C. § 1232g; 34 CFR Part 99) is "a Federal law that protects the privacy of student education records. The law applies to all schools that receive funds under an applicable program of the U.S. Department of Education. FERPA gives parents certain rights with respect to their children's education records. These rights transfer to the student when he or she reaches the age of 18 or attends a school beyond the high school level" (FERPA web site description).

Section 504 and the Education of Children with Disabilities Frequently Asked Questions outlines some key facts you should know about.

ADDitude provides information on dyscalculia, its signs, types, treatment options, and resources, such as the following self-tests:

Center on Instruction: Mathematics offers materials and resources "to build educators’ knowledge of instruction for students with low achievement in mathematics, improve professional development models for math teachers, and build teachers’ skills in monitoring student growth toward important math outcomes." The Center on Instruction maintains a collection of scientifically based research for reading, math, science, special education and English language learners, and exemplars of best practice. It is one of five content centers serving as resources for the 16 regional U.S. Department of Education Comprehensive Centers.

Child Mind Institute includes articles How to Spot Dyscalculia and How to Help Kids with Dyscalculia.

Developmental Disabilities Research Reviews: Special Issue: Pathways to Mathematical Learning Difficulties and Disabilities, 2009, Vol 15, Issue 1 includes several articles on math learning difficulties for various populations. Of particular interest is free access to the following:

- Baroody, A., Bajwa, N., & Eiland, M. (2009). "Why can't Johnny
remember the basic facts?"
*Developmental Disabilities Research Reviews, 15*(1), 69-79. - Jordan, N. C., & Levine, S. C. (2009). Socioeconomic variation,
number competence, and mathematical learning difficulties in young
children.
*Developmental Disabilities Research Reviews, 15*(1), 60-68.

Dyscalculia.org addresses teaching and learning strategies for learners with dyscalculia (math LDs) and dyslexia (reading LDs). A diagnostic is available (fee attached), along with special education resources. See, for example, the Dyscalculia Classroom Action Plan.

Learners with dyscalculia might benefit from a special talking calculator called the Dyscalculator. It is designed to assist with arithmetic by offering four different representations of quantities: as digits, as words, graphically, and spoken aloud. It can also round numbers. This free app is designed for iPad, iPhone. Also see Dyscalculator for Android.

*Education
for All: The Report of the Expert Panel on Literacy and Numeracy
Instruction for Students With Special Education Needs, Kindergarten to Grade
6* (2005) was financially supported
by the Ontario Ministry of Education in Canada. The report recommends
practices, based on research, "to improve and reinforce effective
instruction of reading, writing, oral communication, and mathematics to
students from Kindergarten to Grade 6 who have special education needs" (p. 1).
However, practices discussed can enhance the learning of all
students in mathematics and literacy. Chapters address Universal
Design and Differentiated Instruction, Assessment and Evaluation, Developing
Learning Profiles, Professional Learning Communities, Research to Practice:
What Works for Both Literacy and Numeracy; Effective Instructional
Approaches for Numeracy, Effective Instructional Approaches for Literacy,
Organization and Management, Computer-based Assistive Technology, and
Professional Development.

Education Development Center: Addressing Accessibility in Mathematics contains multiple documents of value. For example, Resources include Assessibility Strategies:

*Accessibility Strategies to Consider*: Strategies to consider when planning and teaching accessible lessons (1 page).*Guiding Questions for Accessibility Strategies*: Guiding questions for planning, implementing, and evaluating strategies (1 page).- Also see EDC's comprehensive List of Published Math Intervention Programs and Assessments for Middle Grades Note: this website, Computing Technology for Math Excellence, is included among those.

Equatio is software that allows users to create equations, formulas, graphs and more digitally. Per its description, users "can speak, draw or type problems and equations directly onto their device. ... Equatio makes math more accessible. Students with learning difficulties or visual impairments can hear their math read aloud to them." All can benefit from the product and it's free for K-12 teachers.

High-Leverage Practices for Students with Disabilities from the Council for Exceptional Children delves into four areas of practice: collaboration, assessment, instruction, and the social/emotional/behavioral elements of the environment. Resources include a video list related to those to help with implementation. Content at this site is beneficial for teaching all learners.

Learning Disabilities Online (LD Online) contains a series of articles with strategies for teaching mathematics to students with learning disabilities, but those strategies are suitable for use with all students. Read how to modify mathematics instruction to promote success and understanding in the areas of mathematical readiness, computation, and problem-solving; how use cooperative learning in the math classroom, and how to break math difficulties down into different types. Another article discusses techniques that have been demonstrated to be effective with secondary students who have learning disabilities in mathematics.

Learning Toolbox from the James Madison University Special Education Program contains tools and resources to enable students with learning difficulties to become better learners. Sections are devoted to secondary learners, teachers of middle and secondary students, and parents. Academic areas and strategies include organization, test taking, study skills, notetaking, reading, writing, math, and advanced thinking. Advanced thinking addresses organizing information sequentially, comparing and contrasting ideas, understanding categories, determining cause and effect relationships, and problem solving.

MathPlayer contains math-to-speech technology. Per the User Manual: "MathPlayer can make documents more accessible by providing a means for assistive technology such as screen readers and screen magnifiers to speak, navigate, and convert to braille math in those documents. As an example MathPlayer works with NV Access' NonVisual Desktop (NVDA) to provide access to the math in Firefox, Internet Explorer, Word and PowerPoint for Windows (MathType is also required to read math in Word and PowerPoint). MathPlayer can also work with Internet Explorer in Enterprise Mode to display the math in web pages." There is a free download.

ModMath is a free math iPad app to help kids with dyslexia and dysgraphia. You can use the touchscreen and keypad to set up and solve math problems without ever picking up a pencil. In addition to basic math problems, Mod Math handles complex algebraic equations too—from multiplication and long division to variables and quadratic equations. Dysgraphia affects kids with dyslexia, ADHD, autism, dyspraxia and other disabilities (adapted from the About section). In-app purchases are available.

National Center on Accessible Instructional Materials: Learn about accessible media, how to create it, policy, and practice.

Number Dyslexia has a goal
to provide "anything and everything related to **Dyscalculia**." The
site also "covers the topics directly or indirectly related to dyscalculia such
as Dyslexia, Dysgraphia, Mental Strength, Tech assistance, Motivational stories
etc. NumberDyslexia will also shares methods and guidances to overcome daily
struggle" (About section).

Signing Math Dictionary (SMD) is a math app by Vcom3D, compatible with iPhone, iPad, and iPod Touch. It is described as "an illustrated, interactive 3D sign language dictionary with 705 math terms defined in both American Sign Language (ASL) and Signed English (SE). The SMD is one in a series of fully animated, illustrated and interactive 3D signing dictionaries. The SMD is designed for grade 4-8 students who are Deaf or Hard-of-Hearing and use ASL or SE in the classroom. The SMD supports access to standards-based math content among elementary and middle school students" (Description section). While not free (about $15), it would also be a valuable tool for teachers and parents.

Supporting ELLS in Mathematics from Stanford University includes highly recommended teaching resources related to the Common Core, including principles for instruction, guidelines for math instructional materials development, and "language of math" task templates (e.g., to support reading math problems, and to support math vocabulary for communication).

Teaching Math to Students Who are Blind or Visually Impaired: S. Osterhaus of the Texas School for the Blind and Visually Impaired offers strategies and resources for teaching mathematics to visually impaired students. She provides links to math education and Nemeth code, tactile math graphics, calculators, current research in math for VI students and more.

Teaching Tips for Children and Adults with Autism by Dr. Temple Grandin (2002) includes tips and strategies that will help educators establish conditions in the classroom most conducive to helping those with autism to succeed. Although not specifically about math, tips include methods teachers can apply for learning math and for how students with autism can best express their understanding.

TIPS for English Language Learners in Mathematics (2005) from the Ontario (CA) Ministry of Education includes grade-level support materials for those working with English language learners in Grades 7 to 10. "This resource contains models for adjustment of instruction for pairs, small groups, or the entire class and ways of differentiating instruction and assessment for English language learners so they can achieve literacy and mathematics goals. These adjustments in student groupings, teaching strategies, timing, and materials are based on recent research of ways to support English language learners" (Introduction, p. 1).

**HOT**:
TTAC Online:
Instructional Strategies are intended to help youth with disabilities from
birth to 22. Strategies are organized by type of disability within
content areas: English, Mathematics, History/Social Science. "TTAC Online
was originally produced by George Mason University professors and students in
the Graduate School of Education, Instructional Technology Program" (About Us
section).

Also consider the following book:

11 Effective Strategies for Teaching Math to Students Who Have Given Up on Learning by Jordan Smith, Jr. (2023). This book is a guide for teaching math to students who need additional support, but the strategies will benefit teaching math to all learners. Chapters delve into building classroom community, motivation, math anxiety, using technology in special education, real-world math, peer-based learning, concrete-to visual-to abstract, using correct vocabulary, schema-based instruction, and retentiion techniques. It also includes a chapter with guidance for creating lesson plans.

The following are among free apps helpful for those with dyscalculia, which are listed and describd at Number Dyslexia:

**Socratic**allows users to take a picture of a math question and get back a step-by-step solution and explanation of the concept. Available: Google Play and in the Apple App Store.**Photomath**is similar to Socratic. It solves math problems from basic arithmetic through calculus, plus combinations and factorials in statistics. Available: Google Play and in the Apple App Store.**Mental Math Practice**provides arithmetic flashcards. Available: Google Play.**Flow Free**is a puzzle game with colored dots to help with spatial reasoning and planning. Available: Google Play and in the Apple App Store.**Smartynote**is meant for students with dyslexia, but it can also read numbers. Available: Google Play.**Lumosity**is a brain training app with puzzles and games that helps with memorization, analytical and critical thinking, and problem solving. Available: Google Play and in the Apple App Store.**NeuroNation**also is a brain training app targeting those with weak memory and concentration, as in those with dyscalculia. Available: Google Play and in Apple App Store.**Prodigy Math Game**is targeted for learners ages 6-12 (grades 1-8) and provides interactive math practice. Available: Google Play and in Apple App Store.**Know Abacus**is a virtual abacus and, like a concrete abacus, helps with developing number sense. Available: Google Play and in Apple App Store.

Committee for Children addresses programs for prevention of bullying and violence, and includes a personal safety curriculum.

Digital Promise Research Map: Social-Emotional Learning includes key findings from research on social-emotional learning (SEL), its effect on learning outcomes, and best practices for integrating SEL into educational settings. A list of additional resources on SEL is also provided.

Managing Classroom Behaviors Using an RTI/MTSS Framework by Jim Wright is posted at Intervention Central. The guide describes evidence-based strategies for Tier 1 behaviors. "It includes specific interventions for non-compliance, defiance, inattention, hyperactivity, and anxiety, along with advice on managing behavioral outbursts."

Positive Discipline Tools for Teachers: Effective Classroom Management for Social, Emotional, and Academic Success by Jane Nelsen and Kelly Gfroerer (2017). The authors present the Positive Discipline model "for teachers who want to foster creative problem-solving within their students, giving them the behavioral skills they need to understand and process what they learn." |
All Learning Is Social and Emotional: Helping Students Develop Essential Skills for the Classroom and Beyond by Nancy Frey, Douglas Fisher, and Dominique Smith (2019). The authors present a five-part model of SEL that includes 33 competencies. They include real-life examples of opportunities for SEL within the K-12 academic curriculum. |

As you strive to learn methods for presenting math concepts to students, don't neglect your need to connect math to your learners' everyday lives. Consider Scholastic MATH, an award-winning math magazine with 10 issues each year designed specifically for middle school and early high school students. Each issue also includes articles on real-world uses of math and how math is used in various careers.

Plus is an internet magazine which is free for
educational and non-commercial purposes. It would appeal to learners aged
about 15 and above. It aims to introduce readers to the beauty and the practical applications
of mathematics. You'll find "articles, which describe
applications of maths to real-world problems, games, and
puzzles; reviews of popular maths books and events; a news
section, showing how recent news stories were often based on
some underlying piece of maths that never made it to the
newspapers; a puzzle for you to sharpen your wits against; a
lucky dip of mathematical curiosities; and opinions on various
maths-related topics and news stories. [*Plus* also has]
a regular interview with someone in a maths-related career,
showing the wide range of uses maths gets put to in the real
world." (About *Plus* section)

CT4ME has additional resources to connect math to everyday life.

The
Mathematics Educators Stack Exchange "is a question and answer site
for those involved in the field of teaching mathematics. It's built and
run *by you* as part of the Stack Exchange network of Q&A
sites." With your help, the site "is working together to build a library
of detailed answers to every question about teaching mathematics."
The site is totally free and no registration is required. Anyone
can ask a question, anyone can answer, and the best answers are voted up
and rise to the top.

ERIC (Education Resources Information Center) is sponsored by the U.S. Department of Education, Institute of Education Sciences. ERIC's search can be restricted to peer-reviewed only or full text articles. Search by descriptors such as mathematics instruction, mathematics achievement, mathematics education, academic achievement, teaching methods, program effectiveness, and more. You can search by source, author, publication date, publication type, education level, and audience. There is a Thesaurus that has multiple subcategories and related mathematical terms. ERIC offers an extensive collection for journal articles, books, research syntheses, conference papers, technical reports, policy papers, and other education-related materials. Note: Your might be interested in a history of ERIC: 50 Years of ERIC: 1964-2014.

isbn.nu
has mathematics books at all levels. Use search phrases such as
*mathematics study teaching secondary* or *
mathematics
study teaching elementary*. This site will then link you to
a resource for purchasing the book.

National Academies Press has over 4,000 books
online, which you can read for free. For example, math
educators might be interested in
*How
Students Learn: History, Mathematics, and Science in the Classroom*
(2005) by Committee on How People Learn, A Targeted Report for
Teachers, Center for Studies on Behavior and Development, National
Research Council.

**National Council of Teachers of Mathematics**:
Educators might be particularly interested in the following books.

**Implementing the Common Core State Standards through Mathematical Problem Solving**is a series of books available by grade bands: K-2, 3-5, 6-8, and high school.- Principles to Actions: Ensuring Mathematical Success for All (2014) addresses "What it will take to turn the opportunity of the Common Core into reality in every classroom, school, and district." You'll find "a research-based description of eight essential Mathematics Teaching Practices" and more.

See other Math Methodology pages:

Instruction--Essay, Assessment and Curriculum: Content and Mapping