Category: Problem Solving

Venn Diagram: A "How To" For Young Learners.

3/22/2015

Teacher: Every item in this hoop follows a rule. Each item is the same in some way. Can you tell me how all of these objects are the same?
The rule is, everything in this hoop must be.....

Student: Everything is red.
Teacher: Everything is red? (points to a bear) Is this red? (points to triangle) is this red?
Now we can say that the rule for this hoop is that everything inside this hoop must be red.

What about this hoop? What could be the rule for this hoop? Everything in this hoop must be....

Student: They're all different colors!
Teacher: They are all different colors. That's a way that they are different. Is there a way that they are all the same?

Student: They're red!
Teacher: Yes, some of them are red. Are all of them red? (points to red one) Is this one red? (points to another red) Is this one red? (points to a yellow) Is this one red? (points to a blue) Is this one red?

Are all of them red?

Student: No....
Teacher: Then that can't be our rule. Everything in this hoop is the same in some way. How are they all the same?

Student: They're bears.
Teacher: Are they ALL bears? (points to one) Is this a bear? (points to another) Is this a bear?
Our rule for this hoop can be that everything in this hoop must be a bear.

Teacher slides the two hoops so that they overlap.

Teacher (points to the yellow hoop): Everything in this hoop must be a...
Student: Bear!
Teacher (points to the red hoop): And everything in this hoop has to be...
Student: Red!
Teacher: And here, in the center, it is part of the yellow hoop (teacher outlines yellow hoop with pointer finger). It is also part of the red hoop (teacher outlines red hoop). Since it is part of this hoop, everything in here has to be a bear. It is also part of this hoop (teacher outlines red hoop), which means that it also has to be....
Student: Red!

Teacher: To belong in the center, it has to be a bear and it has to be...
Student: Red!
Teacher: Can you find anything that belongs in the center? Something that is a bear and red?

The products used in this lesson are Attribute Blocks and Counting Bears.

I highly recommend both of these products for their versatility in math instruction.

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Preschool Math Standards: Problem Solving

8/29/2014

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In order for a child to have a comprehensive mathematical understanding, he must be exposed to mathematical concepts beyond numbers and counting. There are five fields into which we group our Math Standards: Number Sense, Geometry, Measurement, Sorting and Patterning, and Problem Solving.

This blog entry will cover the Academic Standards that fall under the Problem Solving category.

Thinking Ahead - By playing strategy games like "Nim," a child can develop the ability to think one or more steps ahead of her opponent.

What's Missing? - Given a pattern or a set of objects, a child can determine what is missing.

Estimation

Probability - For preschoolers, this is the ability to determine whether an outcome is likely or unlikely. Given the shapes shown below, is it likely or unlikely that I will pick up a square?

Story Problems

Skip Counting - Counting by fives, tens or twos. At this age, this could be categorized with problem solving skills or number sense.

Problem Solving is just one small part of preschool mathematics. We have broken Problem Solving into six standards:

Thinking Ahead
What's Missing?
Estimation
Probability
Problem Solving
Skip Counting

In our classroom, each lesson, game or classroom material has been intentionally planned and placed in the room to fulfill our Academic Content Standards.

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Problem Solving and Expectations.

2/28/2014

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In 1989 NCTM (National Council of Teachers of Mathematics) developed a set of standards for mathematics as a framework to guide each state in developing mathematical standards.

We use these standards as part of the framework in creating our preschool math curriculum because these standards are established, research-based and designed by professionals “dedicated to improving the teaching and learning of mathematics” and “to ensure the highest quality mathematics education to all students”.

We had a very successful day solving word problems. The chocolate chip cookie cereal we used might have something to do with that! Today we were solving with manipulatives (the cereal), but soon we will begin to increase the children’s repertoire of problem solving techniques. I can't wait!

Notice that each child has her own visible workspace. This is an often overlooked necessity when working with young children. Studies have shown that high expectations produce higher accomplishment in the classroom, but we can not have high expectations without providing the materials the children need to meet our expectations.

Example: If I had given everyone the chocolate chip cookie cereal without the "workspace", one child would have the cereal under her legs, one would have his behind him, one would have hers beside her, one would have his cereal in front of three other students, and two might have their cereal in front of them. By the time we got organized and found everyone's cereal, I would have lost their attention and there would be very little math problem solving.

By using a visible workspace we have freed up our time and our minds for higher level thinking.

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Matrix Math!

2/20/2014

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Math is much more than counting! Good math instruction should lead your students to higher level thinking and problem solving.

These children are working on matrices (plural of “matrix”).
In a matrix, each row shares an attribute, all the same shape OR all the same color, and each column shares a different attribute.

A matrix is just a very high level of sorting/classifying. It’s kind of like an EXTREME Venn diagram.
These children are figuring out precisely which color/shape goes in a given square.

This was our first time working on matrices, so I helped them think it through by asking questions (What color needs to go here? And what shape? Can you find a card with that shape and color on it?) but these children are doing all their own work.

Impressive, I know!

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Venn Diagram: A "How To" For Young Learners.

Preschool Math Standards: Problem Solving

Problem Solving and Expectations.

Matrix Math!

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