This document provides definitions and overviews of key math concepts including universal design for learning, differentiated instruction, and multisensory learning. It discusses common signs of math challenges and strategies for assessment and intervention. An overview of the Stages Math app and intervention kit is provided, highlighting features for accessibility, scaffolding, feedback and record keeping. Research references on math disabilities and effective instructional strategies are also included.
This document provides an overview of a presentation on multisensory access to math. It defines universal design for learning, differentiated instruction, and multisensory learning. It discusses common math challenges and signs that may indicate a math difficulty. The presentation demonstrates the Stages Math app and intervention kit, which use a multisensory approach through manipulatives, visual supports, and adjustable settings to meet diverse learner needs in math.
The document discusses the importance of developing conceptual understanding in mathematics teaching and learning. It provides examples of activities and problems that promote conceptual understanding over rote memorization of procedures. Teachers are encouraged to assess for conceptual understanding and recognize its presence or absence. Conceptual knowledge allows students to make connections and think flexibly rather than just follow recipes to solve problems.
This document provides guidance on best practices for math instruction using the Common Core Mathematical Practices and district curriculum. It emphasizes integrating the Habits of Mind and Interaction into daily math lessons through strategies like using a high-level problem of the day, facilitating student math talks, and creating public records of strategies and representations. Teachers are advised to plan lessons that encourage productive struggle and facilitate students discovering mathematical ideas on their own.
This lesson plan template provides details for a 30-45 minute math lesson for 1st grade students on comparing whole numbers up to 100 using symbols like <, >, or =. Students will use cardboard cutouts of blocks in groups of tens and ones to demonstrate comparisons. An instructional PowerPoint will guide students through examples of comparing numbers and determining which symbol applies. Students will then practice comparing numbers on the online program IXL Math. The lesson will close by reviewing the key vocabulary and homework assignment.
The document discusses developing primary teachers' math skills through professional development programs. It addresses the concept of number sense, which refers to a well-organized conceptual understanding of numbers that allows one to solve problems beyond basic algorithms. Examples are provided for dot arrangements and personal numbers to illustrate number sense strategies. Arithmetic proficiency is defined as achieving fluency through calculation with understanding. The benefits of improved teacher math skills are outlined as developing students' number sense, fluency, conceptual understanding, problem solving and engagement. Examples are given for teaching subtraction and extending students. The importance of understanding over procedural fluency alone is emphasized.
Putting the Mathematical Practices Into Actiondlschulz
This document outlines an agenda for a professional development session focused on implementing the Standards for Mathematical Practice. It includes discussions and activities to help teachers understand each standard and strategies for bringing the standards into their classrooms. The session aims to help teachers explore how to make students active problem solvers, encourage mathematical reasoning and modeling, and use tools strategically when solving problems. Sample problems and templates are provided to demonstrate ways to incorporate the standards into instruction.
Your Math Students: Engaging and Understanding Every DayDreamBox Learning
The most important and challenging aspect of daily planning is to regularly—and yes, that means every day—create, adapt, locate, and consider mathematical tasks that are appropriate to the developmental learning needs of each student. A concern Francis (Skip) Fennell often shares with teachers is that many of us can find or create a lot of “fun” tasks that are, for the most part, worthless in regards to learning mathematics. Mathematical
tasks should provide a level of demand on the part of the student that ensures a focus on understanding and involves them in actually doing mathematics.
This document provides an overview of a presentation on multisensory access to math. It defines universal design for learning, differentiated instruction, and multisensory learning. It discusses common math challenges and signs that may indicate a math difficulty. The presentation demonstrates the Stages Math app and intervention kit, which use a multisensory approach through manipulatives, visual supports, and adjustable settings to meet diverse learner needs in math.
The document discusses the importance of developing conceptual understanding in mathematics teaching and learning. It provides examples of activities and problems that promote conceptual understanding over rote memorization of procedures. Teachers are encouraged to assess for conceptual understanding and recognize its presence or absence. Conceptual knowledge allows students to make connections and think flexibly rather than just follow recipes to solve problems.
This document provides guidance on best practices for math instruction using the Common Core Mathematical Practices and district curriculum. It emphasizes integrating the Habits of Mind and Interaction into daily math lessons through strategies like using a high-level problem of the day, facilitating student math talks, and creating public records of strategies and representations. Teachers are advised to plan lessons that encourage productive struggle and facilitate students discovering mathematical ideas on their own.
This lesson plan template provides details for a 30-45 minute math lesson for 1st grade students on comparing whole numbers up to 100 using symbols like <, >, or =. Students will use cardboard cutouts of blocks in groups of tens and ones to demonstrate comparisons. An instructional PowerPoint will guide students through examples of comparing numbers and determining which symbol applies. Students will then practice comparing numbers on the online program IXL Math. The lesson will close by reviewing the key vocabulary and homework assignment.
The document discusses developing primary teachers' math skills through professional development programs. It addresses the concept of number sense, which refers to a well-organized conceptual understanding of numbers that allows one to solve problems beyond basic algorithms. Examples are provided for dot arrangements and personal numbers to illustrate number sense strategies. Arithmetic proficiency is defined as achieving fluency through calculation with understanding. The benefits of improved teacher math skills are outlined as developing students' number sense, fluency, conceptual understanding, problem solving and engagement. Examples are given for teaching subtraction and extending students. The importance of understanding over procedural fluency alone is emphasized.
Putting the Mathematical Practices Into Actiondlschulz
This document outlines an agenda for a professional development session focused on implementing the Standards for Mathematical Practice. It includes discussions and activities to help teachers understand each standard and strategies for bringing the standards into their classrooms. The session aims to help teachers explore how to make students active problem solvers, encourage mathematical reasoning and modeling, and use tools strategically when solving problems. Sample problems and templates are provided to demonstrate ways to incorporate the standards into instruction.
Your Math Students: Engaging and Understanding Every DayDreamBox Learning
The most important and challenging aspect of daily planning is to regularly—and yes, that means every day—create, adapt, locate, and consider mathematical tasks that are appropriate to the developmental learning needs of each student. A concern Francis (Skip) Fennell often shares with teachers is that many of us can find or create a lot of “fun” tasks that are, for the most part, worthless in regards to learning mathematics. Mathematical
tasks should provide a level of demand on the part of the student that ensures a focus on understanding and involves them in actually doing mathematics.
grade 1 representation and making connectionssusan70
The document provides guidance on planning lessons using the backwards design approach. It discusses identifying learning outcomes, determining assessments, planning instructional activities, and following up on student learning. Specifically, it outlines planning for two lessons on addition and subtraction to 10. The first lesson introduces representing number stories in different ways. The second focuses on fact families and connecting representations on a number line. Assessments include student discussions and representations of number stories and problems.
Helping Students Develop Mathematical Process Skills, Really?Kien Lim
This is pdf copy of the presentation given at the CAMT 2015 Conference in Houston.
Session Title (limit 60 characters, including spaces)
Session Description:
Recognizing the importance of College and Career Readiness, TEKS has included the Mathematical Process Standards. Nationally, the Mathematical Practices Standards is in the Common Core. How can we help our students develop these process skills? Is it realistic? Is there an essence underlying all these standards? If yes, what is it? What need to change? Are you game for it? What support do you need? Examples of tasks that make students think will be shared.
The document discusses alternative strategies for teaching addition and subtraction to children, rather than solely using standard algorithms. It argues that children's invented strategies are more meaningful and develop a deeper conceptual understanding than rote memorization of procedures. The document provides examples of children's invented strategies and discusses how teachers can support the development and flexible use of strategies over solely teaching traditional algorithms.
This document provides teaching ideas and resources for problem solving in the GCSE mathematics classroom. It discusses developing a problem solving environment, asking open-ended questions, modeling problem solving techniques, using diagrams, and the importance of regular mini-tests and recalling basics to help students learn. A variety of problem solving resources and example problems are also presented.
Low Fact Fluency and Writing About Math by Marybeth Rotertmarybethrotert
The document discusses a study examining whether second grade students with low math fact fluency can demonstrate conceptual understanding by writing about math problems. It provides background on the importance of math fact fluency and standards calling for students to explain their mathematical thinking. A literature review found that writing about math improved student understanding but did not specify impacts on fact fluency. The author describes giving a pre-test on addition/subtraction facts to 5 students, having them complete worksheets writing about math problems over 10 days, and planning a post-test to measure growth in fact fluency.
The document discusses using calculators in elementary mathematics education. It notes that calculators can help students focus on concepts rather than calculations, but others argue it prevents learning of basic facts. The document advocates restricting calculator use until students have mastered written calculations, but allowing occasional use for projects. When used, students should learn to estimate answers and understand which operations to use. Suggested calculator activities include exploring patterns and place value.
The document discusses strategies for teaching mathematics to students with disabilities in an inclusive classroom setting. It covers recommendations from the National Council of Teachers of Mathematics for establishing principles of equity, curriculum, teaching, learning, assessment, and technology use. Some key strategies discussed for different math concepts include using manipulatives and visual representations, explicit instruction of strategies, focusing on big ideas rather than details, providing additional time and practice opportunities, and employing multi-step problem-solving approaches. The goal is to make math instruction accessible and meaningful for all students.
This is a presentation to help students who always become feared during Maths Exam. This presentation tells about what are the elements that initiates this phobia and what are the possible ways by both the teachers and the students to overcome such Phobia. This presentation also contains Vedic mathematics tricks that helps you to do calculations easily
The document discusses effective tools for formative assessment that teachers can use to evaluate student learning and provide feedback. It provides examples of various assessment tools including observations, questioning, exit/admit slips, visual representations, graphic organizers, peer and self-assessments, kinesthetic assessments, and laundry day. The tools are meant to give teachers insights into students' understanding beyond typical tests and provide opportunities for students to reflect on their own learning.
Exit cards are short written responses students complete at the end of a class to provide teachers feedback on learning. Teachers review the exit cards which takes only a few minutes to assess student understanding and plan differentiated instruction. Exit cards are a formative assessment strategy that helps teachers meet the diverse needs of learners.
Learning & Teaching GCSE MathematicsColleen Young
This document provides teaching resources and ideas for GCSE Mathematics. It includes information on specification changes, assessment objectives, teaching guidance from exam boards, and problem solving strategies. Sample exam questions, topic tests, and diagnostic questions are provided. Additional resources on areas like extension materials, revision activities, and developing recall are also referenced.
The document provides an overview of the key aspects of the Everyday Mathematics curriculum. It discusses how the curriculum teaches mathematical concepts in a spiral approach, emphasizes conceptual understanding and basic skills, and explores a broad range of mathematics. It also notes how Everyday Math aligns with the Common Core standards. The document outlines several program highlights and routine types used in the curriculum, including daily routines, games, math boxes, and math modeling. It provides guidance on homework, fact fluency, assessment, intervention, and creating an engaging learning environment for students.
Presentation Math Workshop#May 25th New Help our teachers understa...guest80c0981
This is presented by a Math teacher,in Army Burn Hall College For Girls ,Abbottabad.
The target group was the teachers of school section. There were certain activities also performed an demonstrated in order to introduce new teaching methodologies and to prepare our teachers to meet the need of the day.
Umber
This document discusses research findings on students' numerical literacy and ability to solve word problems. The research found that most students in years 1 and 2 answered a word problem by simply adding the given numbers instead of recognizing it was not asking for a calculation. A year 4 student was able to correctly solve another problem by realizing the numbers did not add up to the answer and instead divided the numbers. The document advocates for teaching students mathematical processes like questioning, applying strategies, communicating, reasoning, and reflecting as outlined in Newman's model to develop true numeracy over rote learning skills.
Plan effective lesson endings to assess student learning, identify misconceptions, and determine next steps. Suggestions include having students summarize content in decreasing levels of detail, complete diagnostic questions or mini-tests for self-checks, explain mistakes, clarify homework, or allow students to summarize or thank for the lesson. Endings can also set expectations for the start of the next lesson.
Standards of Mathematical Practice and Close Reading Dawn Little
This document discusses how questioning can help students comprehend math concepts. It begins by noting research showing teachers ask 300-400 questions per day, and that questioning structures the classroom environment and how students learn. The document then discusses how questioning supports the Common Core State Standards for reading and the standards for mathematical practice. It provides examples of "thick" and "thin" questions and an activity where students sort questions. The document also discusses using student discourse and metacognition to support questioning and problem solving. It concludes by asking teachers to identify next steps for applying these questioning strategies.
How To Solve A Math Problem!-new and improvedTaleese
This document outlines a 7-step process for solving math problems:
1) Read the problem carefully multiple times to understand what is being asked.
2) Identify what needs to be found and look for clues about the operation(s) needed like addition, subtraction, multiplication, or division.
3) Select an operation and numbers from the problem to try solving it. Even if incorrect, trying something is better than doing nothing.
4) Solve the problem using the selected operation and numbers.
5) Check that the answer makes logical sense.
6) Ensure any multi-part problems are fully answered.
7) Check the work by working backwards with inverse operations.
The document discusses effective strategies for guided math instruction to meet the individual needs of students. It recommends implementing flexible math groupings and targeting instruction based on formative assessments. Key aspects of guided math include problem solving, conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and a productive disposition towards math. Teachers should focus instruction on the five strands of proficiency: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition.
This document provides an overview of a workshop on integrating the 8 Mathematical Practices from the Common Core State Standards into K-2 mathematics teaching. It includes an introduction, pre-workshop survey, activities on writing story problems, teaching kindergarten all day, the 8 practices, and resources. Participants worked in groups to remodel story problems using the practices, and presented their work. Norms for classroom discussion were discussed. The goal was for teachers to learn to use the practices to develop deeper mathematical understanding in students.
The document discusses strategies for developing mental math skills in students. It outlines five core elements: using real-life contexts, mental flexibility, estimation, number discussion, and modeling strategies. Students are provided with a "number toolkit" of strategies to apply across their math learning. Teachers relate math questions to students' lives and use varied real-world contexts. The goal is to give students skills for life, learning, and work. Daily number talks and mental math are emphasized across the school. Formative assessments allow teachers to identify misconceptions and next steps.
Intelligent Adaptive Learning: A Powerful Element for 21st Century Learning &...DreamBox Learning
In this webinar, Dr. Tim Hudson shares insights about leveraging technology to improve student learning. At a time when schools are exploring “flipped” and “blended” learning models, it’s important to deeply understand how to design effective learning experiences, curriculum, and differentiation approaches. The quality of students’ digital learning experiences is just as important as the quality of their educational experiences inside the classroom. Having worked for over 10 years in public education as a teacher and administrator, Dr. Hudson has worked with students, parents, and teachers to improve learning outcomes for all students. As Curriculum Director at DreamBox Learning, he provides an overview of Intelligent Adaptive Learning, a next generation technology available to schools that uses sound pedagogy to tailor learning to each student’s unique needs. This webinar focuses on how administrators and teachers can make true differentiation a reality by focusing on learning goals and strategic use of technology.
The document discusses setting up small group numeracy instruction in the classroom. It recommends organizing students into purposeful small groups based on assessment data to provide targeted instruction. Suggested math stations that students can work at independently include practicing SNAP skills, developing fact fluency through games, using manipulatives, working on math technology programs or workbooks, and meeting with the teacher in small groups. Reflection is important to consolidate learning and promote growth mindset.
grade 1 representation and making connectionssusan70
The document provides guidance on planning lessons using the backwards design approach. It discusses identifying learning outcomes, determining assessments, planning instructional activities, and following up on student learning. Specifically, it outlines planning for two lessons on addition and subtraction to 10. The first lesson introduces representing number stories in different ways. The second focuses on fact families and connecting representations on a number line. Assessments include student discussions and representations of number stories and problems.
Helping Students Develop Mathematical Process Skills, Really?Kien Lim
This is pdf copy of the presentation given at the CAMT 2015 Conference in Houston.
Session Title (limit 60 characters, including spaces)
Session Description:
Recognizing the importance of College and Career Readiness, TEKS has included the Mathematical Process Standards. Nationally, the Mathematical Practices Standards is in the Common Core. How can we help our students develop these process skills? Is it realistic? Is there an essence underlying all these standards? If yes, what is it? What need to change? Are you game for it? What support do you need? Examples of tasks that make students think will be shared.
The document discusses alternative strategies for teaching addition and subtraction to children, rather than solely using standard algorithms. It argues that children's invented strategies are more meaningful and develop a deeper conceptual understanding than rote memorization of procedures. The document provides examples of children's invented strategies and discusses how teachers can support the development and flexible use of strategies over solely teaching traditional algorithms.
This document provides teaching ideas and resources for problem solving in the GCSE mathematics classroom. It discusses developing a problem solving environment, asking open-ended questions, modeling problem solving techniques, using diagrams, and the importance of regular mini-tests and recalling basics to help students learn. A variety of problem solving resources and example problems are also presented.
Low Fact Fluency and Writing About Math by Marybeth Rotertmarybethrotert
The document discusses a study examining whether second grade students with low math fact fluency can demonstrate conceptual understanding by writing about math problems. It provides background on the importance of math fact fluency and standards calling for students to explain their mathematical thinking. A literature review found that writing about math improved student understanding but did not specify impacts on fact fluency. The author describes giving a pre-test on addition/subtraction facts to 5 students, having them complete worksheets writing about math problems over 10 days, and planning a post-test to measure growth in fact fluency.
The document discusses using calculators in elementary mathematics education. It notes that calculators can help students focus on concepts rather than calculations, but others argue it prevents learning of basic facts. The document advocates restricting calculator use until students have mastered written calculations, but allowing occasional use for projects. When used, students should learn to estimate answers and understand which operations to use. Suggested calculator activities include exploring patterns and place value.
The document discusses strategies for teaching mathematics to students with disabilities in an inclusive classroom setting. It covers recommendations from the National Council of Teachers of Mathematics for establishing principles of equity, curriculum, teaching, learning, assessment, and technology use. Some key strategies discussed for different math concepts include using manipulatives and visual representations, explicit instruction of strategies, focusing on big ideas rather than details, providing additional time and practice opportunities, and employing multi-step problem-solving approaches. The goal is to make math instruction accessible and meaningful for all students.
This is a presentation to help students who always become feared during Maths Exam. This presentation tells about what are the elements that initiates this phobia and what are the possible ways by both the teachers and the students to overcome such Phobia. This presentation also contains Vedic mathematics tricks that helps you to do calculations easily
The document discusses effective tools for formative assessment that teachers can use to evaluate student learning and provide feedback. It provides examples of various assessment tools including observations, questioning, exit/admit slips, visual representations, graphic organizers, peer and self-assessments, kinesthetic assessments, and laundry day. The tools are meant to give teachers insights into students' understanding beyond typical tests and provide opportunities for students to reflect on their own learning.
Exit cards are short written responses students complete at the end of a class to provide teachers feedback on learning. Teachers review the exit cards which takes only a few minutes to assess student understanding and plan differentiated instruction. Exit cards are a formative assessment strategy that helps teachers meet the diverse needs of learners.
Learning & Teaching GCSE MathematicsColleen Young
This document provides teaching resources and ideas for GCSE Mathematics. It includes information on specification changes, assessment objectives, teaching guidance from exam boards, and problem solving strategies. Sample exam questions, topic tests, and diagnostic questions are provided. Additional resources on areas like extension materials, revision activities, and developing recall are also referenced.
The document provides an overview of the key aspects of the Everyday Mathematics curriculum. It discusses how the curriculum teaches mathematical concepts in a spiral approach, emphasizes conceptual understanding and basic skills, and explores a broad range of mathematics. It also notes how Everyday Math aligns with the Common Core standards. The document outlines several program highlights and routine types used in the curriculum, including daily routines, games, math boxes, and math modeling. It provides guidance on homework, fact fluency, assessment, intervention, and creating an engaging learning environment for students.
Presentation Math Workshop#May 25th New Help our teachers understa...guest80c0981
This is presented by a Math teacher,in Army Burn Hall College For Girls ,Abbottabad.
The target group was the teachers of school section. There were certain activities also performed an demonstrated in order to introduce new teaching methodologies and to prepare our teachers to meet the need of the day.
Umber
This document discusses research findings on students' numerical literacy and ability to solve word problems. The research found that most students in years 1 and 2 answered a word problem by simply adding the given numbers instead of recognizing it was not asking for a calculation. A year 4 student was able to correctly solve another problem by realizing the numbers did not add up to the answer and instead divided the numbers. The document advocates for teaching students mathematical processes like questioning, applying strategies, communicating, reasoning, and reflecting as outlined in Newman's model to develop true numeracy over rote learning skills.
Plan effective lesson endings to assess student learning, identify misconceptions, and determine next steps. Suggestions include having students summarize content in decreasing levels of detail, complete diagnostic questions or mini-tests for self-checks, explain mistakes, clarify homework, or allow students to summarize or thank for the lesson. Endings can also set expectations for the start of the next lesson.
Standards of Mathematical Practice and Close Reading Dawn Little
This document discusses how questioning can help students comprehend math concepts. It begins by noting research showing teachers ask 300-400 questions per day, and that questioning structures the classroom environment and how students learn. The document then discusses how questioning supports the Common Core State Standards for reading and the standards for mathematical practice. It provides examples of "thick" and "thin" questions and an activity where students sort questions. The document also discusses using student discourse and metacognition to support questioning and problem solving. It concludes by asking teachers to identify next steps for applying these questioning strategies.
How To Solve A Math Problem!-new and improvedTaleese
This document outlines a 7-step process for solving math problems:
1) Read the problem carefully multiple times to understand what is being asked.
2) Identify what needs to be found and look for clues about the operation(s) needed like addition, subtraction, multiplication, or division.
3) Select an operation and numbers from the problem to try solving it. Even if incorrect, trying something is better than doing nothing.
4) Solve the problem using the selected operation and numbers.
5) Check that the answer makes logical sense.
6) Ensure any multi-part problems are fully answered.
7) Check the work by working backwards with inverse operations.
The document discusses effective strategies for guided math instruction to meet the individual needs of students. It recommends implementing flexible math groupings and targeting instruction based on formative assessments. Key aspects of guided math include problem solving, conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and a productive disposition towards math. Teachers should focus instruction on the five strands of proficiency: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition.
This document provides an overview of a workshop on integrating the 8 Mathematical Practices from the Common Core State Standards into K-2 mathematics teaching. It includes an introduction, pre-workshop survey, activities on writing story problems, teaching kindergarten all day, the 8 practices, and resources. Participants worked in groups to remodel story problems using the practices, and presented their work. Norms for classroom discussion were discussed. The goal was for teachers to learn to use the practices to develop deeper mathematical understanding in students.
The document discusses strategies for developing mental math skills in students. It outlines five core elements: using real-life contexts, mental flexibility, estimation, number discussion, and modeling strategies. Students are provided with a "number toolkit" of strategies to apply across their math learning. Teachers relate math questions to students' lives and use varied real-world contexts. The goal is to give students skills for life, learning, and work. Daily number talks and mental math are emphasized across the school. Formative assessments allow teachers to identify misconceptions and next steps.
Intelligent Adaptive Learning: A Powerful Element for 21st Century Learning &...DreamBox Learning
In this webinar, Dr. Tim Hudson shares insights about leveraging technology to improve student learning. At a time when schools are exploring “flipped” and “blended” learning models, it’s important to deeply understand how to design effective learning experiences, curriculum, and differentiation approaches. The quality of students’ digital learning experiences is just as important as the quality of their educational experiences inside the classroom. Having worked for over 10 years in public education as a teacher and administrator, Dr. Hudson has worked with students, parents, and teachers to improve learning outcomes for all students. As Curriculum Director at DreamBox Learning, he provides an overview of Intelligent Adaptive Learning, a next generation technology available to schools that uses sound pedagogy to tailor learning to each student’s unique needs. This webinar focuses on how administrators and teachers can make true differentiation a reality by focusing on learning goals and strategic use of technology.
The document discusses setting up small group numeracy instruction in the classroom. It recommends organizing students into purposeful small groups based on assessment data to provide targeted instruction. Suggested math stations that students can work at independently include practicing SNAP skills, developing fact fluency through games, using manipulatives, working on math technology programs or workbooks, and meeting with the teacher in small groups. Reflection is important to consolidate learning and promote growth mindset.
This document provides a Stage 1 Understanding by Design template for a 2nd grade mathematics unit on multiplication titled "Marvelous Multiplication". The 3-week unit focuses on helping students understand multiplication as repeated addition and using arrays, skip counting, and multiplication tables to find products. The template identifies the relevant content standards and divides the unit into understandings, essential questions, and knowledge and skills that students will gain. It provides examples of each to guide instruction and assesses student learning.
Here are two other multiplication problems that have the same answer as 18 x 4 and 4 x 18:
9 x 8
8 x 9
Both of these multiplication problems have an answer of 72, just like 18 x 4 and 4 x 18.
The document outlines the learning outcomes, assessment strategies, instructional plan, and assessment of student learning for a math lesson on addition of whole numbers up to 1000. It describes representing addition strategies concretely, pictorially, and symbolically, as well as estimating sums. The plan involves using place value cards, ten frames, and a tens-ones mat to build numbers and add with regrouping. Student understanding will be assessed through observation, problem solving, and explaining strategies.
This document outlines a professional development session for teachers on implementing changes to the teaching of mathematics at RPPS. It introduces the "Mathematician's Model" which involves dividing math lessons into four "toolbox lessons" focusing on developing problem solving strategies and mental math skills, and two "Be a Mathematician" lessons using rich, open-ended tasks. Examples of effective rich tasks are provided, emphasizing that they should be problem-based, inquiry-driven, collaborative, and engage students through hands-on experiences. The session celebrates mathematicians as role models and quotes Paul Halmos emphasizing experimentation and problem-solving over memorization of facts.
The document discusses alternative strategies for teaching addition and subtraction to children, rather than solely using standard algorithms. It argues that children's invented strategies are more meaningful and develop a deeper conceptual understanding than rote memorization of procedures. The document provides examples of children's invented strategies and discusses how teachers can support students in developing increasingly efficient strategies over time through the use of models, story problems, and sharing strategies.
Basic Guide of -Kindergarten math program imathscanada
Building a strong foundation in math from an early age is crucial for a child’s academic success. A well-designed kindergarten math program curriculum can provide young learners with the necessary skills and knowledge to excel in math and set them up for future success. In this blog, we will explore what a kindergarten math program curriculum should include, with a focus on math learning centers and math for preschoolers.
5th grade mp and problem solving intro 8.28.12Laura Chambless
This document provides an overview of a workshop on integrating the 8 Mathematical Practices into 5th grade problem solving. It includes an introduction, learning target, descriptions of the practices with student-friendly language, example story problems and remodeling tasks, and discussions of setting up mathematical tasks, supporting student exploration, and sharing solutions. Teachers complete pre-and post-surveys, work in groups to remodel story problems, and identify resources for bringing the practices into their own teaching. The goal is for teachers to develop skills in using the practices to help students build deeper mathematical understanding.
The document discusses key aspects of the mathematical process. It defines mathematical process as thinking, reasoning, calculation, and problem solving using mathematical methods. The main components discussed are reasoning, logical thinking, problem solving, and making connections. Reasoning involves making conjectures, investigating findings, and justifying conclusions. Problem solving requires applying previously learned skills to new situations. Problem posing encourages students to write and solve their own problems to improve problem solving abilities.
The document discusses assistive technology for mathematics instruction. It outlines student challenges
related to visual processing, physical access, math facts, and multiple steps. Environmental factors like
changes to math curriculum and ensuring accessible materials are also addressed. A continuum of tools and
strategies is provided to support math learning. The SETT framework is presented to guide assistive
technology decision making by considering the student, tasks, environment, and tools.
This document discusses integrating mathematics with other subjects and effective teaching strategies for mathematics. It describes how math can be integrated into subjects like science, social studies, literacy, and arts. Six teaching strategies for math are outlined: making conceptual understanding a priority, setting meaningful homework, using cooperative learning, strategic questioning, focusing on real problem-solving and reasoning, and using mixed modes of assessment. The conclusion emphasizes that integrating math into other subjects helps students understand math concepts better and see real-world applications. Effective teaching approaches can improve math learning outcomes.
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.
Touch Math is a program that teaches students to count and do basic math operations by touching specific points on printed numerals. It covers topics from counting to pre-algebra. Each numeral has a set number of touch points corresponding to its value. The program provides lesson plans, teaching aids, and strategies to help students learn math concepts in a tactile way from an early age through grade 3 or as a supplement for students with special needs. Some note it is not a complete math program and students may struggle later if the Touch Math method is not continued to be used.
The document provides an overview of the key aspects of the Everyday Mathematics curriculum. It discusses how the curriculum teaches mathematical concepts in a spiral approach, emphasizes conceptual understanding and basic skills, and explores a broad range of mathematics. It also notes how Everyday Math aligns with the Common Core standards. The document outlines several program highlights and routine types used in the curriculum, including daily routines, games, math boxes, and math modeling. It provides guidance on homework, fact fluency, assessment, intervention, and creating an engaging learning environment for students.
The document discusses how mathematics education has changed with the Common Core standards and provides resources to help parents assist their children. It explains that the Common Core focuses on conceptual understanding, problem solving and real-world applications rather than memorization and procedures. It recommends that parents ask open-ended questions, support homework, incorporate math into daily life and use online interactive lessons and tools. The document lists several free websites that provide math content, practice and support for parents and students.
Empowering Pre-Service & New Math Teachers to Use the Common Core Practice St...DreamBox Learning
How prepared are the K-12 teachers of tomorrow to inspire the next generation of young mathematicians? In this webinar for the edWeb.net Adaptive Math Learning community, attendees learned how essential it is for pre-service teachers to learn, develop, and model the Standards for Mathematical Practice to improve learning for their future students. Ben Braun, Associate Professor of Mathematics at the University of Kentucky, and Tim Hudson, Senior Director of Curriculum Design at DreamBox Learning, discussed ways to ensure that pre-service teachers start their careers understanding how mathematical proficiency requires more than simply content knowledge. Tim and Ben shared ideas for K-12 school leaders and mentor teachers who are responsible for new teacher induction, as well as, implications for college and university faculty teaching both math methods and content courses. They also discussed potential disconnects between pre-service content and methods courses and also eventual in-service expectations, while providing examples of math problems to engage pre-service and new teachers. View the webinar to better understand how to use the Standards for Mathematical Practice.
This document provides an overview of using worksheets in the classroom and making them accessible for students with disabilities using the GoWorksheet Maker app. It discusses the benefits of worksheets, challenges of accessibility, and features of the GoWorksheet Maker app which allows teachers to import worksheets and make them interactive for students on iPads through options like text-to-speech, answer fields, and adaptive tools. The document also provides a case study example of how the app helped one student independently complete worksheets and highlights resources like curriculum kits and training materials available for the app.
Stages has been providing assistive technology and resources since 1999. It offers a systematic framework to assess learners, select appropriate materials, integrate tools into instruction, and track learner progress. The framework involves 5 steps: 1) read the Stages book, 2) assess the learner, 3) observe and collect data, 4) check material recommendations, and 5) integrate tools into daily lessons. Stages software and apps help implement this process through features like universal access, adjustable settings, and data reporting tools. The goal is to design individualized learning and continually compile evidence of progress toward alternate assessment goals.
This document provides an overview of the Stages framework, a 5-step process for designing learning and selecting educational materials for individuals with cognitive or language delays. The 5 steps are: 1) read the Stages book, 2) assess the learner, 3) observe and collect learner performance data, 4) check materials recommendations, and 5) integrate tools into daily instruction. The document describes the components of each step, including assessment activities, observation forms, apps, software, and strategies for tracking learner progress and generating reports.
Stages software has been providing assistive technology and educational tools since 1999. Major milestones include the initial publication of instructional materials in book form, beginning of software development in 2000, and the release of apps and tools compatible with iPads in recent years. The Stages framework is a 5-step process that involves reading instructional materials, assessing learners, collecting performance data, selecting appropriate tools and materials, and integrating those tools into daily lessons. Stages tools like the assessment software, apps, and reporting features aim to individualize instruction and track progress toward IEP goals for students with cognitive or language delays.
The document discusses assistive technology (AT) in the classroom. It defines AT as any item or equipment that helps students with disabilities access the curriculum. When AT is integrated into the classroom, it allows students multiple means to complete their work. The document provides examples of different types of AT for areas like computer access, writing, reading, and more. It also discusses how AT benefits all students and how teachers can make their classrooms more conducive to AT.
The document summarizes the history, goals, design, research, and efficacy of Lexia Learning Systems, a pioneer in technology-based reading instruction. Founded in 1984, Lexia aims to build foundational reading skills through individualized practice. Research shows gains for students in grades PreK-3 and middle school, particularly low performers. Ongoing studies examine outcomes for bilingual students.
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This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
3. Presentation Overview
• Definitions: UDL and Differentiated Instruction,
multisensory learning
• Overview of math challenges
• Brief overview math intervention
• NCTM listserv comments = real world implementation
• Stages Math: Number Sense - features
• Stages Math Intervention Kit
• Stages Math: Number Sense – demo
• Hands-on Stations
4. Definition - UDL
• Multiple means of representation, to give learners various ways
of acquiring information and knowledge
• Multiple means of expression, to provide learners alternatives for
demonstrating what they know
• Multiple means of engagement, to tap into learners' interests, offer
appropriate challenges, and increase motivation
5. Definition - UDL
• Based on creating flexible goals, methods, materials, and
assessments that consider diversity.
• Centers the need for multiple approaches to meet the needs of
diverse learners
• Mirrors the universal design movement in architecture (curb
cuts, and close-captioned television—all universally designed
to accommodate a wide variety of users)
• Features that support challenges benefit everyone.
• Uses technology's power and flexibility to make education more
inclusive and effective for all
6. Definition
Differentiated Instruction
• Strategies that enable all students to participate and make
progress in the general curriculum
• Educators provide additional support to students who need
it during regular instruction
• Facilitates being able to individualize instruction for a
diverse group
7. Definition
Differentiated Instruction
• Can be enhanced with the use of technology scaffolds
• Technology scaffolds increase teacher capacity to
individualize instruction
• Especially useful in support of learners with math,
reading or writing difficulties
8. Definition
Multisensory Learning
• Use many sensory areas to activate brain
• grow student engagement
• build student interest (fun)
• activate prior knowledge while building new concepts
• create associations between new learning and memory
9. Definition
Multisensory Learning
• connect learning to language hearing own or the
teacher's/parent’s voice (auditory)
• facilitates development of new meaning through
multiple representations, associate new concepts
with memory (visual)
• build meaning and memory as hands manipulate
objects to build understanding in numeracy,
place value, basic operations, fractions (tactile)
10. Make Your Own Math for
Multisensory Learning
• Use cardboard, markers and scissors to make your own Cuisenaire rods
or pattern blocks
• Food for fractions (pizza, corn chips...)
• Egg cartons for sorting, counting and place value
Sources
“Math Toolbox in Every Home” http://mathcats.org/
Printable instructions for making and using manipulatives
“15 Homemade Math Manipulatives”
http://theendinmind.net/15-homemade-math-manipulatives-2/
11. Math Challenges
• Learning challenges in mathematics are complex.
• There is no single mathematics challenge.
12. Math Challenges
• Students may be strong in some areas of math
and weak in others.
• From 6–7% of all students exhibit challenges
in one or more areas of math.
13. Math Challenges
• Some mathematics challenges are independent
of reading disability and some are not.
• Research about math challenges has progressed
more slowly than research about reading challenges.
14. Signs of a Math Challenge
• Has difficulty keeping track of numerical information
while counting.
• Forgets arithmetic facts or doesn’t remember as many.
• May use immature problem solving procedures.
15. Signs of a Math Challenge
• Has difficulty with the abstract concepts of time
and direction.
• When writing, reading and recalling numbers: adds,
substitutes, transposes, omits, and reverses numbers.
• Demonstrates poor mental math ability.
16. Signs of a Math Challenge
• Has difficulty keeping score during games; loses track
of whose turn it is.
• Unable to grasp and remember math concepts, rules,
formulas, sequence (order of operations), and basic
math facts.
• Gets lost or disoriented easily; may have a poor
sense of direction.
17. Signs of a Math Challenge
• Children with a math challenge can have one or both
of two memory problems:
1. Getting basic facts into long term memory
and accessing memorized facts.
2. Sifting through all the recalled memorized
facts for the relevant information; e.g.,
2 + 3 might evoke answers of 4, 5, or 6
18. Despite the signs of a math
challenge, a learner may:
• Show normal or accelerated language acquisition:
verbal, reading, writing.
• Have good visual memory for the printed word.
• Excel in other areas.
• Catch up; it may be a developmental delay and
not a more fundamental deficit.
19. Assessing Math Abilities
• Conduct a one-to-one mathematics interview.
• Note how the child does mathematics.
• Search for strategies that work or don’t work,
strengths and weaknesses.
20. Assessing Math Abilities
• Assess the full range of areas: computation, pattern
prediction, sorting, measuring, organizing space
with flexibility.
• Observe and note any verbalization, drawings,
asking for repeat of directions/question.
• Ask child to estimate answer before computing.
21. From the NCTM listserv…
"Strategically" indicates that students will select an appropriate
tool based on the task. For example, given 10 x 5 x 2, a student
might pick up a pencil, calculator or calculate the product
mentally. Providing opportunities for students to reflect on their
choices in terms of efficiency and effectiveness deepens their
understanding of their strategic choices. As teachers, we can use
students' tool selection to provide diagnostic information and help
us prepare other learning opportunities.
22. How to help students
with math challenges:
• Work to define the student’s strengths.
• Encourage students to estimate their answers
before they begin to work out the problem.
• Have students work together in small groups
to solve problems.
• Allow the use of calculators and
manipulative materials.
23. Use of calculators
Research has shown that using calculators
does not:
• promote laziness
• impede development of basic math skills
• create a dependency on technology
Instead it does:
• promote achievement
• improve problem solving skills
• increase understanding of mathematical ideas
Students retain more information and gain a better
attitude toward math.
24. To be successful…
Students should work toward:
• number sense mastery
• good problem solving strategies
• automaticity (recall of facts) this
allows
more brainpower to go toward
problem
solving (not spent on computing)
25. Students with number sense can:
• Count rationally past 100.
• Understand that the sequence of counting doesn’t
change.
• Count objects in any order.
• Know that last number named is total number.
• Count past difficult numbers (19, 29, 100).
• Count backwards, starting with any number.
• Skip count by 2s, 5s, and 10s.
• Relate basic addition and subtraction facts.
• Explain operation of multiplication.
• Explain place values through the hundreds.
26. A Letter to My Math Teacher:
• “I need instant answers and a chance to do the problem over once if I
get it wrong the first time.”
• “Problems written too closely together on the page cause me mental
confusion and distress.”
• “Please allow me more than the standard time to complete problems
and please check to see that I am free of panic (tears in my eyes,
mind frozen).”
• “If possible, please allow me to take the exam on a one-to-one basis
in your presence.”
• “I am not lazy, and I feel really smart in everything but math. That is
what frustrates me the most! Everything is easy for me to learn, but
Math makes me feel stupid! Please, do be patient with me, and
please do not give up on me!”
(source at end)
27. 10 Tips for Software Selection
for Math Instruction
by Beatrice C. Babbitt
1. The less clutter on the screen, the better.
2. Procedures should match those being
taught in school.
3. Choose modifiable software. Software
should allow for customized speed, number
of problems and instructional levels.
4. Choose software with small increments
between levels.
28. 10 Tips for Software Selection
for Math Instruction
5. Choose software with helpful feedback. Provide clues
to the correct answer.
6. Choose software that limits the number of wrong answers for a
single problem. Limit the number of attempts, give clues to the
correct answer, provide the correct answer, reintroduce that
same item at a later time.
7. Choose software with good record keeping capabilities.
29. 10 Tips for Software Selection
for Math Instruction
8. Choose software with built in instructional aids; e.g.,
counters, number lines, base ten blocks, hundreds
charts, or fraction strips.
9. Select software that simulates real-life solutions; e.g.,
multiple roads to a problem solution.
10. Remember that software is a learning tool – not
the total solution!
30. Highlights of Stages Math: Number
Sense iPad app or computer software
28 main activities within 9 key content areas of number sense
35. Highlights of Stages Math:
Number Sense
• Universal and Accessible design for both iPad and computer
mouse, keyboard, switch, touch screen; auditory scanning, text-to-speech, pointer with
dwell on computer
• Feedback for incorrect answers that builds learner understanding
• Scaffolding to support learner success
turn on or off prompting, graphical support, help buttons, etc.; talk boards for
classroom inclusion
• Adjustable settings you can save for each learner
• Record keeping and certificates
36. Karen’s Case Study
Third grade Student
• Cognitive Disabilities
• Dependent on prompts and adults
• Significant fine motor challenges
Stages Math was recommended and
implemented following an AT
Assessment and school-based
team meeting
37. Karen’s Case Study
Danielle D. Special educator reflections:
• Preparation
• Implementation
• Observations
• Next Steps
38. “When I give Hannah (not
her real name) choices, she
chooses
to use Stages Math!”
”It has given me
data that guides my
instruction. I can see
she needs to better
understand Math symbols
and
Math language.”
“I need to use it for
all my students!”
Mia - "I love that app! It's
very fun! It's just the
right level for me! I think
I want to play this every
time I get to do math
games!"
39.
40. Highlights of Stages Math
Intervention Kit
Look at Math Introductory Kit covers a wide range of concepts with a
120-lesson Instructor’s Guide, a heavily illustrated Student Book, and
a PDF for printouts.
41. From the NCTM listserv…
"I need help as it relates to the cognitive and physical tools being
used strategically."
This really got me thinking...
I did a little "Googling" and found this:
Three Ways to Use Appropriate Tools Strategically (Mathematical P
.
(Sandler mentions number bonds as a cognitive "tool.”)
42. Highlights of Stages Math
Intervention Kit
Look at Math Introductory Kit covers a wide
range of concepts with a 120-lesson Instructor’s
Guide, a heavily illustrated Student Book, and
a PDF for printouts.
Place Value Packaging is a
hands-on activity, requiring students
to use number pegs to solve place
value and addition problems.
43. From the NCTM listserv…
I am trying to wrap my head around the word "Strategically". I
need help as it relates to the cognitive and physical tools being
used strategically. Please help!!
I use place value blocks and an assortment of tools to illustrate
fractions. Many times the students play with the materials, such
as building towers. However, as we begin to learn about the
numbers with the tools, the towers disappear and the tools are
being used strategically to illustrate the concept, such as division
of fractions, regrouping, etc.
44. Explore YouTube…
Lots of expert/teacher/parent made exploration activities.
Place Value Introduction
Number Rock Place Value Song
45. Highlights of Stages Math
Intervention Kit
Look at Math Introductory Kit
covers a wide range of concepts with a
120-lesson Instructor’s Guide, a heavily
illustrated Student Book, and a PDF
for printouts.
Place Value Packaging is a hands-on
activity, requiring students to use
number pegs to solve place value and
addition problems.
Talking Calculator gives
students auditory feedback
when solving computations.
46. Highlights of Stages Math
Intervention Kit
Look at Math Introductory Kit covers a wide
range of concepts with a 120-lesson Instructor’s
Guide, a heavily illustrated Student Book, and a
PDF for printouts.
Place Value Packaging is a hands-on activity,
requiring students to use number pegs to solve
place value and addition problems.
Talking Calculator gives students auditory
feedback when solving computations.
Six laminated Day Planner Books
simplify daytime schedules.
47. Highlights of Stages Math
Intervention Kit
Look at Math Introductory Kit covers a wide range of concepts with
a 120-lesson Instructor’s Guide, a heavily illustrated Student Book,
and a PDF for printouts.
Place Value Packaging is a hands-on activity, requiring
students to use number pegs to solve place value and
addition problems.
Talking Calculator gives students auditory feedback
when solving computations.
Six laminated Day Planner Books simplify daytime schedules.
Hands-On Money provides an organized collection of realistic
bills and coins and 3 coin cubes.
48. From the NCTM listserv…
The problem with using manipulatives to teach numbers is that
the manipulatives do not have numbers on them. The teacher is
banking on the students understanding and remembering what is
said; but some students do not hear a lot of what is said. I made
a YouTube video that shows how to make and use
"manipulatives on paper" to effectively address this problem.
(Jeff Sandler, Mastery Learning Systems)
Learning to Count to 10 Using 10 Blocks Number Line
Learning to Count to 20 with Place Value Hands On Money
49. Highlights of Stages Math
Intervention Kit
Look at Math Introductory Kit covers a wide range of concepts with a 120-lesson
Instructor’s Guide, a heavily illustrated Student Book, and PDF for printouts.
Place Value Packaging is a hands-on activity, requiring students to use number
pegs to solve place value and addition problems.
Talking Calculator gives students auditory feedback when solving computations.
Six laminated Day Planner Books simplify daytime schedules.
Hands-On Money provides an organized collection of realistic bills, coins and
coin cubes.
TimeWheel™ a realistic clock
to help learn to tell time
50. Stages Math Intervention Kit =
multisensory access to math
• Universal Design – multiple means of representation, engagement
and expression
• Differentiate Instruction – variety of scaffolds
• Multisensory – manipulative materials
• Access –content accessible through digital interactions
51. Research References
“A Letter to My Math Teacher”, compiled by Renée M. Newman
http://www.dyscalculia.org/teacher.html
“Learning Disabilities in Mathematics”, by C. Christina Wright
http://www.ldonline.org/article/5947
“Mathematical Disabilities: What We Know and Don't Know”, by David C. Geary,
http://www.ldonline.org/article/5881
“Math Intervention: What Strategies Work for Struggling Learners” articles collected by Education Northwest
http://educationnorthwest.org/resources/mathematics-interventions-what-strategies-work-struggling-
learners-or-students-learning
“Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities”, by Russell Gersten
and David J. Chard
http://www.ldonline.org/article/5838
“Strategies for Teaching Math: What are the Facts?” by Carol H. Geller
http://www.ldworldwide.org/pdf/journal/2000/11-00_arithmetic.pdf
“Technology-Supported Math Instruction for Students with Disabilities”
by Hasselbring, Lott, and Zydney
http://209.61.229.180/library/resourcedocs/Tech-SupportedMathInstruction-FinalPaper_early.pdf
http://www.citeducation.org/mathmatrix/
“10 Tips for Software Selection for Math Instruction”, by Beatrice C. Babbitt http://www.ldonline.org/article/6243
52. URLs Demonstrated
Videos
“Three Ways to Use Appropriate Tools Strategically” blog by Jeff Sadlier
• https://www.sadlier.com/school/sadlier-math-blog/three-ways-to-use-appropriate-tools-strategically-math-
practice-5
“Place Value Introduction”
• https://www.youtube.com/watch?v=fshyCNqHIbw
“Number Rock Place Value Song”
• https://www.youtube.com/watch?v=a4FXl4zb3E4
“Learning to Count to 10 Using 10 Blocks Number Line”
• https://www.youtube.com/watch?v=ji-jsPbovv0&index=5&list=PLm4gYQg22haYidp4sISJMX_h4xC7gXKQ_
“Learning to Count to 20 with Place Value Hands On Money”
• https://www.youtube.com/watch?v=45yeM-
At9F4&index=4&list=PLm4gYQg22haYidp4sISJMX_h4xC7gXKQ_
Sources of Home Made Manipulatives
“Math Toolbox in Every Home”
• http://mathcats.org/
Printable instructions for making and using manipulatives
“15 Homemade Math Manipulatives”
• http://theendinmind.net/15-homemade-math-manipulatives-2/
53. Hands-On Stations
Station 1: iPads for Stages Math app – demo first
Station 2: Hands-on “Money”
Place Value Packaging
Talking Calculator
Hands-On Money with Coin Cubes
Station 3: Hands-on “Time”
TimeWheels
Day Planners
Look At Math (Teachers Guide
and Students Workbook)
Use this slide if your audience needs to have the slides as handouts. Post them to Slideshare so that they can be used but not copied.
NCTM identified 5 skill areas: Numbers and Operations; Algebra; Geometry; Measurement; Data Analysis and Probability. Our Stages Math addresses skills in the first area, Number and Operations.
Classic definition
Fine tuning ideas to incorporate
Teaching considerations are planned ahead placing a wide range of materials strategically within the environment. (Stages Math Intervention Kit)
Stages Math Intervention Kit
Give audience a “make your own” option right away to diffuse the tone of a “sales pitch”
refers to a child&apos;s fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons.
an increasingly heated controversy about how to teach mathematics but no disagreement that strategic instruction is key
concept of number sense is as important to mathematics learning as phonemic awareness has been to the reading research field
Needs to work on ability to represent the same number in multiple ways depending on the context and purpose of this representation.
Needs to understand that 1 + 12 = 12 + 1
Counting, 1 to 1 correspondence, quantifying
#2 means that if learners see the numbers 2 and 3, they may not pay attention or understand what they should do with those numbers, and so may come up with 4 (the next number in the sequence), 5 (their sum), or 6 (their product (multiplication)).
Reading the problem. Students are taught how to read mathematical problems, including using reading strategies to understand the problem (e.g., focusing on important information), developing mathematical vocabulary, and recognizing when they do not understand relationships among mathematical terms and quantitative concepts expressed in a problem.
Paraphrasing. Students are taught how to put the problem into their own words and convey meaning.
Visualizing. Students are taught to draw a representation or to make a mental image of the problem. Hypothesizing about problem solutions. Students are taught how to decide the number of operations that are needed to solve the problem, select and order the operations, and then to transform the information into correct equations and algorithms.
Estimating the answer. Students are taught how to stay focused on the type of outcome (e.g., number of yards rather than feet), and then how to predict the answer by using the information in the problem and their projected solution path.
Computing. Students are taught how to recall the correct procedures for working through the algorithms and the necessary math facts for accuracy.
Checking the problem. Students are taught how to check the mathematical problem solving process to ensure that they have understood the problem, accurately represented the problem, selected an appropriate solution path, and solved the problem correctly.
In the interview one focuses as intently on how the child does mathematics as on what or how correct they do it. It is essential to keep in mind that you are searching for what does work at the same time as you are probing to find out what doesn&apos;t work.
include the use of manipulatives, i.e. coins, base ten blocks, geoboards, cuisenaire rods, and tangrams. A calculator is an important tool and can be used to uncover the difference between comprehension and computation difficulties.
NCTM advocates and supports the integration of manipulative materials
Wouldn’t a multisensory calculator help lots of kids? Yes!
Researchers explored the devastating effects of the lack of automaticity in several ways. Essentially, they argued that the human mind has a limited capacity to process information, and if too much energy goes into figuring out what 9 plus 8 equals, little is left over to understand the concepts underlying multi-digit subtraction, long division, or complex multiplication.
http://www.dyscalculia.org/teacher.html
Stages Math, which you will see shortly, demonstrates all these key features.
Students who use appropriate technology persist longer, enjoy learning more, and make gains in math performance.
With software based on principles of Universal Design, students are able to access course materials in ways that are flexible and customizable. A central feature of UDL is its ability to adapt to students with different perceptual and cognitive needs.
Various forms of scaffolding is one of the primary ways software can be customized and aligned with a UDL approach
The student was a member of an substantially separate program for students with cognitive disabilities. She was included at the beginning of the school day and during specials. The student had a difficult time during periods of instruction and sometimes had meltdowns. She was dependent upon adults for most of her work. Stages math was recommended as part of an AT Assessment to promote independence during math work and the team agreed. She struggled with all aspects of Number Sense and other online resources were too visually distracting and could not be customized. Danielle, the special education teacher reported Hannahloved using Stages Math. She used it in the inclusion third grade classroom during math and Hannah was able to work on the iPad independently.
Danielle received Stages Math over the summer and was so excited to use it, she taught herself and then implemented it right at the start of the new school year. Two weeks later, I met with the entire team, including Hannah’s mom, and showed them how they could review the data. Danieele had discovered many of the features on her own. She observed that Hannah was engaged by Stages Math and was able to use it independently. Next steps – she was so excited with Stages Math, Danielle couldn’t wait to try it with other students. In addition, two other special education teachers wanted to get the app to use with their students! They saw the potential!
Mads, this is a note to you – the black ink shows a quote from a different student – the next steps were that two other teachers implemented it with their students (because of the gift codes). A different teacher, Shoshana, gave me the bottom quote that I just added. It came from Mia, a second grade student. (I tired to add another slide but the background doesn’’t copy for some reason).
This data shows one sitting. Data captured over time is pending.
Multiple means of engagement in the same skills aligned with a UDL approach
Key is to be strategic with how manipulative materials are used. There is lots of support for this online. Several examples are included in this presentation.
Multiple means of engagement in the same skills aligned with a UDL approach
Place Value tools start as toys but progress toward helping to formulate math concepts
Show a little bit of each to get the general idea
Multiple means of engagement in the same skills aligned with a UDL approach
Multiple means of engagement in the same skills aligned with a UDL approach
Multiple means of engagement in the same skills aligned with a UDL approach
Video: Learning to Count to 10 – Show 3:20 – 5:00 as an example of a way to incorporate tools in establishing 1 to 1 correspondence, numeral recognition and counting
Video: Learning to Count to 20 – Show 1:58 – up to 4:00 as am example of using play money
Multiple means of engagement in the same skills aligned with a UDL approach
Multiple means of engagement in the same skills aligned with definitions cited earlier in presentation