Student answers

Student answers

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about explaining how some students made mistakes on a maths problem.

In a maths test Room 6 were given this problem:

 

Trading-Cards-150px.png
Puawai had 54 trading cards. She gave 18 to her brother.
How many trading cards does Puawai have left?
 
 
Each student had a different way of working out the problem. Their workings are shown below:
 
sums-trading-cards-problem.png
 
 Each student has made a mistake.  For each student identify what they did wrong.

Question 2Change answer

James answer for trading cards problem
 Explain what James did wrong.

Question 2Change answer

Sarah's answer for the trading cards problem
Explain what Sarah did wrong.

Question 2Change answer

Maraea-trading-cards-problems.png
Explain what Maraea did wrong.

Question 2Change answer

Sione-trading-cards-problems.png
Explain what Sione did wrong.
Task administration: 
This task can be completed with pen and paper or online (with NO auto marking).
Level:
3
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Key Competencies: 
Using language, symbols, and texts
Keywords: 
strategies, addition, subtraction
Description of task: 
Students explain why a range of students' answers to a maths problem are incorrect.
Curriculum Links: 
This resource can help to identify students' ability to apply additive and simple multiplicative ideas flexibly to combine or partition whole numbers to recognise correct strategies.
Key competencies
This resource involves explaining why given addition strategies are correct or not. This relates to the Key Competency: Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Additive thinking, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  Y6 (11/2005)
A sufficient explanation requires some specific detail.
James:

  • used addition instead of subtraction

Sarah:

  • didn't rename
  • didn't carry in the tens column

Maraea:

  • subtracted the smaller number from the larger
  • only subtracted the tens / forgot to minus the 8

Sione:

  • subtracted 20, and then subtracted 2 (instead of adding 2)
  • subtracted 22 instead of 18

[Accept other explanations that correctly identify incorrect details of each of the strategies.]

 easy
difficult
difficult
difficult
Diagnostic and formative information: 
  Common error Likely misconception
James Answer is correct Students are not thinking about the original maths problem – they are looking only at the equation that James has written (which is correct if the original problem is ignored).
All She/he is wrong (general) / wrong because the answer is … Students may have a limited concept of what an explanation is.  Both the general wrong and comparison to the correct answer lack any specific detail about "what they have done wrong" – that the response is wrong is already given in the question.
All Incorrect details Students have some understanding about the nature of an explanation (specific detail), but have formed their own misconception about the arithmetic of the students' strategies shown, and accordingly the details provided are incorrect or would result in an incorrect answer.
Next steps: 

For students who thought James's answer was correct in question a), encourage them to re-read (or actually read) the question and think/discuss what is being asked.  Use questions like "if she gave 18 away what is happening to the number of cards she has?" and "What operation is that?" to prompt a connection between the original problem and the "students' answers".

NOTE: an incorrect operation can be a common error relating to not reading the question or a reading comprehension issue.

Students who answered with an explanation that was too general or with a comparison to the correct answer need to have a "sufficient" explanation modelled and the features of what makes an explanation sufficient made explicit:

  • specific details
  • evidence
  • appropriate use of examples
  • justification
  • clarity to another reader

For students who answered with an explanation where the details were incorrect, the above features and modelling of a sufficient explanation may well supplement their current understanding of an explanation, and with checking for coherence (and meaning) the flaw in their explanation may be identified.

Links to the Number Framework
The Number framework recognises the importance of students being able to select from a broad range of (part-whole) strategies to solve mathematical problems.  This "broad range" is an important indicator for students moving from Early additive part-whole to Advanced additive part-whole for addition and subtraction.
A way to develop a wider range of strategies is to share, and critique (for accuracy and efficiency) alternative strategies in a group or whole class.  This resource is concerned with the critiquing of others' strategies and begins to explore what constitutes a "sufficient" explanation of an incorrect strategy.