Discussion 5

Children’s Reactions to Verbal Arithmetical Problems with Missing, Surplus or Contradictory Data – Ewa Puchalska, Zbigniew Semadeni

Summary

I really enjoyed reading this article partly because it brought back some childhood classroom memories and partly because the article was quite comprehensible. The authors discussed how important it is to sometimes intentionally leave some information out from word problems to unlock the powerful reasoning of our students. They termed this as “Missing, Surplus or Contradictory Data Problems (MSCD). Consider the following questions:

·         There are 26 sheep and 10 goats on a boat. How old is the captain?

·         A 7-year-old was given the following problem: “You have 10 red pencils in your left pocket and 10 blue pencils in your right pocket. How old are you?

·         Pete had some apples. He gave 4 apples to Ann. How many apples does Pete have now?

These questions in my view, are ridiculous because some information is missing, needs more information and quite contradictory. According to the authors, such questions raise debate among students, they get to talk about the illogical reasoning behind the questions. These questions, the authors believe, help students to realize that mathematics is not always soluble.

Ewa and Zbigniew also disclosed that most students notice something odd about a word problem, but prefer to hide their doubts largely due to the teacher’s authority which confirms the problem to be unquestionable.

Stop 1

Have you felt at any point of your teaching that, your students needed more information to a word problem or question the problem but are unable to? How do you make yourself available or approachable for your students to ask doubtful questions?

Swan (1983 as cited by Ewa & Zbigniew) described two interesting approach to teaching decimal place value (not only that I think, but all topics in Math):

1.       The Conflict teaching approach which involves pupils in discussion and reflexion of their own misconceptions and errors. Conflict approach may lead to deeper conceptual understanding.

2.       The Positive only approach made no attempt to examine errors and avoided them wherever possible.

I believe when teachers intentionally use the conflict teaching approach, they could tap into the powerful reasoning of their students to solve math without fear. Deducing from this article, it is important to include MSCD in our lessons to unlock our students’ reasoning skills and create a lively and enthusiastic environment.

Stop 2

I am wondering how often to include MSCD in lessons? Will it not lead to students not seeing the authenticity in math questions or make math questions look ridiculous? (anyway, who says we can’t have fun in math? (lol).