math journal entry

Description

edTPA Task 4 Manual: Mathematics and Math Rubrics
Attached Files:
edtpa-ele-handbook r1.pdf

edtpa-ele-handbook r1.pdf – Alternative Formats
(1.607 MB)

Please click on pages 48-50 of the edTPA Manual to view the Math Task4 Rubrics.

Attached is the edTPA Manual. You will be required to pass edTPA during internship.

Task 4, which is the mathematics component, begins on page 43. Notable sections, which may provide background understanding for you, are…

…page 10: this gives a synopsis of the mathematics task, showing what candidates do, submit, and the rubrics used

…pages 43-68: this gives specific information of Task 4: Mathematics

Example from Math Journal
Example from Math Journal

7. An error analysis is a diagnostic assessment. Think of it as a situation where you are diagnosing or determining what the problem is, much like a physician would do in a health situation. As a teacher, you will need to “diagnose” what errors students are making and why they are making these errors. In this example below, notice that a student completes a test with the following math problems done incorrectly: 1/4 + 2/4 = 3/8; ½ + ½ = 2/4; 3/6 + 2/6 =5/12

a. What does the error “tell” you about the student’s understanding?
The error that the student made was that he/she is adding the fractions straight across, in the same fashion that you would multiply fractions, rather than finding a common denominator. This is why the student got 3/8 for the first answer rather than the correct answer of ¾. The student added the numerators to get a new numerator of 3 and then added the denominators to get a new denominator of 8. This tells me that the student’s understanding of adding is correct, however their conceptual understanding of adding fractions is flawed.

b. Write an objective using the Alabama Curriculum Guide for Mathematics https://www.alsde.edu/sec/ses/Curriculum%20Guides/cgmathematics.pdf based on this student’s struggle.
[M.4.14b.1 ] [M4.14b.2] The student will be able to identify the parts of a fraction, numerator and denominator, and combine this basic addition and subtraction facts with 85% accuracy in ¾ trials.

c. Describe how you will intervene and re-engage the student in a lesson to understand the concept. Use references to specific manipulatives.
To intervene and re-engage the student I would begin by reviewing the different parts of fractions and what they mean. I would start by explaining that a fraction represents a certain part of a whole. I would then discuss with the student about how the denominator represents the total number of pieces in the whole item, and the numerator represents how many pieces we are looking at. For example, if we have a pizza that has 8 pieces and we want to eat 3, the fraction of the pizza is 3/8. We would use a wooden pizza puzzle (Melissa and Doug brand is a great one.) After practicing with this, I would move onto the adding and subtracting portion. The student clearly already can add, as evident in his test. The student had trouble with remembering the rules on finding a common denominator. To remind the student on these rules I would use a fraction chart, or fraction wall, as shown in the picture below. This would help the student visualize the different ways that you can represent fractions. While utilizing this manipulative, I would also refer to the pizza manipulative. I would discuss with the student on how you would add together two different types of pizzas. For example, say a cheese pizza has 8 slices and a sausage pizza has 4 slices. If you want one slice of each pizza, how much pizza are you eating in total? We would start by writing out our denominators, which are the total number of slices in each pizza.
Cheese: ?/8
Sausage: ?/4

Then, we would look at how many pieces we want of each kind, which is the numerator.
Cheese: 1/8
Sausage: 1/4

I would then have the student refer to the fraction wall and compare the 1/8 and 1/4 fractions. After this we would talk about how we cannot just add the two fractions because they do not have the same denominator. If we did this, it would make our total number of slices wrong, which we will look at later. First, we must find a common denominator, which will make our pizzas an equal number of slices. I show the student how we can change the 4-slice pizza into 8 slices because 4 goes into 8 two times. To do this, we multiply both parts of the sausage pizza fraction by 2, which would give us 2/8. After we have the same denominatorwe can add straight across, which would give us 3/8 of the total amount of pizza. If we would not have found a common denominator and only added across, we would get 2/16, or 1/8, which is not the same amount of pizza as doing it the correct way.

Error Analysis
Error Analysis

When you conduct an error analysis, you are determining what error the student is making and selecting an intervention to address/solve the issue. It is much like a physician diagnosing a health issue and prescribing a solution.

Intervention Strategies for Re-engagement
Intervention Strategies for Re-engagement

1. Use higher-order questions that promote student thinking and reasoning.

2. Use small groups and pairs.

3. Use manipulatives.

4. Adjust scope and sequence (amount of material and amount of time spent on concept).

5. Summarize each learning session.

6. Use active learning.

7. Use think-alouds.

8. Use scaffolding.

9. Allow ample think time after asking questions.

10. Use guided practice.

11. Make sure instructions are clear and concise.

12. Use graph paper or ask students to turn notebook paper “landscape” style for help with alignment.

13. Use peer tutors.

14. Assess using a variety of techniques (paper, observations, interviews, etc.)

15. Seat students in locations most conducive to learning.

16. Color-code the operations on a number problem.

17. Limit the amount of information presented at one session.

18. Provide real-life applications and concrete examples.

19. Use music (i.e. to reinforce math facts)

20. Adapt the number of items, time allowed, and/or problem type.

21. Use technology.

Math Journal Outcomes
Math Journal Outcomes

NCTM Standards and Outcomes:

Successful completion of the math journal should equip the preservice teacher to:

NCTM: Problem Solving

build new mathematical knowledge through problem solving;

solve problems that arise in mathematics and in other contexts;

apply and adapt a variety of appropriate strategies to solve problems;

monitor and reflect on the process of mathematical problem solving.

NCTM: Reasoning and Proof

recognize reasoning and proof as fundamental aspects of mathematics;

create and investigate mathematical conjectures;

develop and evaluate mathematical arguments and proofs

select and use various types of reasoning and methods of proof.

NCTM: Communication

organize and consolidate their mathematical thinking through communication;

communicate their mathematical thinking coherently and clearly to peers, teachers, and others;

analyze and evaluate the mathematical thinking and strategies of others;

use the language of mathematics to express mathematical ideas precisely.

NCTM: Representation

create and use representations to organize, record, and communicate mathematical ideas;

select, apply, and translate among mathematical representations to solve problems;

use representations to model and interpret physical, social, and mathematical phenomena.

Preservice teachers will demonstrate the ability to check mathematical results for

reasonableness and explain their mathematical reasoning.