Speaker SMAPP Project Enhancing Mathematics Assessment with - PDF document

Speaker SMAPP Project Enhancing Mathematics Assessment with • Singapore Mathematics Assessment and Validated Resources Pedagogy Project • Sep 2008 – Dec 2012 WONG Khoon Yoong (A/P) • RD & I (Research, Development and Mathematics & Mathematics Education Innovation) project; new assessment National Institute of Education • Funding: Centre for Research in Nanyang Technological University Pedagogy and Practice (CRPP), National khoonyoong.wong@nie.edu.sg Institute of Education, Nanyang An Institute of http://math.nie.edu.sg/kywong Technological University Overview Overview 1 Wong (APEAC, 12/9/13) 2 Team Members Participants 1. Wong Khoon Yoong (PI, from Nov 2010) Schools Teachers Classes Students 2. Zhao Dongsheng (Co-PI) (S1 E) 3. Cheang Wai Kwong Partial 9 59 90 3074 4. Fan Lianghuo (PI, 2008 to Oct 2010) participation Main study I: 4 I: 16 I: 11 I: 406 5. Lee Peng Yee Strong participation of (2011) C: 4 C: 14 C: 14 C: 527 6. Quek Khiok Seng • 2 extended tasks Mathematicians; 7. So Hyo Jeong • Everyday maths ensure mathematical rigour • Attitude 8. Teo Beng Chong 9. Teo Kok Ming S1 E: Secondary 1 (Express); Grade 7; 10. Yen Yeen Peng (CPDD, MOE) average and mixed ability 11. Yvonne Ng Qiu Ting (PM) & Others who left project Overview Overview Wong (APEAC, 12/9/13) 3 Wong (APEAC, 12/9/13) 4 Main Publication Disclaimer The views expressed at this lecture are those • Not for sale; given free to of the author’s and do not necessarily all Singapore secondary represent the views of the schools • Centre for Research in Pedagogy and • E-book (reading): Practice (CRPP) http://hdl.handle.net/1049 • National Institute of Education (NIE) 7/11492 • Singapore Ministry of Education (MOE) Overview 5 Overview 6 Wong (APEAC, 12/9/13) Wong (APEAC, 12/9/13)

Overview Real-Life Contexts 1. Maths disciplinary tasks • Singapore Maths Curriculum (2013): stronger emphasis on “solve real-world 2. IT-based assessment system problems”; “connect mathematics that 3. Attitudes toward learning maths they have learnt to the real world” • Help students gain knowledge about the world, while honing their maths skills • Aligned with international trends Overview Overview Wong (APEAC, 12/9/13) 7 Wong (APEAC, 12/9/13) 9 OECD: Mathematical Literacy Design Framework (2009) • An individual’s capacity • to identify and understand the role that mathematics plays in the world, • to make well-founded judgements and • to use and engage with mathematics in ways that • meet the needs of that individual’s life as a constructive, concerned and reflective citizen Overview Overview Wong (APEAC, 12/9/13) 10 Wong (APEAC, 12/9/13) 11 Two Types of SMAPP Tasks Extended Tasks: Principles a) Links to real life scenario a) 11 extended tasks, multiple b) Real and relevant data competencies (computation, reasoning, c) Curriculum connection explanation), mathematically rigorous; d) Multiple competencies and content knowledge take about one hour to complete; assessment learning experiences; delivered through e) Experience enriching IT system f) Scaled levels of difficulties b) 10 short paper-pencil problems • Zhao, D.S., Cheang, W. K., Teo, K. M., & Lee, P. Y. (2011). Some principles and guidelines for designing mathematical disciplinary tasks for (Everyday Maths Items), similar to Singapore schools. In J. Clark, B. Kissane, J. Mousley, T. Spencer & S. Thorton (Eds.), Mathematics: Traditions and (new) practices: Proceedings PISA; exercises or tests of the AAMT-MERGA conference (pp. 1107-1115). Adelaide: Australian Association of Mathematics Teachers. Overview 12 Overview 13 Wong (APEAC, 12/9/13) Wong (APEAC, 12/9/13)

11 Extended Tasks: IT based 2 Extended Tasks: Findings No. Task Titles Topics Tasks Max Female Male Overall % 1 Paper Recycling Arithmetic Paper 33 20.8 20.5 20.8 63% 2 Red or Black? Arithmetic, Algebra Recycling (273) (86) (364) 3 Malacca Trip Rate, Speed, Algebra, Inequalities Red or 31 16.4 16.5 16.2 52% 4 Water Water Water! Mensuration, Statistics 5 Up Down Up Down!! Statistics Black? (287) (90) (383) 6 Singapore Got Talent Geometry 7 Money Money Money Linear Graphs • Successful with routine questions 8 Three Rockstars on the Wall Angles, Parallel Lines • Weak in unfamiliar units, multi-step questions, 9* When to Retire? Numbers, Algebra giving reasons, explain own ideas 10* Which Mobile Plan? Statistics, Percentages 11* Outing to the Zoo Data handling, Algebra • Cheang, Teo, Zhao, http://repository.nie.edu.sg/jspui/handle/10497/8158 * Based on teachers’ contributions in November 2010 Overview Overview Wong (APEAC, 12/9/13) 14 Wong (APEAC, 12/9/13) 16 Decibel Question: Try It Decibel Question: Results The loudness of sound is measured in decibels (dB). a) Correct answer with working Noise from heavy traffic is about 85 dB and this can (27%); Correct answer, no cause hearing damage if one is exposed to it for 8 hours working (10%); Wrong or more. For every 3 dB over 85 dB, the exposure time proportional reasoning (4%) before damage occurs is decreased by half. b) Full mark (21%); Partial (24.5 %); (a) If the noise is 88 dB, what is the exposure time before Wrong (45%) Popular method: damage occurs? stepwise decrease (b) John likes to listen to his music using ear-plugs at high volume of 100 dB. How long could he do this • 39%: relevant to daily life (most before damage occurs? relevant and challenging) Overview Overview Wong (APEAC, 12/9/13) 17 Wong (APEAC, 12/9/13) 18 Easiest: Sale (72%) Everyday Maths Items: Admin A particular item costs $6. Shop X advertises, “buy four items for the • 5 items administered in March 2011 as price of three”. “pre” test (a) How much does a customer have to pay for 4 such items in shop X? (0.98/1) • 5 items in Sept 2011 as “post” test (b) What is the percentage discount for the customer who buys 4 such items from shop X? (1.61/2) • But not parallel items (c) Another shop Y offers, “buy three at the regular price and pay • Pre-post labels for identification only 50% for the fourth item.” Shop Z offers a voucher of 10% on the total amount paid. Your parents wish to buy 4 such items. Out of these 3 shops (X, Y, and Z), which shop gives the best deal? (3.52/5) (d) Other than the amount you have to pay, what other reasons would you give to your parents to support your choice? (0.34/1) Overview 19 Overview 20 Wong (APEAC, 12/9/13) Wong (APEAC, 12/9/13)

Everyday Maths Items: Findings Everyday Maths Items: Groups Context n  814 Question Facility Index (Topic) Group Male Female Overall Sample Size Sale S1E 1 71.7 (Percentage, discount) Tourism 38.0 37.9 38.0 2 64.9 (Interpretation of table and pie chart, rate) Intervention 327 Re-arranged (11.4) (12.4) (12.1) Kool Biscuits: Reduced fat 3 61.8 in order of (Percentage) 37.6 42.6 40.6 Population facility 4 57.4 487 Comparison (Interpretation of table, significant figures, rate) (11.4) (12.5) (12.3) Types of fires 5 54.6 (Interpretation of table, percentage change) 37.7 40.5 39.5 Decibels Overall 6 40.8 (11.4) (12.6) (12.3) (Four operations, rate) Earthquake 7 36.6 (Powers of 2) Sample Size 284 530 814 Mobile plan 8 35.5 (Rate, line graph) Hokkien char mee 9* 26.1 (Interpretation of chart, percentage) Math Olympiad 10* 22.2 (Line graph, bar graph, misuse of graphs) Overview Overview Wong (APEAC, 12/9/13) 21 Wong (APEAC, 12/9/13) 22 Everyday Maths Items: IT-Based Assessment: Trends Observations • Lack of experience with real-life contexts • International trend: Develop IT-based assessment of construct-response items; • Inappropriate use of maths skills efficiency and commercial, technical • Amount of reading issues • Maths beyond S1 level; more suitable for • Singapore: Math Explorer can grade upper secondary multi-line steps; defunct • Student perceptions: neutral in terms of • SMAPP: IT-based assessment based on interest, relevance; a bit challenging, less pedagogy, assessment for learning confident Overview Overview Wong (APEAC, 12/9/13) 23 Wong (APEAC, 12/9/13) 25 Assessment for Learning ( AfL ) IT Platform with AfL Features 1. Deliver tasks (extended) • Provide informative feedback to students to enhance 2. Capture answers; closed their performance (Sadler, Black, Wiliam, Hattie, etc.) & open questions 3. Automatic & Semi- automatic marking Assessment Teaching 4. Customisable feedback 5. Student responses to online feedback (*) 6. Reports by questions, students, class 7. Follow up activities (*) Marking Feedback (Evidence) (*) Not successful Overview 26 Overview 27 Wong (APEAC, 12/9/13) Wong (APEAC, 12/9/13)