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I want you to think back to an experience I'm sure most of you all had in a math class. We've afll been given a math question asking us to first estimate the answer than compute it after to see how close we were. For example:
Question:
"If Jenny gets $.47 for every Apple that she sells how many dollars while Jenny have if she sells 30 apples per day and works 90 days in the summer?"
Answer:
Estimation:___________
Computation:_________
Show your work:
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Now if you were like me I'd be more concerned about making sure my estimation was as close as possible to the correct answer because I was worries that the teacher would think I didn't have a good understanding of the content if it was far off. For that reason my approach to this question would be to fill out the show your work section first, then the answer. Finally I would put a number not far off of the correct answer as my estimate.
Looking back on this and trying to understand why I'd (I wanted to say children but that wouldn't be accurate because I'm not sure I'd be any less of a culprit to than I was back then) approached this question this way I came up with a couple reasons:
- I was caught up in the idea that I always had to have the correct answer.
- I was worried the teachers would be disappointed in me if the estimate was far off.
- I didn't understand the importance of developing strategies related to estimation.
First I'd highlight the important parts:
"If Jenny gets $.47 for every apple that she sells how many dollars while Jenny have if she sells 30 apples per day and works 90 days in the summer?"
Next I would round the numbers to something more manageable:
-90 days in the summer would become 100 days.
-30 apples per day could remain 30 apples/day.
-$.47 for every apple would become $.50/apple.
From here I would say 30 apples/day for 100 days is 3000 apples. Then I'd think if Jenny makes 1/2 of a dollar per apple she would have half as many dollars as she sold apples. That would be 3000/2 which is an easy 1500.
Making my estimation become; $1500 for Jenny over the summer.
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If we look at this suggested process for estimation it resulted in an answer that was only a few hundred off and a 15.4% error - which if we consider the fact it took hardly any mental math to solve is pretty impressive.
If we take the time to encourage students to think of ways to answer simple questions, like this apple problem, through basic reasoning and utilizing estimation we will be developing their adaptive learning skills. In my opinion this is one of the best ways to set the foundation of have students thinking outside the box and develop creative solutions to complex problems.
Our first steps to move students in this direction is slowing down our lessons and providing basic techniques creating manageable problems. We want to give the students the opportunity to make educated guesses. Once students start developing some skills and strategies for estimation then introduce more complex, challenging problems.
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- Did you have any experiences similar to the one I outlined?
- Did you have an experience very different from this one?
I really enjoyed reading your blog this week! I can relate to the experience you described around estimation. I too think I was focused on getting the right answer and what the teacher would have thought if my estimation was off. I also found it easier to just solve the problem then to really think about the question and how I would estimate. I think knowing why we struggled (and disliked/avoided) with estimation is going to help us as future teachers. As you mentioned, hopefully we can help encourage students to develop their estimation skills by slowing down our lessons and providing them with the opportunity to focus on estimation. Looking forward to reading your next post!
ReplyDeleteI'm glad you can relate to this as well! Hopefully we can start turning these notions of estimation around.
DeleteHi Mike,
ReplyDeleteI can definitely relate to your experiences that you had with estimation while growing up in math class, I too would always just try to aim for the correct answer. As students growing up we are always focused on finding the correct answer or in other words "what is on the other side of that equals sign." Although finding the correct answer can be important in some math problems, with estimation it is good to understand the processes that can be used which can be transferable to real life applications such as calculating a tip at a restaurant.
Thanks for your insights, I enjoyed reading your thoughts this week.
Ryan,
DeleteI like how you brought up the fact that students are always being taught to solve for "what is on the other side of that equals sign." That in it's self is an interesting topic. Educators need to be careful we are not engraining children with the idea that equations are solely to produce an answer. A lot of the time in higher math the problem becomes balancing equations. When students focus to much on producing a single answer to place on the other side of the quals sign they miss out on the true meanings of equations.
To clarify, I feel that we need to focus on the idea that equations are composed of two sides that equal each other i.e., 4+6=10 just as 4+6=7+3.
Cheers,
Mike