Chapter 7

What?
Chapter 7 is about Constructivism. In constructivism, learning is defined as an active process in which learners construct their own meaning based on prior knowledge and experience. Advantages of defining learning this way are prior knowledge and personalization. Disadvantages are personal misconceptions and incorrect interpretations that can take place during "learning". The power of schema comes into play when interpretting facts. As teachers we need to figure out what our students' schematas are through discussions and brainstorming. A concept is a grouping of objects/events that have something in common or a category that we fit things into in our head. In order for teachers to teach a concept they need to be able to define them clearly and give an example of the best prototype (typical example of a concept) that won't confuse the students. Teachers can fix misconceptions by 1) identifying existing misconceptions before instruction begins, 2) convince students in a non-threatening way that their existing beliefs are inadequate, 3) motivate students to learn correct explanations, 4) maintain self-esteem, and 5) monitor what students say and write for persistent misconceptions. Jerome Bruner is one well-known constructivist whose theory is "knowing is a process, not a product". Discovery learning is where the learner draws from his/her own past experiences and exsiting beliefs to explore concepts while the teacher acts as a guide and not a instructor. Such teaching techniques as discovery learning promote problem solving skills in students.
So What?
As a future teacher it is important to realize that students are bringing prior knowledge and misconceptions with them to the classroom. As a math teacher, it is very important that students understand the mathematical steps and the correct way to solve problems. In some content areas clearing up all misconceptions may not be necessary, but for math it is crucial that all students are on the same page with the teacher. Also I think that it is very important that the many concepts in math are very clearly explained and good prototypes are given so that misconceptions are not created in the classroom.
Now What?
An example of a 5 E- Lesson plan is:
Engage- Provide the students with a straightedge and compass and ask them to draw as many things as they can using only those tools
Explore- Have the students find different ways to construct 30, 60, and 90 degree angles using only their straightedge and compass
Explain- They then will work in groups to collaborate and get ideas from each other
Elaborate- Give board time to those who volunteer to explain their methods to the class
Evaluate- Allow students, with guidance from teacher, to look for any errors in their methods or things that may not actually be true...followed up with confirmation from teacher about their methods and clearing up any misconceptions that may have arose.