Elementary Tasks

This is how I sorted the following elementary tasks:

High Level Cognitive Demand:    J, M, N

Low Level Cognitive Demand:  A, B, C, D, E, F, G, H, I, K, L, O, P

Please keep in mind, I use to be a high school teacher!!! From my frame of reference, I ranked many of the tasks low, however, those of you who work with elementary students on a daily basis have a better frame of reference.

As I reviewed each task, I thought about the thinking involved to solve each of them.  For a high level cognitive demand task, I used the following as a criteria:  how much reasoning, number of steps to solve, manipulatives, how much information was provided for students, evaluate, analyze, draw conclusions, and non-routine problem.  For a low level cognitive demand task, I used the following as a criteria:  recall of information, show understanding of concept, use a formula, explain their thinking, and and solve a problem.

In most of the tasks I ranked low, students would show an understanding of the problem.  For example, In task C, I ranked that as high, but when I thought about it, students are only demonstrating an understanding of division by providing a real-life situation.  Task G may be difficult for students because they have not mastered the steps of division and those are just routine division problems.  When I first reviewed task H, I thought the answers could be A and B.  Then I reread and realized that the problem said "most" of the students had pockets so it must be B.  This task measures how to interpret graphs.  In Task K, students had to solve by using a number sentence then explain with a picture or words.  This shows understanding of the word problem.  Many times, people think because you justify, summarize, or explain it bumps the question to a high level of cognitive demand and that is not always true.

In the tasks I selected for a high level of cognitive demand, there was a level of reasoning that students had to do and there maybe more than one answer or several methods to solve.  For example, in Task J, students could have several different answers to the problem.  Students need to have an understanding of 1/2 and realize that 1/2 is not the same number for different sizes but it is the same ratio.  I am not sure about task M. Would students know what leveling off mean?  Maybe this problem is low and the choice of vocabulary would trick students.  Let me know what you think.

Martha’s Carpeting Task and Fencing Task

In the Martha’s Carpeting Task, the cognitive demand is low because the dimensions are given.  Students should know “long” is the length, “wide” is the width, and Area = Length X Width.  I assume the teacher has introduced the area formula to students; therefore, I would classify this problem as Recall/Reproduction in Webb’s Depth of Knowledge because students only need to recognize that “square feet” refers to area in the question and calculate (i.e. multiple the dimensions) to find the answer. 

In the Fencing Task, the cognitive demand is higher because only the fencing (i.e. perimeter) is given.  Students need to know how perimeter and area are interconnected.  Also, students must determine the maximum area for the rabbits in both situations (i.e. 24 and 16 feet of fencing).  I believe students would draw a picture, list the factors of 24 as well as 16, and use trial and error to find the answer.   Based on their answers in questions 1 and 2, they must organize their thinking and explain how to determine the most room or area for any amount of fencing.  Thus, students would describe a strategy on how to derive an answer.  Strategies may vary.   I believe this problem would be at the Skill/Concept level in Webb’s Depth of Knowledge.   I also considered the Strategic level because this problem requires reasoning, drawing conclusions about how to figure out area for any amount of fencing.  This question goes beyond just memorizing a formula. 

Furthermore, I think the cognitive demand of any math problem would also depend on the instruction.  For example, if the teacher reviewed several types of fencing tasks similar to this one, then students are just regurgitating what the teacher has already shown them.  Therefore, deep thinking is removed. 

Condominium Problem

Condominium Problem
In a particular condominium community 2/3 of all of the men are married to 3/5 of all of the women.  What fraction of the entire condominium community are married?

When I first looked at the problem, I added the two fractions together and got 16/15.  I knew that did not seem reasonable.  I had to think about it for a moment.  Then I realized this is a part to whole problem.  The part represents married people and the whole represents everyone in the condominium community.  Once this clicked in my mind, I just set the problem up using variables M and W.  So this is how I solved it.

M = men                            2/3M + 3/5W
W = women                              M + W
       
Assumptions:  the number of men must equal the number of women; cannot marry yourself so I must have an even number of married people as a final answer

2/3M = 3/5W   from this equation I solved for M and got:   M = 9/10W

Then I substituted for M in my original equation:
2/3(9/10W) + 3/5W
9/10W + W

Next, I simplified and combined like terms on the top and like terms on the bottom:
6/5W
19/10W

Next, I cancelled out the W's and divided the fractions.  My final answer is   12/19.   There are 12 married people out of a total of 19 people.

I liked this problem because I had to think and process.  I will share it with teachers!

Introduction

I am Shannon Register from a little town called Whiteville, NC.  I am the middle child of three siblings and I use to suffer from the “middle child” syndrome.  I thought the world revolve around me until I had my beautiful daughter, Kaylin.  Now, the world revolves around her.  In my spare time which is not much, I spend it with my husband and daughter.   Currently, my family lives in Fayetteville, NC. 

After graduating from NC State University with a BA in mathematics education and BS in mathematics, I moved back home to Whiteville and taught high school mathematics for several years.  Then moved to Fayetteville where I taught for several more years and served as an assistant principal and principal as well.    I am the newly named Assistant Superintendent of Secondary Education (Grades 6 – 13) in Hoke County.  I have worked in Hoke for the past 7 years and started in the position of Curriculum Coordinator for Science and Mathematics in grades 9 – 12.  My passion is mathematics.  I LOVE math!  I love the challenge of solving problems and problem solving.  When I taught mathematics, I always had at least 90% of my students proficient on the end-of-course tests.  Everyone would ask “What is your secret?”  I did not have a secret.  As I reflect, I believe it was the relationships that I cultivated with my students.  I focused on relationships first then mathematics.  I firmly believed in the six-point lesson, explicitly teaching problem solving skills, and standard-based instruction.

In my different roles as a supervisor of curriculum, I observed different approaches to teaching mathematics such as textbook-dependent instruction, activity-based instruction, inquiry-based instruction, etc.  I believe exemplary mathematics teaching is ensuring that instruction is student-centered to include scaffolding strategies to meet the needs of students.   As mathematicians, we must use a conceptual understanding framework of mathematics not just memorization of formulas.  We must foster curiosity, problem solving skills, and allow students to discover and make connections to previous knowledge. 

I am very excited about this course because it will provide me an opportunity to delve into the pedagogy  of mathematics and get a better grasp of conceptual understanding in mathematics and how we as educators need to shift our thinking and instruction to ensure students are equipped for the 21^st century.  I am confident in leading in mathematics, however, I want/need to add more tools to my toolbox and assist teachers with making a 21st century shift in the delivery of content.  

                                    My two babies!  Kaylin (daughter) and Anthony (husband)