High Cognitive Demand - Sorting Task

Martha's Carpeting Task

 In this problem, I drew a picture and labeled the length 15 and the width 10. I then used the A=l x w formula and plugged in the numbers to get 150 sq. feet as the answer.


Fencing Task

With this problem, there was a little more work involved:

1- To get the greatest area, you would have to try all of the combinations that would give you 24 ft on the perimeter: 7x5, 6x6, 9x3, 8x4, and 10x2. Using the area formula for each one, you find that a pen that is 6x6 on each side gives you 36 sq. feet which is the most room.

2- Again, you have to look at all of the combinations that would give you 16 ft on the perimeter: 5x3, 6x2, 7x1, and 4x4. In this case the largest are is 16 sq ft, meaning each side would be 4 ft. long.

3- In both problems, the perfect squares yielded the greatest area in the pen. If you have an amount of fencing that you can not use a perfect square with, you can always draw a picture to figure it out.

Similarities: both problems are area problems, both require a prior knowledge of area and how to find it

Differences: the amount of thinking/reasoning required for each problem, the number of ways in which the problem can be solved, and the need to generalize, 



Elementary Tasks

High Level Cognitive Demand	Low Level Cognitive Demand
Task A: interpret unit of measure	Task C: real life situation and solve
Task B: continuing patterns	Task D: respond to graph questions
Task F: fractions	Task E: place value
Task H: use graph to make predictions	Task G: solve division with calculator
Task M: interpret average (application)	Task I: multiplication
Task N: analysis	Task J: comprehension (explain)
Task P: application	Task K: comprehension (explain)

High levels of cognitive demand include: making connections, analyzing information, drawing conclusions, abstract thinking, and completing procedures (tasks) with connections to meaning

Low levels of cognitive demand include: stating facts, following procedures, solving routine problems, having single cognitive answers to a problem, and memorization with connections  to meaning

Discussion

A. Does a particular feature (e.g., writing an explanation as part of your answer, drawing a picture to explain what you did, using manipulatives to solve the task) indicate that the task has a certain level of cognitive demand?

While I do not think because a task has a particular feature that it indicates a certain level of cognitive demand, high cognitive demand tasks requires students to make sense of them. They have to read, determine what the questions is and how to use the information provided in the task. There are often multiple ways of finding the correct answer(s) to the task. High cognitive demand questions invites students to explain their thinking, make new connections, describe their process of figuring out the answer, and/or critique other's ideas.  Low level cognitive demand generally focuses on correct answers.

B. Is there a difference between "level of cognitive demand" and "difficulty"?

Yes. The level of cognitive demand describes the type of thinking required by a task, not whether the task is "difficult".

C. What effect does context (e.g., setting in which the task is used, students' prior experience, grade level) have on the level of cognitive demand required by a task?

The tasks in which students engage provide the contexts in which they learn to think about subject matter and different tasks may place differing cognitive demands on students. There is a connection with how the question is written, how it is presented and how it is implemented that will have an effect on the cognitive demand.

Problem Solving

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?

To find the fraction of the total population that are married, I found the lowest common numerator

3/5 of women: Multiply top and bottom by 2 to get 6/10

2/3 men: Multiply top and bottom by 3 to get 6/9

Add 6/10 + 6/9= 12/19 of the entire condominium community are married

Introduction

     Hello! Math has always been one of my FAVORITE subjects in school and I have always enjoyed teaching math to students. In this class, I hope to learn more about the math curriculum, instruction, and assessment so that I can help teachers deliver instruction in such a way that students are able to understand the concepts being taught. I received my undergraduate degree in Elementary Education (K-6) and my Master of School Administration degree from UNCW! This past spring makes 2 years that I have been taking classes in Educational Leadership with a focus on Curriculum and Instruction.

Stephanie Willis

About Me......
     I am a native of Wilmington, N.C. I graduated from E.A. Laney High School, where the FAMOUS (if you're into sports) Michael Jordan attended school. I lived in Raleigh for about 3 years while attending N.C. State University, before transferring to UNCW. Upon graduating (the first time) with my Elementary Education degree, I worked in Brunswick County as a Pre-K teacher for 3 years and then I moved to 1st grade for 3 years. I think I still would have been teaching, if not for my assistant principal (at the time) who pulled me aside one day and talked to me about applying for the Principal Fellow's Program because of what she saw in me as a classroom teacher. Nevertheless, I figured I would apply and if it was meant to be, I would get accepted into the program. I guess it was meant to be, because I found myself taking a leave of absence from work while completing the 2 year program. While taking classes, I worked on campus in the Education Building in King Hall and taught an EDL200 class and worked with different professors on projects. After my internships at a 3-5 school in Pender County and my high school, I was employed by Pender County Schools as an Assistant Principal at the same school where I was an intern. After a few years and transitions, I became principal at the same school. I then moved into a county role managing a 4.5 million dollar Safe Schools, Healthy Students grant and for the last 5 years I have been working as the Coordinator/Administrator of our Alternative Learning Program which I built from the ground up.

GO PANTHERS!

      My husband (who is also a Wilmington native) and I have been married for 18 years (will be 19 in September) and we have one son who is 16 years old and VERY active in school and in the community. I have been a soccer mom, t-ball mom, basketball mom, football mom, and lacrosse mom since he was 4 years old. Football and Lacrosse seem to be the sport of choice as he enters his junior year of high school.....at Laney. Our spare time consists of working in the community as I am
also the Co-Founder/Director of a girls mentoring group called GRITS (Girls Rocking in the South). We love to travel and are AVID fans of the Carolina Panthers! We try to attend at least 2-3 games each season at Bank of America Stadium.

     One thing that is unique about me is my ability to connect with students who are considered "at risk". I have a passion for helping student see the best in themselves when others have a hard time finding the best in them. Every student should have someone that can be their advocate even when they have pushed the limits and made the wrong decisions. I tend to be that person for a lot of the students that are assigned to our alternative program.

How I feel about mathematics............
     Math is very exciting to me! It's like taking the pieces of a puzzle and making it all fit together. I have always loved math in school (except for the proofs and theorems in Geometry) When it comes to learning mathematics, I feel eager. When it comes to teaching mathematics, I feel confident. School mathematics should be engaging and FUN! Being good at mathematics means being able to apply the concepts in a variety of ways.

What exemplary mathematics teachers do to help their students learn mathematics.....
     Since I have not been directly involved with the math curriculum in a few years, I would need some refreshing, but I feel confident in my ability to lead others in the area of math since I consider myself to be a quick learner. An exemplary leader is one who meets the learner where they are and builds a trusting relationship so the learner feels that they can take risks when asking questions and feel supported. Exemplary leaders in the area of mathematics make sure that they are teaching math in a way that meets the learning styles of all learners and is engaging for all students. They use data to drive their instruction, and they use a variety of assessment tools to check the pulse of their learners frequently.