94 Students making the connections between algebra and word problems

CENTRE FOR EDUCATIONAL DEVELOPMENT Students making the connections between algebra and word problems http://ced.massey.ac.nz Teacher to Adviser Team Leader, Numeracy and Mathematics Centre for Educational Development Massey University College of Education Palmerston North New Zealand a.lawrence@massey.ac.nz Palmerston North (New Zealand) NZAMT-11 conference New Zealand schools Years 1- Primary Years & Intermediate Years -13 Secondary Full primary Year 7–13 Issues in education in New Zealand • Numeracy and literacy • Curriculum • Assessment – NCEA – Technology – National testing You didn’t tell me it was a word problem \little league movie_WMV V9.wmv Difficulties with word problems • • • • • Educators frequently overlook the complexity of Mathematical English Vocabulary Half of the sum of A and B, multiplied by three Connectives Word order Syntactic structure Half of the sum of A and B multiplied three Punctuation Context is complicated Contextualising maths creates another layer of difficulty – the difficulty of focusing on the maths problem when it is embedded in the ‘noise of everyday context’ (Cooper and Dunne, 2004, p 88) Placing mathematics in context tends to increase the linguistic demands of a task without extending the mathematics (Clarke, 1993) The national standard in NZ • “use algebraic strategies to investigate and solve problems… Problems will involve modelling by forming and solving appropriate equations, and interpretation in context” • “must form equations…at least one equation” (assessment schedule, NZQA) Effective strategies • Explicit expectations • Focus on translation – from English to algebra (encoding) – from algebra to English (decoding) • Create the ‘press for algebra’ Tasks encourage informal strategies Teachers commonly start with problems that are easy for students to in their head in order to demonstrate the “rules of algebra”… BUT Most students only see a need to use algebra when they are given problems that they cannot easily solve with informal methods A common problem A rectangle is cm longer than it is wide If its area is 21 cm2, what is the width of the rectangle? This one is not hard You know that 21 is times so it’s got to be It’s obvious Once you see it, it’s obvious… Why would a student use algebra? But algebra is what I would always first At least now I know I will have to be so careful with the problems I use Effective strategies • Explicit about expectations • Focus on translation • Create the ‘press for algebra’ – problems with ‘tricky’ numbers – problems that don’t ‘unwind’ • Focus on the whole problem – the complete problem solving cycle Focusing on the whole problem Knowing what to let the variable be is critical Initially it seemed like it didn’t matter I understood what I was doing because I had translated it into words first Making sense Translating into words was really helpful before we had to solve the equations… It made it easier to solve them and it made it make more sense Questions raised • What are algebra word problems? • Why students find them difficult? • What can teachers to help their students tackle them with more success? Teachers can make a difference • Make explicit connections between algebra and word problems • Develop skills of encoding and decoding • Use tasks which press for algebra • Focus on the full problem-solving cycle • Emphasise flexible approaches to solving problems Hell’s library Thank you a.lawrence@massey.ac.nz Connecting with algebra It is glaringly obvious that it has worked The whole idea of starting with the word problems and working on how to translate it and then develop the skills from that I think that whole way of them understanding the use of algebra made them connect much better with the topic Getting the point They understood the point of algebra I had students answering in class with confidence who normally don’t… and seemingly enjoying what they were doing! Student improvement I feel a lot better about algebra now Before I didn’t know how to write equations and now I More focus on solving for a few I can write equations but I still don’t know what to with them It’s really good but it’s like “What I next?” - like, I don’t even know the steps What you after that, and what you after that? I really needed teaching for solving ’cos then I would have been done! ... relationship Algebra word problems in NAPLAN What is it about algebra word problems? • What are algebra word problems? • Why students find them difficult? • What can teachers to help their students. .. solve algebra word problems using a fully algebraic method They translate into algebra and use algebra to find the answer Students commonly use a variety of informal solution strategies They work... tackle a word problem? • What makes you decide to use algebra to solve a word problem? • Can you write a word problem that all your students use algebra to solve? Solving algebra word problems