## Reflection: Adaptive Technology Khan Academy and Simplifying Radicals - Section 1: Assessment Overview

Many educators ask, "what is the role of the teacher during these online modules? Is there anything that we can do?" The role of the teacher doesn't change at all in this lesson. Putting work online doesn't represent any type of fundamental shift in my pedagogy. It is simply a change in format. Like any lesson I coordinate, my role is to facilitate discussion and push student insight. In order to do that, I need to be hyper aware of student misconceptions and strategies.

The two main areas needed to solve these problems involve prime factorization and the law of exponents that states (ab)^x = a^x * b^x. This is a great time to circulate and ask them questions like, "why did you rewrite the square root of 8 as the square root of 4 times the square root of 2? Did that change the value in any way?" I also like to ask contrasting questions like, "does the square root of 16 equal the square root of 4 plus the square root of 4?" This is another opportunity to spiral back and contrast (x+y)^.5 versus (xy)^.5 Many students believe that these are equal (it is a major misconception).

The key is to ask students a follow up question. This requires preparation.

The series of exponent activities on Khan Academy can be done all in a row or spread out. They can be placed anywhere in the unit with great success. I don't worry if students are perfectly prepared for any particular exercise at any time. Instead, I use these assessments whenever I think that they fit the mood and progress of the class as a whole. The digital environment is such a different experience that students will approach the problems with excitement and will often not connect the work to their experiences in class (at least not automatically and especially not in the beginning). As I teach, I know that I need to make that connection for them. To do that, I end each class with a discussion about the problems they tried and even review them in the beginning of the next class session. The goal is to constantly spiral over the same concepts, but take every approach possible.

Khan Academy is constantly changing its layout and its scoring system, but for this activity I would ask students to log in (optional) and work until their achieve mastery. This is a topic you need to discuss with students. "Mastery" in Khan Academy might mean something like getting 20 correct, but I want students to complete about 10 questions and only continue if they think they need more practice. I have had many students complain about Khan Academy. They get frustrated, because if they make a single mistake they need to basically start from the beginning. They find this discouraging. They kept working and working even when they understood the topic. They spent hours trying to get "mastery" and would give up if they hit the wrong button or number. Instead, they need to stop and reflect. They need to think, "do I need more practice?"

Preparing to Teach this Lesson
Adaptive Technology: Preparing to Teach this Lesson

# Khan Academy and Simplifying Radicals

Unit 12: Gimme the Base: More with Exponents
Lesson 5 of 15

## Big Idea: We can use prime factorization to break down the number inside a radical sign and then use those factors to simplify the expression.

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Standards:
Subject(s):
Math, Scalars, positive exponents, Exponents and Exponential Functions, khan academy, zero exponen, properties of exponents, Math 8, exponentiation, Laws of Algebra, skill development
60 minutes

### Shaun Errichiello

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