MATH 211 UF Liping Mas Knowing & Teaching Elementary Mathematics Question

Math 211 ProjectWinter 2022
This project is an important opportunity to demonstrate your level of understanding of the content
of the course and you must pass the project to pass the course. It is graded for proficiency, sufficiency,
accuracy, meaning, method, and mastery.
Submission Deadline: Friday, March 4, 2022 at 11:59pm
General Expectations:
• Work will be your own. You will not receive help from tutors, classmates, online, or other
unauthorized resources. You may ask your instructor for help.
• Work on new problems will be in final draft form: thoughtfully worked, neatly written, and
complete.
• For new problems, evidence of engaging in the mathematical practices is required. Your thinking
process should be evident in your work, even if you did not manage to arrive at a final solution.
• Strong effort should be clear.
• Visuals should be meaningful and lead to a method. You should not start with a method before
you have developed meaning.
• Reference the Common Core State Standards as indicated. (http://www.corestandards.org/
Math/)
The project will include the following two sections that will each be uploaded to Canvas
as separate assignment submissions:
1) New Material and Reflection
2) Summary and reflection on Liping Ma’s Knowing and Teaching Elementary Mathematics
Page 1
Math 211
Project
Winter 2021
1. New Material and Reflection: This section should be submitted as a single Word or PDF
Document to the appropriate place in Canvas. Hand written work is fine as long as it is well
organized and neatly written then scanned/photographed and pasted into the document so it is
easy to read without zooming in
Complete ALL of the following questions:
1. Jackson is a 211 student who has always struggled with addition in other bases. Carefully
show Jackson how to compute 6A9thirteen + 28Bthirteen (letters here represent specific digits
in base thirteen). Do this computation using
(a) the standard algorithm
(b) a strategy
(c) a visual that mirrors the steps of your strategy
Be sure to emphasize place value and decomposition. Any step you take should be explained.
Name at least three Common Core standards that a student doing something comparable
in base ten would need to use. (For example, computing 7fifteen + 9fifteen = 11fifteen might
correspond to the first grade standard 1.OA.C.6 about adding within 20)
2. Claire is a student who has always struggled with multiplication. Carefully show Claire how
to compute 37nine × 42nine using
(a) the standard algorithm
(b) partial products with a visual.
Be sure to emphasize place value, partial productions and decomposition. Any step you
take should be explained. Name at least three Common Core standards that a student
doing something comparable in base ten would need to use. (For example, computing
7fifteen + 9fifteen = 11fifteen might correspond to the first grade standard 1.OA.C.6 about
adding within 20)
3. Addition, subtraction, and multiplication are all worked from right to left in the standard
algorithms but division is worked from left to right. Try to do the problem 936 ÷ 4 from
right to left (i.e. dividing up the ones first). Can it be done? If so, show your process with
a visual. If not, explain why it cannot work this way.
Page 2
Math 211
Project
Winter 2021
2. Summary and reflection on Knowing and Teaching Elementary Mathematics
This section should be submitted as a single Word or PDF Document to the appropriate place in
Canvas. It should be typed, but pictures of hand written work may be included within the text
as long as work is neatly written and easy to read without zooming in. Your response should
be well-constructed, thoughtful, and concise–less than 1 page single spaced.
Choose ONE of the following prompts and give a thorough response.
1. After reading Chapter 1 from Knowing and Teaching Elementary Mathematics by Liping Ma,
(see link in “Required Materials” page of our Canvas site) answer the following questions.
(a) In the Section “The U.S. Teachers’ Approach: Borrowing Versus Regrouping”, Ma suggests some problems with how several of the U.S. teachers presented the problem of
subtraction with regrouping. List three of these and explain how they show lack of
conceptual understanding. Refer to the section “The Chinese Teachers’ Approach: ‘Decomposing a Higher Value Unit’ ” and explain how the Chinese teachers would correct
these approaches.
(b) The Section “Instructional Techniques: Manipulatives” discusses the U.S. teachers’ use
of manipulatives while the section “Manipulatives and Other Teaching Approaches”
elaborates on the Chinese teachers’ use of manipulatives. Give at least two examples
of ineffective use of manipulatives for the concept of subtraction with regrouping and
explain why they are ineffective. What are some effective approaches to using manipulatives from the two groups?
2. After reading Chapter 2 from Knowing and Teaching Elementary Mathematics by Liping
Ma, (see link in “Required Materials” page of our Canvas site)answer the following questions.
(a) In the section “The U.S. Teachers’ Approach: Lining Up Versus Separating Into Three
Problems”, Ma gives us part of Ms. Fay’s explanation of the student’s mistake. Explain why her explanation is procedurally focused rather than conceptually focused even
though it uses the term “place value”.
(b) Refer to the Section “Knowledge Package”. What different concepts should be a part
of a complete conceptual understanding of multi-digit multiplication. Give reasons to
include each concept.
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