Free Fractions Tools | Conceptua Fractions Conceptua Math includes interactive, visual tools that are ideal for teacher-facilitated, whole-class instruction, "Number Talks" and for parents supporting their students at home. These tools, available free of charge, are located under the Tool Library tab in our full curriculum. The full Conceptua Math curriculum includes integrated teacher supports, adaptive teaching, student investigations, and much more. Teachers Build Instructional Expertise with Supports Teachers start with scripted Lesson Openers to introduce concepts and generate fraction Number Talks with the whole class. Lesson Closers help students to summarize their learning. Sample Opener > Students Learn through Guided Lessons The Guided Lessons form the foundation of the program. Sample Guided Lesson > Students Apply Knowledge through Investigations Real World Investigations provide opportunities for students to use authentic data and apply their mathematical knowledge. Sample Investigation >

English - Leerplanevaluatie Formative evaluation Curriculum developers use a cyclical approach to increase the quality of the product. In order to test the quality of draft products and to gain suggestions for improvement, data is collected during formative evaluation activities. Planning and conducting formative evaluation activities take a number of steps. For a closer look at this iterative or cyclical curriculum development approach, please have a look at the following 2-minute clip: Evaluation Matchboard To support the planning of formative evaluation Nieveen, Folmer and Vliegen (2012) developed the 'Evaluation Matchboard'. Please refer to the following source for more details: Nieveen, N., & Folmer, E. (2013). The back of the matchboard provides the definitions of the various development stages, the quality criteria, the methods and the activities. Brief instructions for using the Evaluation Matchboard: More information

Yummy Math | We provide teachers and students with mathematics relevant to our world today … Encouraging Mathematical Thinking: Introduction Being a professional educator takes time -- time to plan, time to practice, time to grade, time to communicate -- and I never have enough time. However, I now realize that adding reflection and research to my agenda have made my life as a teacher easier, not more difficult. -- Judith Koenig, Project teacher This paper reflects our working knowledge about how teachers engage students in mathematical thinking, and why this is important. We focus in particular on discourse in the classroom. By this we mean the use of questioning, listening, writing, and reflection as a means of encouraging reciprocal conversation -- the kind of teaching that allows every person to have a voice in creating mathematical understanding. We are a group of mathematics teachers and Math Forum staff who differ in our perspectives and backgrounds. How can teachers guide students' oral communication, for example, through active listening and careful paraphrasing of their language?

Using Writing In Mathematic Using Writing In Mathematics This strand provides a developmental model for incorporating writing into a math class. The strand includes specific suggestions for managing journals, developing prompts for writing, and providing students with feedback on their writing. In addition, the site includes two sample lessons for introducing students to important ideas related to writing about their mathematical thinking. Teaching Strategies For Incorporating Writing Into Math Class: Moving From Open-Ended Questions To Math Concepts Starting Out Gently with Affective, Open-Ended Prompts Writing about thinking is challenging. Begin with affective, open-ended questions about students' feelings. Have students write a "mathography"-a paragraph or so in which they describe their feelings about and experiences in math, both in and out of school. Encourage students to keep their pencils moving. Try requiring 20 words per answer, even if they have to copy the same words again to reach 20. 1. 2. 3. 1. 2. 1.

4.2.1 Making Triangles Task Using one band for each triangle, make as many different sizes and shapes of triangles, as you can on the computer geoboard. Explain to a friend the ways in which these triangles are different and how they are alike. [Stand-alone applet] How to Use the Interactive Figure We will refer to the pegs that the rubber band is attached to as nodes. To attach the rubber band to more than two nodes, drag the rubber band from the middle.To move a rubber band to a new node, click on the current node and drag the rubber band to the desired node.To remove a rubber band from a node, click on the node to select it (a double circle appears), then click on the Delete Node button.To delete a rubber band, click on it to select it, then click the Delete Band button.To clear the geoboard, click on the Clear All button.To color the interior of a shape, click on the rubber band and then click on a color. Students enjoy working with geoboards, whether they are interactive computer geoboards or physical ones.

Kay Toliver: Math and Communication Math and Communication by Kay Toliver Before I taught mathematics in grades 7 and 8 at East Harlem Tech, I taught all of the other elementary grades, starting with the first and gradually moving up through each grade, one at a time. It may have been this background which led me to want to use mathematics instruction to develop my students' communication skills, because I saw that, for all students in all grades, communication skills were among the most important abilities that I could help them to develop. Over the years I have learned that there are two sides to this coin. Not only can I use math class to develop children's abilities to speak, read, write and listen, but by stressing these communication activities I am able to be a better mathematics teacher. By encouraging students to speak up in class, to explain their reasoning, and to define the words that we are using, I learn a great deal about how well they understand the lesson. Make it easy for students to speak up.

Making Mathematics: Support for Teachers "I can think of two good criteria ... for deciding what to teach: whether the knowledge gives a sense of delight and whether it bestows the gift of intellectual travel beyond the information given, in the sense of containing within it the basis of generalization." —Jerome Bruner Mathematics is a discipline with the potential for important insights, beautiful symmetries, and unexpected discoveries. All of our students are capable of experiencing this potential for themselves. From 1999-2002, the Making Mathematics project provided mathematicians as mentors and curricular materials to help teachers and students explore the full richness of our discipline together. The NCTM Principles and Standards list five processes which make it possible for students to work as mathematicians: problem solving, reasoning and proving, communicating, making connections, and creating representations.

math playground Solve math word problems with Thinking Blocks, Jake and Astro, and more.Model your word problems, draw and picture, and organize information! advertisement Addition and Subtraction Thinking Blocks Jr Multiplication and Division Fractions Ratios and Proportions Thinking Blocks - All Topics Word Problems - Grades 1 to 6 All Four Operations - Grades 2 to 5 All 4 Operations - grades 3 to 5 Various Concepts - Grades 5+ Various Concepts - Grades 3 to 6 Math Problem Solving Challenges Build Reading Skills with Fun and Engaging Word Games! Dolch Word Recognition Spelling Words Letter Recognition Giraffe Karts Grammar Octo Feed Homonyms Verb Tenses Word Typing Jets Antonyms and Synonyms Sky Chase Double Vowels Spelling Bees Furious Frogs What's the Word? Synonyms Must Pop Words Parts of Speech Free! Copyright © 2016 Math Playground LLC • All Rights Reserved

Intersubjectivity in Mathematics Learning: A Challenge to Intersubjectivity in Mathematics Learning: A Challenge to the Radical Constructivist Paradigm? This paper appeared in "Journal for Research in Mathematics Education" Vol. 27, No. 2, p. 133-150, March 1996 Abstract Radical constructivism is currently a major, if not the dominant, theoretical orientation in the mathematics education community, in relation to children's learning. There are, however, aspects of children's learning which are challenges to this perspective, and what appear to be "at least temporary states of intersubjectivity" (Cobb, Wood & Yackel 1991 p. 162) in the classroom is one such challenge. In this paper I discuss intersubjectivity, and through it offer an examination of the limitations of the radical constructivist perspective. Constructivists, whether radical, weak or social (Cobb 1994), draw their inspiration from Piaget for whom the individual is the central element in meaning-making. Intersubjectivity and Social Constructivism More poetically, Vygotsky says (1986):

Math Games in 15 Minutes or Less Web Math Games in 15 minutes or less 1. IXL Learning This site has plenty of activities and games, from linear functions to probability, to help students in grades K–8. 2. Math Playground Shuttle missions, flashcards, and arcade games are only a few of the fun games offered. Take advantage of these lessons for a variety of math subjects and grade levels. 3. Math games bring out kids’ natural love of numbers. 1. 2. ’Round the Block Have students stand in a square. 3. 4. 5. Even 10 minutes of fun math games can jump-start learning. 6. 7. 8. 9. 10. Teach quick math concepts with fruit, dice, even Twister! 11. 12. 13. 14. 15. Paul Ernest Paper Paul Ernest University of Exeter Epistemological issues, although controversial, are central to teaching and learning and have long been a theme of PME. A central epistemological issue is that of the philosophy of mathematics. It is argued that the traditional absolutist philosophies need to be replaced by a conceptual change view of mathematics. It is widely recognised that all practice and theories of learning and teaching rest on an epistemology, whether articulated or not. "In fact, whether one wishes it or not, all mathematical pedagogy, even if scarcely coherent, rests on a philosophy of mathematics." Such issues are a recurring theme in PME, which is not surprising since Piaget, who might be named the honorary god-father of PME, developed probably the most important developmental psychology theory of the century, with epistemological goals explicitly in mind. It is to the credit of PME that it is continually seeking to explore its theoretical and philosophical foundations.

Teachers model off their real-world approaches to teaching math Math teachers Amy Hogan, of Brooklyn Technical High School, and Ellie Terry, of the High School of Telecommunication Arts and Technology, present an election modeling project their students worked on last fall. How much voting power does a New Yorker really wield? How can statistics presented by the media manipulate readers? These are a few of the questions that math teachers in New York City are asking their students as they try to bring complex and abstract concepts to life. The lessons cover a mathematical practice known as modeling that has been around for decades but is now getting a closer look in schools around the city as teachers try to align their math lessons to Common Core standards that require real-world applicability. Using modeling to present lessons is one of two instructional focuses that the Department of Education has laid out this year for math teachers. In the prize-winning lesson, Honner had students design hats out of paper materials.

Research Sampler 8: Students' difficulties with proof by Keith Weber What is proof and what is its role in mathematics? What difficulties do students have with proofs? Proof is a notoriously difficult mathematical concept for students. What is proof and what is its role in mathematics? Many mathematicians and mathematics teachers would consider the answers to this question straightforward. Fields Medalist William Thurston [1994] argues that it is important to distinguish between formal proofs and proofs that mathematicians actually construct. Davis and Hersh [1981] argue that it is probably impossible to define precisely what type of argument will be accepted as a valid proof by the mathematical community. At different places in the mathematics education literature, a proof has been defined as an argument that convinces an enemy [Mason, Burton, and Stacey, 1982], an argument that convinces a mathematician who knows the subject [Davis and Hersh , 1981], or an argument that suffices to convince a reasonable skeptic [Volmink, 1990]. Ritual.

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