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MathAmigo Your Helping Hand

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Learning with MathAmigo In all domains of learning, the development of expertise occurs only with major investment in time, and the amount of time it takes to learn is roughly proportional to the amount of material being learnt. Singley and Anderton The transfer of Cognitive Skills Havard University Press, 1989 Although many people believe talent plays a role in who becomes an expert in particular area, even seemingly talented people require a great deal of practice in order to develop their expertise. Ericsson et. al, The role of deliberate practice in the acquisition of expert performance, Psychological Review (1993) MathAmigo gives the chance for students to practice and: 1.Engage in lots of varied math work 2.Work at their pace 3.Develop their own strategies 4.Use feedback to improve the strategies 5.Learn with understanding

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Mastery MathAmigo aims at helping students master the different ideas and skills. Once a student has mastered a stage MathAmigo automatically moves them to the next stage, if they struggle it moves them back. The next stage might present a broader view of the concepts, it might deal with the maths in more depth or simply present a different way of looking at the ideas. You can link these stage activities together to create a set up. This way you can personalize the materials to suit each student.

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Scope and Sequence Years K-8 Counting to algebra Correlate to Standards Personalized to meet the needs of the students

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Types of Activity Concept building Developing Fluency Problem Solving MathAmigo has 3 types of activity aimed at:

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Concept Building Concepts are the foundation of mathematics – we must take care in building them. We can know our number facts but puzzle why is 7 x 0 = 0? The activity helps students understand that multiplication is repeated addition we can see that: 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0 In Stage 1 multiplication is presented as addition of sets of objects In Stage 2 the idea is repeated with numerals instead of objects. In Stage 3 the notion of repeated addition is made specific. In Stage 4 we revert to sets objects: this time displayed as an array – laying a foundation for understanding area

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Developing Fluency The new science of learning does not deny that facts are important for problem solving and thinking … However, the research shows clearly that usable knowledge is not the same as a mere list of disconnected facts. Experts knowledge is connected and organised around important concepts… John Bransford et. al, How People Learn (p9) National Academy Press (2000)

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Look at the information screen and study the pattern. Developing Fluency

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Based on the pattern. What is the missing number? Developing Fluency How did you calculate your answer?

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In this activity students use basic number facts and operations. They make choices, about how the make the calculation. What is this missing number and how did you calculate it? Developing Fluency Engagement in the activity: 1.Reinforces students factual memory through usage 2.Helps students understand the relationship between the basic operations MathAmigo develops factual fluency by offering students a wide range of different situations and contexts to use their knowledge.

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Introducing Problem Solving MathAmigo does not encourage the teaching of methodology. If you build strong conceptual foundations you can offer students tasks that you might normally regard drill and practice in a way that includes problem solving. Consider this example:

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Introducing Problem Solving The common way to teach this is making the students learn a mechanical algorithm (in this case a throw-back to Victorian schools).

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Introducing Problem Solving The common way to teach this is making the students learn a mechanical algorithm (in this case a throw-back to Victorian schools).

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Introducing Problem Solving We present the activity in the horizontal format to avoid encouraging this approach. If the students have a strong understanding of the number system and place value you can ask them to answer the question without teaching them a methodology. Here are two different ways answered by some 9 year old students: 67 + 49 is 60 plus 40: thats 100 and 7 plus 9 is 16 which makes the answer 116. 67 + 49 is 60 plus 50 which is 110 and 7 is 117 minus 1 equals 116. There is a place for learning methods, but not at the expense of not developing the mathematical thinking skills shown by these students.

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Look at the pattern opposite. Mayan Number System: it is a vigesimal (base 20) system Problem Solving Problem Solving is the application of knowledge you have to situations you are unfamiliar with. Solving this requires students to apply their understanding of place value and the number system.

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1 Teaching for Mastery: Variation Theory Anne Watson and John Mason NCETM Standard Holders’ Conference March 18 2016 The Open University Maths Dept University.

1 Teaching for Mastery: Variation Theory Anne Watson and John Mason NCETM Standard Holders’ Conference March 18 2016 The Open University Maths Dept University.

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