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SOLO in Mathematics Mitchell Howard Lincoln High School

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Activity : Discuss for 1 min with the person next to you 1.Why did you come to this presentation? 2.What do you hope to get from this workshop?

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Aims for my talk 1.A brief explanation of SOLO 2.Why SOLO in Mathematics? 3.Some SOLO Pedagogy 4.Get you involved in thinking about how to use SOLO in the learning of Maths

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Thinking at Lincoln The focus is on ensuring students achieve deep learning outcomes and learn how to learn.

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Activity 2: Describe map - SOLO Much like a spider diagram or brainstorm Students could do this on a template, or just sketch up in their books or on mini white boards or scrap paper

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Activity : Describe map - SOLO Use the map to write what you know about SOLO? Then write a statement about what you think SOLO Taxonomy is SOLO Surname of HAN What this talk is supposed to be about The next passing FAD in education SOLO is the surname of a cool space guy from Star wars. It is also a word which is being a used a lot in education at the moment. Today Im attending a workshop about it. We will come back to your statement soon

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Everyday SOLO Language UNISTRUCTURAL MULTISTRUCTURAL RELATIONAL EXTENDED ABSTRACT PRESTRUCTURAL

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Prestructural What does it mean? What do you know about SOLO? Err….. What??

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Prestructural What does it mean? At the prestructural level of understanding, the student response shows they have missed the point of the new learning.

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Unistructural What does it mean? What do you know about SOLO? Err….. Its got some funny symbols!?!

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Unistructural What does it mean? At the unistructural level, the learning outcome shows understanding of one aspect of the task, but this understanding is limited. For example, the student can label, name, define, identify, or follow a simple procedure.

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Multistructural What does it mean? What do you know about SOLO? Its a thinking taxonomy with funny symbols and a type of mark scheme.

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Multistructural What does it mean? At the multistructural level, several aspects of the task are understood but their relationship to each other, and the whole is missed. For example, the student can list, define, describe, combine, match, or do algorithms.

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Relational What does it mean? Its a way of structuring your thinking. It follows on from having your ideas to being able to link your ideas together by explaining or comparing & contrasting them to show a greater understanding of a topic. Rubrics can be used to assess their level of achievement. What do you know about SOLO?

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Relational What does it mean? At the relational level, the ideas are linked, and provide a coherent understanding of the whole. Student learning outcomes show evidence of comparison, causal thinking, classification, sequencing, analysis, part whole thinking, analogy, application and the formulation of questions.

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Extended abstract What does it mean? Its a way of structuring your thinking. It follows on from having your ideas to being able to link your ideas together by explaining or comparing & contrasting them to show a greater understanding of a topic. It then allows you to formulate your own prediction or generalisation, discussing the topic in question. I predict that if I use SOLO Taxonomy within my lessons, I will see an increase in Merits and Excellences as students learn to structure their answers better and they can transfer their knowledge to another context. What do you know about SOLO?

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Extended abstract What does it mean? At the extended abstract level, understanding at the relational level is re-thought at a higher level of abstraction, it is transferred to another context. Student learning outcomes show prediction, generalisation, evaluation, theorizing, hypothesising, creation, and or reflection.

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Self Assessment: So What Level do you think you were at with your initial statement about SOLO Taxonomy?

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How do the symbols relate to NCEA? ACHIEVED MERIT EXCELLENCE

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The Verbs

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The Hattie and Brown Asttle example: Algebra patterns Given: How many sticks are needed for 3 houses? How many sticks are there for 5 houses? If 52 houses require 209 sticks, how many sticks do you need to be able to make 53 Houses? Make up a rule to count how many sticks are needed for any number of houses Houses123 Sticks59___

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In your notes is a copy of this generic mathematics and SOLO rubric. You can read at your leisure but it relates well to what is happening at level 1

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Planning a unit of work, making connections

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Task : How many ways can you represent this fraction?

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Some ideas: Diagram: Pieces of pie or divided grids Number line or a scale Mixed number Decimal, Percentage, Ratio A context: 7chocolates divided between three people A number sentence: addition/subtraction/multiplication/division.

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Activity: construct a SOLO rubric Based on the responses you have made, and what you know of your students could you: construct a hierarchy of understanding? Measure understanding? Show students where to go next?

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0 2143 5 Borrowed from Louise Addison

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0 2143 5

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0 2143 567 of 1

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0 2143 567 of 2

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0 2143 567 of 3

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0 2143 567 of 4

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0 2143 567 of 5

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0 2143 567 of 3

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0 2143 567 of 7

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0 2143 567

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Implications on teacher planning Multiple representations of mathematical ideas/concepts How do we help students to make the connections between them? Differentiation – different types of learners will bring different ideas/experiences and connect with different representations. Differentiation – How do we cater for the ability range in our classes?

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Equivalent Fractions: Doing versus Understanding Pictures Algorithm – Double top and bottom – × or ÷ numerator & Denominator by same number Relate to +/- Fractions of different denominator Relate to ratio Algebraic Fractions

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Fraction Tiles

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I cant find any combination of tiles that are equal to ½ I can find sets of tiles that have the same denominator (or are of the same colour) that add up to ½. I can find sets of tiles of different denominators that add to ½ I can explain how to find combinations of tiles (of different denominators) that add to ½ I can explain and relate fraction tiles to other representations of fractions such as Number sentences. I can write a general rule about the mathematics involved in this activity which makes it quicker and easier to do this kind of task with fractions that are not included on this set of fraction tiles.

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Next

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Giving structure to open ended tasks A Dan Meyer inspired task

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In impoverished rural areas, clean water is often miles away from the people who need it, leaving them susceptible to waterborne diseases. The sturdy Q Drum is a rolling container that eases the burden of transporting safe, potable watera task that falls mostly to women and children.

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SOLO LevelCriteria PreI dont know where to start I dont know what volume or capacity is UniI can estimate the dimensions or I can calculate the area of a circle MultiI can calculate the volume of the water container. RelationalI can calculate the capacity of the water container as well as the weight. I can calculate the dimensions needed for the container to carry a given capacity Extended abstract I can design an alternate shapes or purpose for the container. Or I can make a formula that can be used to calculate the volume or capacity given any dimensions.

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Using the terminology and referring to the symbols in class discussion:

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The Picture (graph) The Numbers The Context A Guide for responses in Level 3 Statistics internals The Points on the graph are going down hill from left to right The gradient of my regression line is negative As one of my variables increases the other decreases My smoothed data looks non-linear But I have a high r squared smoothed data will tend to get increased r squared value

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The equation The Number pattern The Picture (graph) The Context. (dot diagram or skateboard ramp etc) Level 1 - Understanding quadratic patterns and graphs I have two answers for x when y=0 I have one positive and one negative answer The parabola cuts the x –axis twice (2 roots) I can only have a positive answer for the number of people Has an x squared Differences not the same Is a parabola Some of the dots form a square shape

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1.3 Investigate relationships between tables, equations and graphs Number Patterns Written description Picture Contextual scenario TableGraph Formula or Equation Initial amount and the rate of Increase/decrease Y = c + mx m is the gradient or rate c is the initial value Is it discrete - counted (e.g. matchstick pattern) So Dots on graph Continuous – Measured (e.g. liquid filling a container) So Solid line What happens at x = 0 What do values increase/decrease by each time A taxi has a flag-fall of $2.00 and charges $2.60 per km Draw the pattern as well as the next few

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SOLO level Uni-structuralI can represent/ interpret the pattern in one way Multi-structuralI can represent/ interpret the pattern in more than one way Relational -structuralI can choose the best representation to solve a problem Extended abstract-structuralI can generalise a pattern and use it to solve a problem or make a prediction.

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LevelSuccess criteriaExplanatory notes AchievedMake links between various representations of a linear pattern. Quantitative Write a formula or form a linear model. Demonstrate knowledge of gradient and intercepts MeritMake links between various representations of a pattern in context Qualitative. Forming and/or using a quadratic model. ExcellenceForming a generalisation. Evaluate effects of a change in particular pattern. Form a model and correctly solve a problem. Cope with unusual models such as piecewise or exponential.

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v

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v

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Next Did the regular theory of graphing linear functions. Contextual questions Some quadratic theory. Then

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Some key ideas Different representations – making connections Differentiation - different types of learners Common language to describe understanding Self assessment – real power is from students self assessing from a rubric

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Where to next for me Learning experiences which lend them selves to relational and extended abstract thinking. Malcolm Swan

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Card match activities Malcolm Swan

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Malcolm Swan Classify in a 2 way table

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Evaluating statements about fractions Always true, sometime true or never true? Statement 1: A fraction is a small piece of a whole Statement 2: When you multiply one number by another the answer must always be bigger Statement 3: You can't have a fraction that is bigger than one Statement 4: Five is less than six so one fifth must be smaller than one sixth Statement 5: Any fraction can be written in lots of different ways Statement 6: Fractions don't behave like other numbers Statement 7: Decimals and fractions are completely different types of numbers Statement 8: Every fraction can be written as a decimal

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Thanks for listening mho@lincoln.school.nz

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Classifying mathematical objects i.Odd one out ii.Classifying using two-way tables Interpreting multiple representations Card match activities Evaluating mathematical statements – always true sometime true never true Creating problems i.Exploring the doing and undoing processes in mathematics ii.Creating variants of existing questions Analysing reasoning and solutions i.Comparing different solution strategies ii.Correcting mistakes in reasoning iii.Putting reasoning in order

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