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Multiple Ways to Teach a Concept

Multiple Ways to Teach a Concept

Use the tables below to do the following:

Select two concepts covered in Topics 1 and 2 of the course. Then, select one example problem for each of the concepts you selected.

Search the internet for two videos teaching each of your selected concepts. You will select four videos in total. Select two videos that teach the concept in two different ways for each of your concepts.

Solve your selected example problems using the methods employed in the two videos for each concept. Please show all the work. (Hint: If you solve the problem on paper, take a picture and copy and paste it to the Word document. You do not have to type to solve the answer.)

Concept #1 Example Problem
Problem Solving with Patterns

 

There are 20 students in your classroom. On Friendship Day,

every student gives a card to each of the other students. How many cards are exchanged?

Video link #1 Video link #2
https://www.youtube.com/watch?v=QErRuYVCPjg https://www.youtube.com/watch?v=ikjdpZ64vVs

 

Solving the problem using the method from Video #1 Solving the problem using the method from Video #2
The formula for this problem is n(n-l), where “n” is the number of students and “l” is the number of cards given out by each student. In this case, n = 20 and l = 19, so the formula would be (20)×(19) =380. This same pattern can solve other problems with Friendship Day cards. Using the difference table sequence, assuming two students are in the classroom, each student would give out one card. If there are three students in the classroom, then each student gives out two cards (one to two), a total of 6 cards. The pattern will be 0, 2, 6, 12, 20, 30, 42,54, 68 …….to the 20th student 380 cards.

 

Concept #2 Example Problem
Converting Between Bases

 

Convert the decimal number 100 to base 4.
Video link #1 Video link #2
https://www.youtube.com/watch?v=nm6wmLD5F9s https://www.youtube.com/watch?v=hIs3A6gGz2w
Solving the problem using the method from Video #1 Solving the problem using the method from Video #2
When 100 is divided by 4, the quotient is 25, and the remainder is 0.

When 25 is divided by 4, the quotient is 6, and the remainder is 1.

When six is divided by 4, the quotient is 1, and the remainder is 2.

When one is divided by 4, the quotient is 0, and the remainder is 1.

Then, we will write the numbers from last to first.

It will be 1210 base-4

 

 

 

 

 

By (1),(2),(3),(4),

The result is 1210

Part 2 Reflection:

Mathematicians use different methods to solve math problems. Research shows different problem-solving styles can effectively solve the same problem since people differ in learning styles (Pomalato et al., 2020). Some methods are more effective than others depending on the complexity of math problems, required accuracy, and the ability to think abstractly.

Different styles are essential as they allow students to find the best method. In the professional world, different methods are also used to solve problems. Consequently, using multiple problem-solving strategies will be an asset in your future career. Some students may find that they are more successful in problem-solving when they use a specific method, while others may switch between methods based on the problem at hand. Personality traits, cognitive skills, and social factors influence the preference for a particular problem-solving style.

When working on a professional project, there are bound to be several problems that come up; therefore, having numerous problem-solving capabilities is useful. Besides, a person with multiple ways of solving a problem will be better equipped to find a solution (Salaeva, Eshkaraev & Seytov, 2020). It is also true in the world of mathematics. There are different math problems, and each one requires a different approach. Using multiple methods to solve a problem will make you more successful in your studies and future career. Teachers must also know these different problem-solving styles and teach their students how to use them. The goal is for students to become flexible thinkers to apply the appropriate method when solving a problem.

When working on a project, it is essential to verify the accuracy of my work. It can be done by using different methods to solve the problem. I can use the most familiar method if there is more than one way to approach a problem. It will help ensure the accuracy of my work. For instance, I have been working on a project that requires me to use a calculator. Several different calculator types are available, each with its functions. If I am unsure how to use the calculator, I must switch between methods until I find one that works best for my situation. In addition, I can use different methods like substitution, elimination, and graphing to solve a problem in algebra. In calculus, I can also use different methods like integration or differentiation. I will verify the answers I get by using a different method. I will also use these different approaches to solve math problems in the future.

Moreover, different styles can be used to get a different perspective on the problem in my business. For instance, I plan to approach math problems from a graphical perspective to understand how the data is related. For example, if I am trying to solve a business problem, I might approach it from a financial or graphical perspective. It will help me get a different perspective on the problem and possibly find a solution I would not have thought of otherwise.

References

Pomalato, S. W. D., La Ili, B. A. N., Fadhilaturrahmi, A. T. H., & Primayana, K. H. (2020). Student Error Analysis in Solving Mathematical Problems. Universal Journal of Educational Research, 8(11), 5183-5187.

Salaeva, M., Eshkaraev, K., & Seytov, A. (2020). It is solving mathematical problems in unusual ways with excellent limits. In European Scientific Conference (pp. 254-257).

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Question 


Multiple Ways to Teach a Concept

Use the tables below to do the following:

Select two concepts covered in Topics 1 and 2 of the course. Then, select one example problem for each of the concepts you selected.

Search the internet for two videos teaching each of your selected concepts. You will select four videos in total. For each of your concepts, select two videos that teach the concept differently.

Solve your selected example problems using the methods employed in the two videos for each concept. Please show all the work. (Hint: If you solve the problem on paper, take a picture and copy and paste it into the Word document. You do not have to type to solve the answer.)

Concept #1 Example Problem
Video link #1 Video link #2
Solving the problem using the method from Video #1 Solving the problem using the method from Video #2
Concept #2 Example Problem
Video link #1 Video link #2
Solving the problem using the method from Video #1 Solving the problem using the method from Video #2

Part 2 Reflection:

In 250-500 words, explain why it is essential to be able to solve math problems using different styles. How is this going to help you in your future professional practice?