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SOLO in Mathematics

SOLO in Mathematics . Mitchell Howard Lincoln High School . Activity : Discuss for 1 min with the person next to you. Why did you come to this presentation? What do you hope to get from this workshop?. Aims for my talk. A brief explanation of SOLO Why SOLO in Mathematics?

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SOLO in Mathematics

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  1. SOLO in Mathematics Mitchell Howard Lincoln High School

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

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

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

  5. 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

  6. 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 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 I’m attending a workshop about it. We will come back to your statement soon SOLO

  7. Everyday SOLO Language PRESTRUCTURAL UNISTRUCTURAL MULTISTRUCTURAL RELATIONAL EXTENDED ABSTRACT

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

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

  10. UnistructuralWhat does it mean? Err….. It’s got some funny symbols!?! What do you know about SOLO?

  11. UnistructuralWhat 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.

  12. MultistructuralWhat does it mean? It’s a thinking taxonomy with funny symbols and a type of mark scheme. What do you know about SOLO?

  13. MultistructuralWhat 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.

  14. RelationalWhat does it mean? What do you know about SOLO? It’s 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.

  15. RelationalWhat 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.

  16. Extended abstractWhat does it mean? It’s 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. What do you know about SOLO? 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.

  17. Extended abstractWhat does it mean? At the extendedabstract 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.

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

  19. How do the symbols relate to NCEA? ACHIEVED MERIT EXCELLENCE

  20. The Verbs

  21. 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

  22. 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

  23. Planning a unit of work, making connections

  24. Task : How many ways can you represent this fraction?

  25. 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.

  26. 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?

  27. 0 5 1 2 3 4 Borrowed from Louise Addison

  28. 0 5 1 2 3 4

  29. ⅓ of 1 0 5 6 7 1 2 3 4

  30. ⅓ of 2 0 5 6 7 1 2 3 4

  31. ⅓ of 3 0 5 6 7 1 2 3 4

  32. ⅓ of 4 0 5 6 7 1 2 3 4

  33. ⅓ of 5 0 5 6 7 1 2 3 4

  34. ⅓ of 3 0 5 6 7 1 2 3 4

  35. ⅓ of 7 0 5 6 7 1 2 3 4

  36. 0 5 6 7 1 2 3 4

  37. 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?

  38. 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

  39. Fraction Tiles

  40. Next • We repeated the exercise for Which made connections for the algorithm of adding fractions.

  41. Giving structure to open ended tasks A Dan Meyer inspired task

  42. 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 water—a task that falls mostly to women and children.

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

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

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

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