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TExES Physics/Mathematics 7-12 (243): Practice & Study Guide62 chapters | 688 lessons | 60 flashcard sets

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Lesson Transcript

Instructor:
*Rachel Tustin*

Dr. Rachel Tustin has a PhD in Education focusing on Educational Technology, a Masters in English, and a BS in Marine Science. She has taught in K-12 for more than 15 years, and higher education for ten years.

Logical reasoning is a practical skill students need to learn in order to be successful in math and science courses. In this lesson, we will look at the challenges to teaching logical reasoning. Additionally, we will look at teaching logic in the context of science.

Teaching logic can be a challenge for teachers with any age group of students, but especially for adolescents. At an age when puberty is beginning to set in, and hormones and distractions can run rampant, it can be challenging to engage students in an activity that requires prolonged deep thought.

In the adolescent mind, for a lot of students, it is as if you are trying to teach them to play a complex game, such as chess, for the first time. Meanwhile, within their minds, there is a dance party with music blasting in the background. This may seem an impossible task, but not so if you can engage the students visually and kinesthetically in the process.

If you have been a teacher for a while, you understand very well that **logic** and adolescence are not terms often linked together. Logic is the ability to apply systematic thinking, or steps, to solve a problem or derive a pattern. For example, in math when you are given a sequence such as 2, 5, 8, and 11, how do you know what number comes next in the sequence?

You have to apply a series of steps to determine what that pattern may be. First, you subtract each number from the one that came before. In this case, that will give you a difference of three, and you can apply that to find the other numbers in the sequence.

In middle and high school, adolescent students are beginning to move from the concrete operational to the formal operational stage. For concrete operations, students need concrete examples, or manipulatives, to solve problems. As adolescence moves into formal operational, they begin to become capable of reasoning without manipulatives. However, the odds are that in any given classroom you have students who use both stages of operational thinking.

So, how do you teach logic to students, some of whom may not have developed the ability to perform reasoning in situations with which they lack concrete experiences? The trick is to make the logic process as hands on, and physical, as possible for your students. Make logic **kinesthetic**, so that students have a physical movement to associate with the steps in the logical reasoning process. This method should make it easier for them to understand.

So, let's revisit the mathematical sequence from above. On paper, it may be daunting to students. However, a good place to start is to try making it more visual for the students.

Ask each student to line up and hold up a piece of paper or a small white board to represent each number in the sequence. Then have another set of students determine the difference between each number in the sequence (i.e., + 5, or -4, or whatever the difference may be). They can write the difference on a white board or a different color of paper, whichever makes it easiest to see that they are not in the sequence when they join the line.

Next, have the last group of students determine exactly what mathematical function needs to be performed to get the next number in the sequence. Do they have to divide by 5? Add 2? Each student, or team of students, should be assigned a space between the two numbers. Once they have that written on paper or a whiteboard, they can stand in front of or replace (depending on the size of your class) the difference in the two numbers.

From there, students can derive a pattern to determine the next numbers in the sequence and test it out. Getting students up and moving helps them visualize what is happening better, especially as you move from simple to more complex sequence patterns.

Logic can be easily linked to science in the classroom because often logic problems are not mathematical in nature, and require some experimentation to solve. Therefore, students can easily apply the steps of the scientific method and create a procedure to test their solution for more complex logic problems.

For example, you present students with a problem of having three baskets, each filled with five plastic Easter eggs. You could use rice or sand to fill the eggs and seal them with tape. Be sure all the eggs are the same weight except one, and make it at least 100 grams less. Ask the students how they could determine which egg weighs less. Here is the catch, though; they only get to weigh one egg on the scale.

Divide your students into teams, and give each team a set of eggs set up like the problem above. Then ask students to hypothesize which egg weighs slightly less than the others. Give them parameters to conduct their test. For example, can they roll their eggs down a ramp and calculate speed? Can they have a bucket of water to sink their eggs into? Once students are done running their procedure, they can share their results with the class. In the end, as a class, they can weigh their eggs to see if their tests were correct.

**Logic** is the ability to apply systematic thinking, or steps, to solve a problem or derive a pattern.

When teaching logic and scientific problem solving to middle or high school students, you have to consider where they are in their development. Students are likely to be between the concrete operational and formal operational stage of development, so their ability to think abstractly is probably somewhat limited. Therefore, you want to find creative ways to engage the students both visually and **kinesthetically** in the problem-solving process.

For concrete operations, students need concrete experience or manipulatives to solve problems. As adolescents move into formal operational, they begin to become capable of reasoning without manipulatives. The trick is to make the logical process as hands on and physical as possible for your students. For problems without manipulatives, make logic **kinesthetic**, so students have a physical movement to associate with the steps in the logical reasoning process.

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TExES Physics/Mathematics 7-12 (243): Practice & Study Guide62 chapters | 688 lessons | 60 flashcard sets

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