Making math accessible for all students
Friday, July 18, 2014
Wednesday, January 23, 2013
Post-Secondary Education
My good friend and colleague Jaf and I have had multiple discussions on college as a goal for students. He contends (I paraphrase but hope he'll comment on here) that not all students are college material and as such this universal push is overly simplistic. I understand the reasoning behind this and agree to a degree.
I contend that college is more of a generic term for post-secondary education. "College" typically refers to a 4 year institute of higher learning but community college and even more technical schools would fall under the "college" moniker. When we prepare students to be effective college students, I am thinking that a student who wants to go to UConn to be a nurse, another who wants to go to Manchester Community College to get an associates degree in technology and a third who want to attend Lincoln Tech for welding all have to learn self-help skills: notebook organization and use, completing homework, etc.
This may be part and parcel to a discussion on the purpose of education. I think this is an incredibly important topic and would love to hear from others, especially educators.
I contend that college is more of a generic term for post-secondary education. "College" typically refers to a 4 year institute of higher learning but community college and even more technical schools would fall under the "college" moniker. When we prepare students to be effective college students, I am thinking that a student who wants to go to UConn to be a nurse, another who wants to go to Manchester Community College to get an associates degree in technology and a third who want to attend Lincoln Tech for welding all have to learn self-help skills: notebook organization and use, completing homework, etc.
This may be part and parcel to a discussion on the purpose of education. I think this is an incredibly important topic and would love to hear from others, especially educators.
Tuesday, January 22, 2013
Representations of Concepts
Concrete-Representational-Abstract (CRA) is a continuum of representations for concepts. Bruner is famous for advocating this. Other terms used are concrete-pictorial-symbolic.
Typically math teachers rely on symbolic/abstract (P=2L + 2W below). This is often too abstract for many students and they do not develop conceptual understanding. Pictorial/representation (the rectangle below) is still too abstract for many. Concrete is a level students can intuitively access. In the example below I taught a lesson perimeter and area of a rectangle to 6th graders. They were first asked to create a pen for their animals and then count how many fence pieces were needed. This led to the rectangle and eventually the formula.
A teacher candidate asked about CRA for students in higher level courses. Some even many students in these courses do need all three. When the concepts are more challenging and abstract the concrete representation is harder to develop often times but it can be done. For example, area under a curve and integration can be modeled by using a loaf of sliced bread.
Typically math teachers rely on symbolic/abstract (P=2L + 2W below). This is often too abstract for many students and they do not develop conceptual understanding. Pictorial/representation (the rectangle below) is still too abstract for many. Concrete is a level students can intuitively access. In the example below I taught a lesson perimeter and area of a rectangle to 6th graders. They were first asked to create a pen for their animals and then count how many fence pieces were needed. This led to the rectangle and eventually the formula.
A teacher candidate asked about CRA for students in higher level courses. Some even many students in these courses do need all three. When the concepts are more challenging and abstract the concrete representation is harder to develop often times but it can be done. For example, area under a curve and integration can be modeled by using a loaf of sliced bread.
Steps and Task Analysis
A teacher friend of mine in the ASD community shared an anecdote for me to share. Her son had trouble figuring out perimeter. He was counting the squares and didn't want to count the corner squares twice. The solution? The squares were pieces of sod to fill in the inside while the outer sides of the squares were fence pieces. This shows how kids can get caught up on the smallest details that teachers overlook. This can be addressed using task analysis.
Below are examples of task analysis. The top photo taken at Burger King shows a sequence of photos showing how to pour a soft cream ice cream. The bottom is a task analysis break down of all the steps in solving a linear equation - ALOT of steps!
Below are examples of task analysis. The top photo taken at Burger King shows a sequence of photos showing how to pour a soft cream ice cream. The bottom is a task analysis break down of all the steps in solving a linear equation - ALOT of steps!
Wednesday, August 1, 2012
Sunday, November 20, 2011
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