Building Cubes Lesson Reflection
My lesson plan is a review of linear relationships, further investigation of quadratic relationships, while introducing cubic relationships. This is accomplished on mini pc’s, using an applet that allows students to build and manipulate cubes. The students will generate a table from the applet which models linear, quadratic and cubic relationships. As directed by my professor, I did not change my lesson plan from the original draft.
I taught my lesson to my eighth grade math students. The lesson went very well!! There was one little change that I made from first hour to second hour, but other than that no big changes. The change I made was to demonstrate with a larger cube. This allowed for my students to see all of the differing cubes that they were to be identifying. The 2×2x2 cube did not allow for this, and that caused some confusion in my first hour. I also decided to have my second hour add my school website as a favorite on the computers; this was done simply to save time. The lesson overall was a huge success, learning was done and students enjoyed the process.
Question Set One
What was learned? What were the learning goals of this instructional experience? What were the underlying assumptions (explicit and implicit) about the nature of knowledge?
The learning goals were to explore the “painted cube” situation, which has linear, quadratic, and cubic functions and also compare linear, quadratic, and cubic functions. This was the first introduction to cubic relationships. I assumed that students could and would affectively navigate the internet to reach the applet. I knew that students could record data, identify linear relationships and start to identify quadratic relationships.
What are the affordances for how knowledge/information is being represented? What are the constraints?
The technology being put into this lesson added that “awe, cool” part to this math lesson. That moment is a very important part of trying to get an eighth grader to learn. However, when an eighth grade student is allowed on a computer one must always be watching their every move, this becomes frustrating sometimes. They like to visit their My Space pages etc., and they are good at getting around the firewalls.
How does learning take place? What elements of constructivism did you observe? What elements of behaviorism did you observe? Were any other learning theories present?
Social constructivism was very obvious in my lesson. There were many in depth mathematic conversations/arguments taking place during my lesson, which resulted in students constructing a deeper understanding of what they were doing. They also exhibited behaviorism when they followed my modeled behavior of how to build and manipulate the cubes.
Was your lesson intended to supplement or supplant existing curriculum? Or, was it intended to enhance the learning of something already central to the curriculum or some new set of understandings or competencies?
My lesson is a part of my curriculum. I actually have taught this lesson without the applet for the past 5 years. In the past my students had to build the cubes and then imagine where the paint would be if they painted the outside of the cube. This was difficult for many students; spatial visualization is hard for many of them.
How are important differences among learners taken into account?
My lesson allows for different learning styles to be met. I am not continuously using the same approach and the students are not continuously doing the same thing.
What do teachers and learners need to know in order for your lesson to be a success? What demands are placed on teachers and other “users”? What knowledge is assumed?
Teachers and learners need to be able to use the applet to make this lesson a success. Also both teacher and learner need to be able to navigate the internet. I assume that the teacher has a math background, giving them the knowledge to answer student questions about linear, quadratic, and cubic relationships.
How did you assess what students were doing and what they were learning from this activity? How did you hold them accountable for the work they did?
As my students were working I was walking around the classroom making sure my students were on task and completing the problem. After my students worked through the problem we went over their answers as a class, making sure that we all were in agreement. The students also turned in the table and completed problem after the quiz that week.
Question Set Two
What role does technology play in your lesson? What advantages or disadvantages does the technology hold for this role? What unique contribution does the technology make in facilitating learning?
Technology plays a key role in allowing my students to collect the needed data to complete the problem. There were many advantages. I will mention two. One is that it saved time, before when completing this problem it would take three days. With the applet it was completed in 2 class periods. The other advantage is that the applet let students manipulate and visualize cubes in a way that is not possible in their hands. The most unique contribution was the “awe cool” part of the technology, if a teacher can get the education ‘hook’ in the students are along for the learning without even knowing it.
What did you expect your students to make of their use of technology in your lesson? How did they react when using the technologies? What questions did students have, and how did you respond to them?
I was very confident that my students would like using the mini computers; the applet was an added bonus, cool thing they could use. They enjoyed using both. My students didn’t have any technology questions. They did have math questions, and I responded with the correct answers.
How would you describe how students were making sense of the content with the technology?
Having taught this lesson without the technology gives me added insight into this question. My students were making much better sense of the content because they could all see the painted parts of the cube. None of my students had to imagine painted cubes; it was actually painted for them. This allowed for my students to complete the table in a timely and accurate fashion.
