Deciphering and Understanding Mathematical Word Problems Practical Approaches
Deciphering and Understanding Mathematical Word Problems Practical Approaches for the Primary Classroom Practical Pedagogies Cologne, Germany November 1st-2nd 2018
Twitter: #pracped18 Provider: Jean Knapp (Mathematics Specialist Teacher & Consultant) [email protected] Twitter: @MissJK24319629 Background The Vocab ulary Gap Childrens vocabulary skills are linked to thei
r economic backgrounds. By 3 years of age, there is a 30 million word gap b etween children from the wealthiest and poorest fa milies. By 18 months, children in different socio-economic groups display dramatic differences in their vocabu laries. By 2 years, the disparity in vocabulary devel opment has grown significantly (Fernald, Marchma n, & Weisleder 2013). At two years old, childrens understanding and use
of vocabulary as well as their use of two-three wor d sentences predicts their performance when they begin primary school. Roulstone, S et al (2011) Investigating the role of l anguage in childrens early educational outcomes Simply in words heard, the average child on welfa re was having half as much experience per hour (6 16 words per hour) as the average working-class c hild (1,251 words per hour) and less than one-third that of the average child in a professional family (2
,153 words per hour) (Hart & Risley 2003, 8 To understand what is key or important we mu st understand the unimportant. We cant discard something we dont understand. Research Considered Mathematical reading is about precision (Fuentes, 1998) and very few children are taught explicit ways to read it (Kenney, Hancewicz, Heuer, Metsisto & Tuttle, 2005).
Some words have a mathematical and real world meaning (Barton and Heidema, 2002). A study by Knifong and Holtan (1977) also did not show th at reading ability levels affect a childs ability to solve wor d problems. Frustration over the inability to understan d the mathematical language caused errors in solving t he problem.
Fuentes (1998) states that every word in a word problem i s necessary for it to be solved. Have you seen this model? Discuss its limitations. RUCSAC is not a solu tion and m
ay be part of the pro blem Questions Is it time to ditch RUCSAC? Is a word problem a story? Would a guided reading approach work? Are numberless word problems a solution? What role do verbs and problem types play in solvi
ng word problems (does this mean we need to be cautious of operation word lists? Which models support an improved understanding of word problems/mathematical language used? How important is morphology in supporting the un derstanding of mathematical vocabulary? Is a Word Problem a Stor y? Yes
In the beginning/then/ now Reading left to right Sentences Characters No Tenseless/hypothetical Unusual contexts Jo Boalers Maths World
Sometimes grammatic ally incomplete No plot/motives/conne ctions to reality Numberless Word Problems Hegarty, Mayer, and Monk (1995) - Studies o
f successful and unsuccessful problem solver s. They found that unsuccessful problem sol vers had more difficulties than successful pr oblem solvers in translating the word proble m to mathematical representations because they were more focused on the numbers tha n on informative words within the problem. Hegarty, M. (1995) - Comprehension of arithmetic word problems: A c omparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87, 18-32.
Numberless Word Problems https://bstockus.wordpress.com/n umberless-word-problems/ What is the value of this approach? How could you apply this to the following problem ? Extension: Let children choose their own numbers. What works?
Are there any choices that do not work? Why? Toy Cars At the start of June, there were some toy cars in the shop. During June, some more toy cars wer e delivered. Some toy cars were sold.
Toy Cars At the start of June, there were 1,793 toy cars in the shop. During June some more toy cars were delivered Some toy cars were sold. Toy Cars At the start of June, there were 1,793 toy cars in the shop.
During June, 8,728 more toy cars we re delivered Some toy cars were sold. Toy Cars At the start of June, there were 1,793 toy cars in the shop. During June, 8,728 more toy cars we re delivered 9,473 toy cars were sold.
Toy Cars At the start of June, there were 1,793 toy cars in the shop. During June, 8,728 more toy cars were delivered
9,473 toy cars were sold. How many toy cars were left in the shop at the end of June? Can you think of another step you could add to this problem ? What does sold mean about the calculation you need in this problem? How could we turn this into a money problem? How could we turn this into a measurement problem? Chicken
Why do you think the weight of the chicken is r elated to cooking time? Work out what you can from this information. Cooking Times Look at the cookin g times and tempe ratures for the turk ey in the table (
https://www.ocado. com/content/misce llany/pdfs/CS0441_ Turkey_page_4.pdf ). Work out what you Verbs and Problem Types
Mathematical Verbs & Situations Which operations are connected to these words often s een in word problems? Buy How much money do they have left? Quickest time Slowest time Take Collect
Plant Remove Give Change (from buying) Get another Give away Raise money Save Posters by Steve Cooke - NALDIC
Caution with Mathematical Mea ning of Operations Agata had 36 books. She had 15 mor e books than Maria. Then Maria gave 6 of her books to her friend. How ma ny books does Maria have now? Why did a Year 5 more advanced EAL learner get the answer 45 an d not 15?
Addition or Subtraction? *Jozef had 10 apples. He had 7 more than Maria. How many did Maria have? *Farida and Alex had 15 stickers altogether. Farida had 9 stickers. How many stickers did Alex have? *Miguel had some sweets. He gave his friend 6 sweets. Now Miguel has 13 sweets. How many sweets did he have
in the first place? Examples from Steve Cooke (NALDIC) Morphology Numeric Prefixes https://membean.com/treelist
THE FRAYER M ODEL APPLIC ATION IN MAT HEMATICS https://nonexamples.com/compare Mathematical Words & Building Connections
Created for the DfE 2008 Extend: How is your example NOT an example of ? Using your Environment/Experiences Activity Exploring Mathe matical Vocabul
ary A few ideas.. Useful ideas for Vocabulary D evelopment in Mathematics Think of other words which mean the same thing (synonyms). Can you think of a word which means the same as _________? Co nsider opposites too. What does this word mean here? Does it always mean this? (Co ntext!)
Restricting words to describe a word (ATM: Fourbidden) Personal dictionaries to note the words they are unsure of and fi nd a definition. Pre-teach vocabulary Vocabulary Pictionary Guided Reading Approaches
A Guided Reading Approach ? Some possible strategies to assess u nderstanding Re-reading a problem, sequence the proble m, where does the problem take place? Are there other words we could use for wit hout changing the meaning of the probl em?
What words do you already know? Are any words unfamiliar? What does mean? Doe s it always mean this? What will you do firs t? Identify the first part of the problem. Show me which part of the problem your eye s are drawn to first. Summarising the problem in your own words .
Mathematica Mathematica Context Who? What? Instructional l Language l Symbols /Action Language s J. Knapp 2008 Instructions in Test Papers
Maths is as much about English as Mathematics. How many of these (for your Year Group) would your class be familiar with? Would any of these instructions cause difficulty? Missing number box simple Missing number boxes complex Simple number response Complex number response Rearranging digits into a calculation Circle on a time table Circle single example that has two required variables present
Convert before circling examples that match given criteria Draw the translation Explain Demonstrate method Provide all possibilities Provide an algebraic rule Current Conclusions & Implications
Mind Mapping connections within words Simplifying the numbers in the initial modelling Exploring a book talk (Corbett, P) approach - teacher demonstration Scan text for unknown words and not just the bold ones (Kest er Phillips, D et al, 2009)
Regular vocabulary exploration Consistent messages with support staff and parents Word morphology having a cross-curricular impact Problem types Implications Balance of timetabled Mathematics and Literacy in School Guided approach Time References Fuentes, P. (1998). Reading comprehension in mathematics. Clearing Ho
use, 72(2), 81-88. Kotsopoulos, D. (2007). It's like hearing a foreign language. Mathematic s Teacher, 101(4), 301- 305. Hegarty, M. (1995).Comprehension of arithmetic word problems: A com parison of successful and unsuccessful problem solvers. Journal of Educ ational Psychology, 87, 18-32. Knifong, J. D., & Holtan, B. D. (1977). A search for reading difficulties among erred word problem s. Journal for Research in Mathematics Education, 8, 227-230. Maikos-Diegnan, J. (2000). Mathematical word problem comprehension. Unpublished Masters Thesis, Kean University. ERIC Document ED 451 4
81. Retrieved on October 22, 2007. https://www.tes.com/news/school-news/breaking-views/acronyms-rucsac -prevent-children-thinking-mathematically-we-need-a https://dynamath.scholastic.com/pages/dynamath-expressions/2016-17/ the-case-against-keywords.html https://www.whatihavelearnedteaching.com/the-problem-with-using-key Resources available via this link from Google Drive: https://drive.google.com/open?id=1f
XAToAsoPv5PIHeXQdyMFnskL5JcUC5V Review & Next Steps Numberless Word Problems Emphasis on Verbs Morphology
The changing meaning of mathematical words through problem type Vocabulary Scaffolds Guided Reading Approaches
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