Suppose you wanted to assess a student's prior knowledge/understanding of addition/subtraction. You have invited her to tell you something she knows about adding. Her response is "5+5=10".
What will you say next?
Wednesday, August 27, 2008
Prior Knowledge
Most educators agree about the value of assessing a student's prior knowledge to determine how best to proceed with instruction. There are several strategies we might use to do that; for the purpose of this post, let's think about good questions that have potential to make student thinking visible.
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18 comments:
I believe that before taking this class, I would have assumed that the student understood that operation and moved on to subtraction.
This year I will ask her to describe a place where she might see that or experience it. I will also ask the student to tell me what it means. I may also ask her to show me with materials (I will have out a ruler, some blocks and fraction bars), as well as a marker and paper.
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I would ask 5 what plus 5 what? (as I had red and green cubes on the table) And then hopefully lead her to say something like 5 red cubes plus 5 green cubes equal 10 cubes altogether-- and either draw it out with red and green markers or use red and green cubes to demonstrate it.
In my world, kindergarten, children often rattle off rote addition facts without understanding what they mean. This is a perfect spot for the why question or show me how 5+5=10 (build it with math materials).
I think my big question would be "why?" or "how do you know?". Before guiding or prompting I would make sure to have plenty of materials to choose from, in case they needed help breaking down the process of what really goes on with the addition fact (that they have most likely just memorized).
I would want to know that she really understands what 5+5=10 means so I would ask her to explain a bit more. 5 what + 5 what? I would ask her to show me with some concrete materials...make a model to show her thinking. If she can successfully do this, I can then move on to see whether she understands the connection between addition and subtraction by asking her what would happen if I took 5 away from 10?
I think that I would ask the child to show me how she knows that 5+5=10, and could she show me with different manipulatives or everyday objects and then I might ask her if there is more than one way to show 10, does it always have to be 5+5?
I have just spent this last week getting my 1st grade classroom ready, although ready is never the case! As I reflected on this question and the comments made, I thought of the materials that I have been sorting through. I think I would ask her to show me how 5+5=10 using a pan balance. In thinking about reducing the amount of distractions, I'd start with just one color/kind of material, like unit cubes or pennies. Once she demonstrates understanding, move to other ways to make 10 (8, 12, 9, . . .), introduce multi-colored materials (unifix cubes), etc.
I've been studying/using the New Zealand number frameworks which is their national math curriculum (on line!), and I really like how they break up numeracy assessment (and instruction) into knowledge and strategies. The strategies part looks at how a child solves problems (such as the addition one you gave us). It shows the way children progress developmentally (such as solving addition at first by counting all the objects, then imaging the objects, then counting on from the larger number, and then using part-whole strategies such as adding 9+5 by adding 10 +5 and then subtracting one). The knowledge part outlines the knowledge children need to progress through the developmental strategy stages. If anyone is interested in looking at the New Zealand assessment/curriculum(it has wonderful lessons and materials all on line) it can be found at www.nzmaths.co and then go to the numeracy project.
Along similar lines, I might ask, "What does 5+5=10 mean? 5 what? 10 what? How do you know this? Why is this addition? What if you don't have 5 but have a different amount? Are the 2 numbers always the same (5 and 5)? etc. Subsequent questions would obviously depend upon student response.
I would first tell her that she's RIGHT! But... I would ask her to demonstrate using cubes (or other), and ask her to give a unit for her numbers. For example, "5 what plus 5 what...?" Then... I might start discussing that equal sign. :-)
Getting the students to think about what exactly is meant by 5, of what? and then using hands on examples or real world examples to explain the meaning of 5 & 5. It would be helpful to use 5 students plus 5 more, and them count up. Take a look at the symbol of the plus sign and have them say in their own words what it means...a kid definition. Also, have them transfer the symbol to another equation with different manipulatives. The bottom line is that the kids need to put their own meaning to the symbol and be able to truly understand it in their terms.
I was reminded of your post this week as I started math screening with some first graders. A question posed from the Number Knowledge Test is "If you have 4 chocolates and someone gives you 3 more, how many chocolates do you have altogether?" No manipulatives or visuals are allowed for this question.
After each answer was given, I asked questions, such as "How do you know that?" or "How did you figure out the answer?” or “What were you thinking in your head?" That's when it really became interesting. Some had no idea how to explain their answers, indicating to me either they truly had no idea how their answer popped into their heads or that maybe they were not familiar with giving explanations. Some readily expressed their thinking (counting up using their fingers, thinking 4+4 and then taking 1 away, etc.)
The most interesting explanation came from a little boy who knew the answer, he said, because he had played "Bimopoly(!)" that weekend at the family camp. When prompted with several more questions, like "How did that help you?" and "Tell me more so I can understand what you were thinking in your head," he revealed that he had thought of the dice in that game. In his mind he saw four dots on one and three dots on the other and then counted all the dots just like they were chocolates. It took him a long time to get out all the words of his explanation, but I'm so glad that he stayed with it. His answer underscores the importance of making connections. By not providing any materials, he used a recent experience to figure out a way to solve this problem. His explanation told me that he made an appropriate connection, recognized patterns of three and four, used the "counts up from one" strategy when adding sets, knew that this problem required the combining of sets (addition), and that he could do all that by visualizing it. This could be used as a different approach to find out what a student might know about adding, as posed in your post.
Linda, can you give me more info about the Number Knowledge Test? Others many be familiar with it, but I am not. How/where could I purchase it?
Thanks--
Debbie, this is my first attempt to try the Number Knowledge Test. I discovered it when I read an on-line article called "Screening for Mathematics Difficulties in K-3 Students" from the Center on Instruction, a research center in NH. See http://www.centeroninstruction.org/files/COI%20Math%20Screening.pdf
The test itself can be found at the Number Worlds website http://clarku.edu/numberworlds/index.htm
Click on the button marked "Assessment." The test is free to download.
I have been working with a 2nd grader, who is in special ed. First, I would ask him to show with manipulatives 5+5=10, then ask him to explain how he got there or what he did and what he was his thought process.
what I am looking for from him is an explanation : a group of 5 blue marbles grouped (combined) with 5 red marbles makes a total of 10 marbles.
If he is able to verbalize this I may give him more problems to ensure he has the understanding.
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