【Math】Examples of Thinking Tools Usage
【Jellyfish】6th Grade Permutations and Combinations The teacher presents the wrong answers to the questions. We then set up an activity to think about how to point out the mistakes and give advice.
【2 Circle Venn】5th Grade Integer
Use it in such a way that students find the overlap in the grouping into multiples of 2 and multiples of 3, and notice that multiples of 6 are overlapping.
【Y】4th Grade Quadrangle
"We introduced LoiLoNote because we wanted the children to use the LoiLoNote thinking tool, but we were careful not to let it become the purpose of the learning.
The students' free thinking led the class to focus on a single idea, and I could feel their joy at having discovered the regularity on their own.
While arranging the pattern blocks without gaps, the learning was about sharing realizations and discoveries about regularity and the characteristics of squares."
【Y】3rd Grade Times tables In learning to count the number of ・ (dots) using times tables, a "Y-chart" was used to classify how the answers were obtained.
【2 Axes】6th Grade Organize the cases in order
In the unit "Organize the cases in order," various solution methods are possible, but "whether the order is relevant or not" and "whether it is a diagram or a table" are considered to be the most important differences. Based on this point of view, by comparing and examining using the coordinate axes, it is possible to understand the better way to solve the problem.
【Y】5th Grade Angle of the figure
The thinking tool will be used in the third of a total of seven periods of the unit plan.
We set up an activity to explain how to find the sum of the interior angles of a quadrilateral.
Using the fact that the sum of the interior angles of a triangle is 180 degrees, which we had learned in the previous period, we came up with a way to find it without having to cut out the interior angles.
In the LoiLoNote, the students filled in diagrams, formulas, and explanations for finding the sum of interior angles and submitted them.
We shared them with the children and used the Thinking Tool,
We categorized the ideas into "draw one diagonal line on a rectangle and divide it into two triangles" and "draw two diagonals and divide it into four triangles."
【X】5th Grade Area
"We used previously studied items such as squares, rectangles, triangles, and trapezoids to figure out how to find the area of a rhombus. Each idea is a visualization of which method was used. This flow can be followed by similar activities for triangles, trapezoids, and rhombuses. This teaching material conveys to children the origin of arithmetic: "Formulas are not learned by being told, but created."
【3 Circle Venn】5th Grade Least Common Multiple
【Y】6th Grade Line Symmetry Figure
"Introductory Situation for Linearly Symmetrical Figures
By using the diagrams and pictures in the textbooks before the students are taught the basics of the subject matter,
By accepting the diversity of views and ideas, students are encouraged to listen to the explanations of others and to explain their own ideas."
【Pyramid】5th Grade Percentage
A situation where students use information on their own, rather than being taught by a teacher. They select information, organize and summarize it, think about how it is used in their surroundings, and output it. The students are asked to submit their answers to the Submission Box, where they share their answers and learn from each other whether the answers are the same or not, and whether they have discovered anything new.
【Data(6)】6th Grade Fraction
"At the end of the unit, in pairs of three, create questions (and explanations) to understand fractions divided by fractions using the test function of LoiLoNote.
Explain that the number of questions is to be created from 1 to 3 in 20 minutes and 5 minutes, then created. Then 10 minutes for peer evaluation of the same group members,
Then a flow class with 10 minutes to find a recommended test for anyone in the class."
【PMI/KWL】5th Grade Velocity
"On the theme of which animal is the fastest, three different animals, first ask students to raise their hands for the animal they think is the fastest, using only images.
Then, utilizing the data in the upper left corner, draw two horizontal lines on the PMI/KWL sheet and have the students think about the speed from each perspective, such as how many meters they run per second or how many seconds it takes per meter."
【Concentric Circles】4th Grade Perpendicular, parallel and quadrilateral
After learning about perpendiculars and parallels, have the students write on their own that even quadrilaterals come in many different shapes, and place about five cards on the concentric circles chart.
They are all quadrilaterals, but with the condition that the innermost two sets of sides are parallel and the outer one set of sides is parallel. (It might be interesting to let the students think about this.)
The students themselves can also move each card to develop convergence from divergence.
They can visually see that each quadrilateral can be grouped into a parallelogram if two sets of sides are parallel, a trapezoid if one set of sides are parallel, and a rectangle otherwise.
【Webbing】4th Grade Large Numbers
"Ask the students to write three large numbers.
After this, switch tools and move the three written large number cards to the diamond chart with the largest number on the top card, the second largest number in the middle, and the third largest number on the bottom.
Ask the child the rationale for each of the three cards ranked. What divided the student in terms of points? This is a scene for thinking and verbalization."
Proposal from Mr. Iwashima
"The image is a scene of the property of equality in the first grade of junior high school, but in the second grade "Do we add or subtract?" and in the third grade and beyond, when thinking (especially to gain proficiency) about how many arithmetic operations are involved, by describing the "problem," "operation (formula)," and "why I thought so", students will be able to correctly understand the relationship between quantities and express it in an equation. Become more proficient in this area"
"I think it is also a good idea to put the reason down and let them move it around. I have been practicing many mistake finding puzzles with candy, thinking that it would be an effective way to learn. I think it can be used for other types of error searches as well."
"This is the use of the information analysis chart in finding commonalities in the 5th period. This is used not only in arithmetic but also in many other situations, so it may not be worth introducing, but I believe it is very effective for finding commonalities."
I suppose we could use an X-chart to determine the range and mate by the angles between the right angle, the second right angle, the third right angle, and the fourth right angle when we take the picture at the first hour."
Advice from Professor Haruo Kurokami
"I think it is nonsense to use them when solving problems. It is more important to learn the tools (both graphs and formulas) that are already specialized for arithmetic. I think they are best used for metacognition, to organize patterns of solving, to think about variations of how to make mistakes, and to relate and systematize the content, and I think they are very effective."
"But since we don't create time throughout the unit to organize solution patterns, to identify and organize the possibility of mistakes, or to relate the content beyond the unit, we can't use it that way. If you can do such a class, you can use it, and in fact, it would be very interesting."
Q: Can anything be used in situations where students are looking for ways to solve the question?
"It cannot be used directly. What you can use is a method of decomposing a figure (drawing a line), or a corresponding image with the formulas you have learned before (a list or a table of formulas). The former is the method of drawing a diagonal line in the case of a trapezoid, or fitting it to a rectangle. The latter is an image of quadrature formulas for various triangles. In any case, thinking tools can be used to set up situations in which you can create your own images of such methods and their correspondences, but when solving problems using formulas, I think the only way is to use what you have already learned in arithmetic. If the students have metacognized the previously learned material using thinking tools, it will be easier for them to apply the formulas. That is the most important part of the learning process, and using thinking tools is the best way to achieve that."
"If you listen too closely to the teachers in the field, you will be asked what you should do to solve the problem in front of you, but you will not be able to solve the problem because you have not organized your knowledge to solve the problem in front of you in your own way. If you use thinking tools to organize your knowledge, you will be able to use the organized knowledge to solve the problem. In this case, the thinking tools are being used and are useful in the sense that the thinking tools are used to organize the knowledge and then to create a solution to the problem."