Relational Understanding of Integration

Tips/Advice on the lesson:

Hello fellow teachers! This webquest was created in order to have students solve problems for a concept and then after learn about relational understanding in order to reflect on their previous work. This method can be used with any type of math concept for any grade, not just integrals like I used. Relational understanding is very important for students to have in mathematics. This is why reading the Skemp article is so important so that students can learn about the different between relational and instrumental understanding. This activity will probably take up a whole 50 minute class period, but you can be the judge of that depending on your class. Have students work on some problems for your concept, and then after have them discuss relational understanding. This will get them thinking about whether or not they implemented relational understanding when they worked through the problems. When they're working in groups, make sure all students are contributing to the process and creating the mind map. This is great way to see how student work together and are able to present their ideas to the class. I love this activity! 

Standards

Standards Covered: 

There are no specific state standards for this concept, because calculus concepts are usually for AP and not in the basic high school curriculum. However, I did implement a number of the standards of mathematical practice that are stated in the Alabama College and Career Ready Standards: 

• Make sense of problems and persevere in solving them.
• Reason abstractly and quantitatively. 
• Look for and express regularity in repeated reasoning.

These are all very important standards of mathematical practice that should be considered when implementing this activity in the classroom! 

Credits

What helped me:

I have had much experience as a math education major in learning about different methods, use of technology, and professional development in advancing my mathematics education knowledge. The content I have learned in these classes and my different experiences in math classrooms helped me create this webquest. There are also different resources that I used. 

The resources I used in order to create this webinar are:

Khan Academy Videos:

Indefinite Integral

https://www.khanacademy.org/math/calculus-home/integration-calc/antiderivatives-calc/v/antiderivatives-and-indefinite-integrals

Definite Integral 

https://www.khanacademy.org/math/ap-calculus-ab/ab-accumulation-riemann-sums/ab-def-integral/v/definite-integrals-intro

Integration Worksheets:

Indefinite Integral

https://www.mathworksheets4kids.com/calculus/integration/basic-1.pdf

Definite Integral

http://tajimasolis.weebly.com/uploads/3/7/3/4/37346235/worksheet_-_definite_integrals.pdf

Skemp Relational Understanding Article 

Skemp, R. (1978). Relational understanding and instrumental understanding. Arithmetic Teacher, 26(3), 9-15.

(Attached below)

Alabama Course of Study: Mathematics

Alabama State Department of Education. (2016). Alabama college and career ready standards. Montgomery, AL.

https://www.alsde.edu/sec/sct/COS/2016%20Revised%20Alabama%20Course%20of%20Study%20Mathematics.pdf

Calculus Textbook:

Stewart, J., (2016). Calculus: Early Transcendentals, 8th Edition. Boston: Cengage Learning.