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NAPLAN Numeracy 2009

Activity 1. Take a cardFind the answer to the algorithm/problem(if you need a calculator move on)Create a question using the algorithm/problem. Purpose of the activity. Where any of the algorithms DIFFICULT?Would you expect your students to be able to do these?All from NAPLAN 2009 ? Did you r

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NAPLAN Numeracy 2009

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    1. NAPLAN Numeracy 2009 Presented by Bob Wellham K-12 Mathematics Consultant, Swansea

    2. Activity 1 Take a card Find the answer to the algorithm/problem (if you need a calculator move on) Create a question using the algorithm/problem

    3. Purpose of the activity Where any of the algorithms DIFFICULT? Would you expect your students to be able to do these? All from NAPLAN 2009 – Did you recognise them? Why are they different?

    4. Newman’s Error Analysis Reading Can students read the words of the problem? Comprehension Can students understand the meaning? Transformation Can students determine a way to solve the problem? Process Skills Can students do the mathematics? Encoding Can students record and interpret their answer?

    5. Newman’s Prompts Read the question. read What does it mean? mean What will I do to solve it? do Do the maths. maths Write the answer. answer

    6. Common Practice Research carried out in Australia and Southeast Asia suggests that about 60% of students’ errors in responding to written numeracy questions occur before students reach the process and encoding skills level. (i.e. before Newman steps 4 & 5) However 80% of remediation programs and common teaching practice is to focus students on revision of process skills. (Newman step 4)

    7. National Numeracy Review Report (2008) From the earliest years, greater emphasis needs to be given to providing students with frequent exposure to higher-level mathematical problems rather than routine procedural tasks, in contexts of relevance to them, with increased opportunities for students to discuss alternative solutions and explain their thinking.

    8. What does this mean for us? If we continue to remediate ONLY algorithms (like the Activity 1 questions) there is little chance of student outcomes improving.

    9. So what do we do? Help students to ……… - read the questions - comprehend what they read - provide strategies that aid understanding - teach students to answer multiple choice questions – many guess or are mislead.

    10. How can we do this? Focus on worded problems Increase the metalanguage used Get students explaining how they get answers Scaffold strategies Assessment for learning Explicit teaching of concepts

    11. Explicit teaching of mathematical terms & symbols Students need to say new words as well as hear and see them. How do you verbalise 7- 5? 7 minus 5 7 take away 5 take 5 from 7 from 7 take 5 subtract 5 from 7

    12. Understanding the vocabulary Words that are only used in mathematics eg. parallelogram Words that have the same meaning in mathematics as in everyday language eg. equal Words that have a different meaning in mathematics as in everyday language eg. volume

    13. Significance of context and positional terms in mathematics Instead of concentrating on key words, students need to look at the words in the context of the whole problem. Five is how many more than three? Five is three more than which number? Which number is three more than five? Prepositions can change meaning and the choice of process- What is half of 4? Four is half of what ? Increase by 7, Increase from 7, Increase to 7

    14. Consider literacy strategies HERE – require literal comprehension of directly stated information “reading ON the lines” HIDDEN – require interpretation of information “reading BETWEEN the lines” HEAD – require inferences to be made and information to be evaluated and applied “reading BEYOND the lines”

    15. A lack of concept knowledge An 11 year-old student explained this approach to solving written questions in numeracy: "Problem solving is easy. If there are more than two numbers, I always add; otherwise, I subtract. If I'm not sure if it's multiplication or division, I divide and, if there is a remainder, I multiply instead" (Hope, 1987, p. 57).

    16. Another light moment !!!

    17. Assessment for learning Mathematics is sequential – learnt work is the building blocks of new learning. Find out what students know and program the learning to the next level.

    18. Using SMART data SMART data is a great tool to analyse where to start. Using Item Analysis you can find where your students differ most from the state – this is usually a good starting point.

    19. Who is best to analyse the NAPLAN data? The teachers. What should they look for? Strengths & weaknesses Individual performances Find out what students know Find out what has to be taught Are the NAPLAN results a true indication If NOT why?...... It is not the test, it is consistent acros the state, so it gives a good “yard stick”

    20. From my superficial analysis of schools in this Region Year 7 - Fractions, Decimals & Percentages Patterns & Algebra – Number patterns Measurement – Area Space & Geometry – scale, Edges on 3D object, protractor. Year 9 - Fractions, Decimals & Percentages - Patterns & Algebra – Algebraic Techniques

    21. Year 7 Number Patterns - C8, C12, C24, C27, NC8, NC10 & NC13 Fractions, Decimals & Percentages - C19, C31 & NC30 Measurement - NC9 Space & Geometry - C5, C13 & NC21

    22. Year 9 Algebraic Techniques - C19, C21, C24, NC20, NC30 & NC22 Fractions, decimals & percentages - C9, C12, C15, C29, NC14, NC17, NC27 & NC29 Measurement - C17, NC6 & NC8

    23. Tape Diagrams Students draw a tape to support their thinking during problem solving

    24. To get to work, I travelled on the train for 24 minutes and I walked for 7 minutes. How long did it take me to get to work? This is how a student represented the problem using a tape diagram. Points to note: Tape diagram enables us to represent all the relevant information It is only a diagram to help us visualise the transformation of the problem, so being precisely accurate is not necessary As a means of organising, I like to place above the tape information about the whole tape and below it information about its partsThis is how a student represented the problem using a tape diagram. Points to note: Tape diagram enables us to represent all the relevant information It is only a diagram to help us visualise the transformation of the problem, so being precisely accurate is not necessary As a means of organising, I like to place above the tape information about the whole tape and below it information about its parts

    25. There were some oranges in a box. Because we bought 14 more oranges, there are now 21 oranges in the box altogether. How many oranges were in the box at first? Reveal ‘There were some……………….’ Task Draw a tape diagram for this problem. Reveal diagram. This is how a student represented the problem using a tape diagram. Questions where the answer is not the largest number create particular problems for many students. Reveal ‘There were some……………….’ Task Draw a tape diagram for this problem. Reveal diagram. This is how a student represented the problem using a tape diagram. Questions where the answer is not the largest number create particular problems for many students.

    26. Questions where you could use Tape Diagrams in NAPLAN 2009 Year 7 C17, C18, C31, NC18 Year 9 C15, C29, NC4, NC17, NC27 Remember, this is a process that can be applied in a variety of questions – NOT just NAPLAN

    27. Multiple Choice Questions

    28. Multiple Choice Questions Worksheets adapted from website www.thinkingblocks.com

    29. More information or assistance? Articles Nine Ways to Catch Kids Up. Singapore Math: Simple or Complex? Learning from Singapore Math. pdf copies of these can be found at www.hccweb2.org/bobsblog …… as well as a copy of this PowerPoint Email ME … robert.wellham@det.nsw.edu.au

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