Expert answer:the perspectives of culturally relevant teaching
Solved by verified expert:In this assignment, you will choose one of the Algebra tasks given below and use a rubric to analyze the task. This rubric is the result of a framework connecting higher level tasks with the perspectives of culturally relevant teaching, thus refining the descriptions of two of the categories presented by Smith and Stein as (a)procedures with connections to concepts, meaning and understanding of mathematics, culture and community, and (b) doing mathematics for the purpose of becoming empowered intellectually, culturally, politically and socially. These two renamed classifications are given for the purpose of having teachers of mathematicsrethink the extent to which selected mathematics tasks challenge students to ask relevant questions of themselves and the world around them (Matthews, Jones, and Parker, 2013).
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MAED 5352 Patterns and Algebra
Module 1: Culturally Relevant Cognitively Demanding Tasks
Introduction
Submit Assignment by 11:59 PM, Sunday.
Please fill in these blanks for each assignment
Student:
Date:
Grade Level/Subject Area:
Overview: Culturally Relevant Cognitively Demanding Tasks Introduction
In MAED 5351 you read about the research done by Smith, Stein, and colleagues regarding the selection of
tasks that are cognitively demanding for students (these articles are provided for you in this course as well).
The tasks can be classified on four levels, with higher-level tasks classified as “Procedures with Connections”
or “Doing Mathematics” (Stein and Smith, 1998; Smith and Stein, 1998). This week you also read about
Culturally Relevant and Culturally Responsive Pedagogy – connecting mathematics to students’ cultures and
experiences (Enyedy & Mukhopadhyay, 2007; Gilbert, et al, 2008; Gutstein, Lipman, Hernandez and de los
Reyes, 1997; Irvine, 2009; Ladson-Billings, 1997; Leonard and Guha, 2002; Metropolitan Center for Urban
Education, 2008; Moses and Cobb, 2001; Nelson-Barber and Estrin, 1995).
Due to the increasing diversity in many classrooms as well as the need to make mathematics relevant for all
students regardless of cultural background, it is important for teachers to be familiar with this type of instruction.
In this assignment, you will choose one of the Algebra tasks given below and use a rubric to analyze the task.
This rubric is the result of a framework connecting higher level tasks with the perspectives of culturally relevant
teaching, thus refining the descriptions of two of the categories presented by Smith and Stein as (a)
procedures with connections to concepts, meaning and understanding of mathematics, culture and community,
and (b) doing mathematics for the purpose of becoming empowered intellectually, culturally, politically and
socially. These two renamed classifications are given for the purpose of having teachers of mathematics
rethink the extent to which selected mathematics tasks challenge students to ask relevant questions of
themselves and the world around them (Matthews, Jones, and Parker, 2013).
Objectives
•
Choose an Algebra task from the choices given below
•
Classify the Cognitive Demand of the task on one of the four levels presented by Smith, Stein, and
colleagues (should be one of the higher two levels), providing a thorough rationale
•
Evaluate the task as Culturally Relevant or not, using the CRCD framework and providing a thorough
rationale
•
Critique the framework used to make the evaluation
NOTE: Save your file as a Word (.doc or .docx) or PDF file. Any other format is not guaranteed to be
readable by the person grading your work.
©2017 University of Texas at Arlington
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MAED 5352 Patterns and Algebra
Instructions
Choose one of the following tasks to evaluate AS IS:
Earning Money
One summer you charge $20 to mow a lawn and $10 to trim bushes. It is one week before school starts
and you want to make $300 in one week to buy new shoes and clothes before school starts. For every
lawn you mow, you also trim the bushes. How many lawns did you mow? If you do not trim any bushes
during the week, how many lawns will you have to mow to earn that $300? Explain your answers using
verbal, graphical, tabular, and symbolic representations.
How Much Does a Locust Eat?
In your Social Studies class you learned that a large swarm of 50 billion locusts can eat 3,000 tons of
crops in a single day. Many restaurants offer hamburgers that weigh a quarter pound (meat only before
cooking). Suppose everyone in your school ordered a quarter-pound hamburger for lunch. How many
school days would it take for all the students in your school to eat the amount eaten by the swarm in a
single day? Explain how you found your answer.
Weighty Issues
According to a 2006 report from the Centers for Disease Control, 33.6% of Americans between the ages
of 2 and 19 are either overweight or on the brink of becoming so, up from 28.2% in 2000. That’s about 25
million overweight kids. Assuming this trend continues at a constant rate, how many kids do you predict to
be overweight in the year 2050? W hat about the year 2100? Is it reasonable to assume a constant growth
rate for this trend? Why or why not.
Math-a-Thon
You are helping to raise money for cancer research at St. Jude’s Children’s Research Hospital by
participating in your school’s Math-a-Thon. You will take pledges from your community based on the
number of math problems you answer correctly.
• Your neighbor pledges $6.00 per problem.
• Your teacher pledges $1.00 for the first problem, $2.00 for the second problem, $3.00 for the third
problem, and so on.
• Your Mother pledges $.10 for the first problem, and will double it for each problem after that.
Describe the number of problems you must solve for each of the three pledges to make the most money.
Driving Decisions
You family’s SUV uses gas at a rate of 17 miles per gallon of gasoline. Its current sale value is $16,000.
You see a commercial for a new hybrid car advertised at $22,000 that uses gas at a rate of 40 miles per
gallon of gasoline. Estimate the mileage your family vehicle drives per week, and decide if your family
should keep your current automobile or sell it and buy a hybrid. Defend your position using tabular,
graphical, symbolic, and verbal representations.
Reduce, Reuse, Recycle
You can recycle five aluminum cans to make one new one. How many new cans would you be able to
eventually make from 250 aluminum cans? (Remember to recycle the cans you make into more cans!)
Based on your family’s aluminum can usage, estimate how long it would take your family to recycle 250
aluminum cans. Why is recycling important to our environment?
©2017 University of Texas at Arlington
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MAED 5352 Patterns and Algebra
For the selected task, you will do the following which is all included in the template below:
• State the appropriate grade for task as is, based on a standards document (i.e., National Council of
Teachers of Mathematics [NCTM] standards, Texas Essential Knowledge and Skills [TEKS], Common
Core State Standards [CCSS], your state’s standards)
• Indicate which of the above standards you used and include the exact text from the standard you used to
make this decision
• Brief description of the mathematics involved to solve the task (a full solution is not necessary)
• Classification on Cognitively Demanding framework (it should either be “procedures with
connections” or “doing mathematics”) and thorough rationale based on cognitive demand readings (Stein
and Smith, 1998; Smith and Stein, 1998).
• Culturally relevant or not – rationale based on your input in the CRCD rubric (below) and readings
• Discussion of how to maintain the cognitive demand of the task.
• Reflection/critique of rubric – is it appropriate for determining if a cognitively demanding task is culturally
relevant? Why or why not? What is missing? What is helpful?
©2017 University of Texas at Arlington
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MAED 5352 Patterns and Algebra
Rubric
Use this rubric to guide your work on the Module 1 assignment.
Tasks
Basic Information
(max 5 points)
Mathematics
Involved
(max 5 points)
Cognitive Demand
Classification
(max 15 points)
Target
Acceptable
Unacceptable
Indicate appropriate
grade and standard
used to make this
decision
Indicate appropriate
grade or appropriate
standard
No appropriate grade
given and/or no text
from standard
specified and/or no
standard referenced
(NCTM, CCRS,
CCSS, etc.)
(5 points)
(3-4 points)
(0-1 point)
Clear description of
mathematics involved
(full solution not
required)
(5 points)
Classification of task
as higher level of
cognitive demand
(“procedures with
connections” or “doing
mathematics”) along
with thorough,
scholarly rationale
Description of
mathematics involved
in solution is not clear
(3-4 points)
No description of
mathematics involved
in solution
(0-1 point)
Classification of higher No classification of
level cognitive tasks is task
missing a rationale
(0-1 point)
(3-4 points)
(5 points)
Rationale for
classification is based
on readings; citation(s)
included
If a rationale is
included, it is not
based on readings
and/or not cited
No rationale for
classification
(5 points)
(2 points)
Discusses two valid,
reasonable ways to
maintain cognitive
demand of task
(5 points)
Names two ways to
maintain cognitive
demand of task or
discusses only one
way to do so
(1 points)
Statement about
whether or not task is
culturally relevant
without a rationale
No discussion of
maintaining cognitive
demand of task
(0 points)
(3-4 points)
(0-1 point)
If a rationale is given,
it is not based on the
No rationale and/or
incomplete rubric
(1 point)
Culturally Relevant
Framework
(max 10 points)
Clear statement about
whether or not task is
culturally relevant with
thorough, scholarly
rationale
No statement about
whether or not task is
culturally relevant
(5 points)
Rationale based on
©2017 University of Texas at Arlington
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MAED 5352 Patterns and Algebra
Rubric
Critique/Reflection
(10 points)
completed rubric and
readings; citation(s)
included
readings OR the rubric
is incomplete
(3-4 points)
(5 points)
Answers all questions:
1) is the rubric
appropriate for
determining if a
cognitively demanding
task is culturally
relevant? 2) Why or
why not? 3) What is
missing? 4) What was
helpful?
Answers most of the
questions: 1) is the
rubric appropriate for
determining if a
cognitively demanding
task is culturally
relevant? 2) Why or
why not? 3) What is
missing? 4) What was
helpful?
(9-10 points)
(6-8 points)
(0-1 point)
Answers few to none
of the critique
questions
(0-3 points)
Basic Information
What is the title of the task you chose? What do you feel is the appropriate grade for this task?
Please indicate which standards document you used to make that decision. In the box below, also paste the
exact text of the standard you chose.
Mathematics Involved
What mathematics is involved in solving this task?
©2017 University of Texas at Arlington
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MAED 5352 Patterns and Algebra
Cognitive Demand
Please state the four levels of cognitive demand, presented by Smith and Stein. This task is on what level of
cognitive demand according to these researchers’ framework? Please provide a rationale, based on
readings and include citation(s). If you use the authors’ words please cite appropriately.
What are two ways you could maintain the cognitive demand of this task if you were to use it in a classroom?
©2017 University of Texas at Arlington
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MAED 5352 Patterns and Algebra
Culturally Relevant
Culturally Relevant Cognitively Demanding (CRCD) Task Rubric. Use the following rubric to help you
begin discussing the cultural relevance of this selected task. If it helps to quantify the levels, you can use
numbers (High = 3; Moderate = 2; Low = 1).
Description
Degree in Task Structure
High
Moderate
Low
Mathematics task explicitly requires students to
inquire (at time problematically) about themselves,
their communities, and the world about them.
May draw from connections to other subjects and
issues.
Mathematics task draws from students’ community
and cultural knowledge.
Task may explicitly seek to add to this knowledge
through mathematical activity.
Task is mathematically rich and cognitively
demanding, embedded in cultural activity.
Task asks students to engage the discontinuity and
divide between school and their own lives – home
and school.
Task is real-world focused, requiring students to
make sense of the world through mathematics.
The explicit goal of the task is to critique society –
that is, make empowered decisions about
themselves, communities and world.
©2017 University of Texas at Arlington
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MAED 5352 Patterns and Algebra
Is this task culturally relevant? Please provide a rationale, based on your input in this rubric as well as
readings. Include citation(s). If you used numbers, include the rating information (i.e., the score you
gave the task).
Is the rubric appropriate for determining if a cognitively demanding task is culturally relevant? Why or why not?
What is missing? What was helpful? If you used numbers, how did those numbers help you rate whether or not
the task was culturally relevant?
©2017 University of Texas at Arlington
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MAED 5352 Patterns and Algebra
References
Enyedy, N., & Mukhopadhyay, S. (2007). They don’t show nothing I didn’t know: emergent tensions
between culturally relevant pedagogy and mathematics pedagogy. The Journal of the Learning Sciences,
16(2), 139–174.
Gilbert, J. E., Arbuthnot, K., Hood, S., Grant, M. M., West, M. L., McMillian, Y., … & Eugene, W. (2008). Teaching
algebra using culturally relevant virtual instructors. IJVR, 7(1), 21-30.
Gutstein, E., Lipman, P., Hernandez, P., and de los Reyes, T. (1997). Culturally relevant mathematics
teaching in a Mexican American context. Journal for Research in Mathematics Education, 28(6), 709-737.
Irvine, J. J. (2009). Relevant: beyond the basics. Teaching Tolerance, 36. Retrieved from
http://www.tolerance.org/magazine/number-36-fall-2009/feature/relevant-beyond-basics
Ladson-Billings, G. (1997). It doesn’t add up: African American students’ mathematics
achievement. Journal for Research in Mathematics education, 28(6), 697-708.
Leonard, J., and Guha, S. (2002). Creating cultural relevance in teaching and learning mathematics.
Teaching Children Mathematics, 9(2), 114-118.
Matthews, L. E., Jones, S. M., & Parker, Y. A. (2013). Advancing a framework for culturally relevant, cognitively
demanding mathematics tasks. In J. Leonard & D. B. Martin (Eds.), The brilliance of Black children in
mathematics: Beyond the numbers and toward a new discourse. Charlotte, NC: Information Age Publishing.
Metropolitan Center for Urban Education. (2008). Culturally Responsive Differentiated Instructional
Strategies. New York, NY: NYU Steinhardt School of Culture, Education, and Human Development.
Moses, R. P. and Cobb, C. E. (2001). Radical equations: math literacy and civil rights.
Boston: Beacon Press.
Nelson-Barber, S. and Estrin E. T. (1995). Bringing Native American perspectives to mathematics
and science teaching. Theory into Practice, 34(3), 174-185.
Smith, M. S., and Stein, M. K. (1998). Selecting and creating mathematical tasks: From research to
practice. Mathematics Teaching in the Middle School, 3(5), 344-350.
Stein, M. K., and Smith, M. S. (1998). Mathematical tasks as a framework for reflection: From
research to practice. Mathematics Teaching in the Middle School, 3(4), 268-275.
©2017 University of Texas at Arlington
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