Assessing-Learning-in-Math-Classrooms.pptx

Assessing Learning in
Math Classrooms

Comprehension Checkpoint No. 2
Identify which is the Content Standard, Performance
Standard and Learning Competency.
ASSESSING LEARNING IN MATH CLASSROOMS
Day 1, November 8, 2021
Determines the relationship of the volume between a rectangular prism and a
pyramid; a cylinder and a cone; and a cylinder and sphere.
Demonstrates understanding of volume of solid figures and meter reading.
Apply knowledge of volume of solid figures and meter reading in mathematical
problems and real-life situations.

Identify which is the Content Standard, Performance
Standard and Learning Competency.

Classroom Assessment: A Review

The Critical Role of Assessment
in Teaching and Learning
Mathematics

As part of the tasks of mathematics teaching, what should
mathematics teachers know and understand about
classroom assessment?
use formative
assessments to
gather cross-sectional
views of students’
work, progress and
performance to adjust
and improve
instruction;
utilize appropriate
and useful
summative
assessments to
determine the impact
of mathematical
learning activities on
students’ learning;
use authentic
assessments and
constructs rubrics that
reflect knowledge of
students’ thinking
processes and errors.

Observation
Analysis of
learner’s
product
Talking to
learners
Test
What
assessment
methods can we
use to find out
what our
learners know
and can do?
When do we use
each method?

To help our learners perform well in relation to the
learning standards, what can we use to operationalize
and assess their progress from basic to complex skills?
The learning
standards in the
curriculum
reflect
progressions of
concept
development.
Classroom assessment
must challenge
learners to demonstrate
what they know and
can do using a broad range
of cognitive
processes, from basic to
complex, as follows:

Programme for International
Student Assessment
Trends in
International
Mathematics and
Science Study

Sample TIMSS Test Items

TIMSS 2011 Mathematics Framework
Creating
Evaluating
Analyzing
Applying
Understanding
Remembering
Reasoning
Applying
Knowing

Knowing
• This domain covers the facts, concepts,
and procedures students need to know.
• Facility in applying mathematics, or
reasoning about mathematical situations,
depends on familiarity with mathematical
concepts and fluency in mathematical skills.
• The more relevant knowledge a student is
able to recall and the wider the range of
concepts he or she understands, the greater
the potential for engaging in a wide range of
problem-solving situations.

Applying
• This domain focuses on the ability of
students to apply knowledge and
conceptual understanding to solve
problems or answer questions.
• With problem solving being central to this
domain, they should be able to apply
mathematical knowledge of facts, skills, and
procedures or understanding of mathematical
concepts to create representations.
• Representation of ideas forms the core of
mathematical thinking and communication,
and the ability to create equivalent
representations is fundamental to success in
mathematics.

Reasoning
• This domain involves going beyond the
solution of routine problems to
encompass unfamiliar situations,
complex contexts, and multi-step
problems.
• It includes intuitive and inductive reasoning
based on patterns and regularitiesthat can be
used to arrive at solutions to problems set in
novel or unfamiliarsituations, which may be
purely mathematical or may have real-life
settings.

Identify the domains of these test items based on
TIMSS 2021 Mathematics Framework.
Item 1 – Knowing
Item 3 – Reasoning
Item 4 – Applying
Item 5 – Reasoning

Development of Valid and
Appropriate Assessment
Items/Tasks in Mathematics

When writing Test Items following TIMSS 2011
Item Writing Process and Guidelines, please:
• Write questions that match the topics in each content
domain, and pay particular attention to writing questions
that cover the range of the three cognitive domains.
• Consider the best item format for the question. About
half of the items you develop should be multiple-choice and
the other half should be constructed-response items worth 1 or
2 score points.

• For each item, consider the timing, grade
appropriateness, difficulty level, potential sources of
bias (cultural, gender, or geographical), and ease of
translation.
• For multiple-choice items, keep the guidelines for writing
multiple-choice questions in mind. In particular—ask a
direct question, make sure there is one and only one
correct answer, and provide plausible distracters.

• For constructed-response questions, write a full credit
answer to the question in terms of the language,
knowledge, and skills that a good fourth- or eighth-
grade student could be expected to possess. This tests
the clarity of the question and also provides guidance about
whether to allocate 1 or 2 score points to the item.
• Develop a specific scoring guide for each constructed-
response item.

Writing Multiple-choice Test
(following TIMSS 2021 Item Writing Process and
Guidelines)

A multiple-choice item
asks a question or establishes the situation for a response
For TIMSS 2011, this type of item provides four response
choices, or options, from which the correct answer is selected.

Characteristics of a Multiple-choice Item
The stem is the
initial part of the
item in which the
task is
defined.
The distracters
are the incorrect
response options.
The options
refer to the entire
set of labeled
response
choices
presented under
the stem.
The key is the
correct response
option.
In a test following TIMSS 2011 Framework, half of the items will be four-option multiple-choice items and
the rest will be constructed-response items.

Writing Multiple-choice Test:
The Stem
• Phrase all stems as a direct question.
The circumference of a circle with
a radius of 2 cm is _____.
Instead of this:
What is the circumference of a
circle with a radius of 2 cm?
Try framing it like this:

The Stem
• Provide sufficient information in the stem to make the question
clear and unambiguous to students. An exception would be
items asking which is the best estimate of a quantity.
What is the perimeter of a lot if one of its
side is 5 meters?
Instead of this:
What is the perimeter of a square lot if
one of its side is 5 meters?

The Stem
• The stem should not include extraneous information
Maria is a very kind-hearted Grade 4
pupil of Maligaya ES. She helps her
mother in their sari-sari store during her
free time. One day, Julio, Maria’s
classmate, bought five kilos of rice in
Maria’s store. Every kilo of rice is P45.00.
If Julio’s money is P500.00, how much is
the change?
Instead of this:
Julio bought five kilos of rice with his
P500.00 money. If each kilo is P45.00,
how much will be his change?

The Stem
• Avoid using negative stems. If it is absolutely necessary
to use a negative stem, highlight the negative word, (e.g.,
capitalize, underline, or put in bold type so that it stands out
for the student). If the stem is negative, use only
positive response options —do not use double
negatives.
Which is not a prime number?
Instead of this:
Which is NOT a prime
number?

The Stem
• If there is not one universally agreed upon answer to the
question, it is best to include “of the following” or some
similar qualifying phrase in the stem.
What is the value of π?
Instead of this:
Of the following, which is
closest to the value of π?

The Stem
• Avoid questions for which a wrong method yields the correct
answer
What is 22?
Instead of this:
What is 32?

Structure of the Response Options (or Alternatives)
• Write multiple-choice items with four response options,
What is 32?
X. 6
Y. 8
Z. 9
Instead of this:
What is 32?
A. 4
B. 6
C. 8
D. 9

• Make sure that one of the four response options or
alternatives is the key or correct answer. Make sure there
is only one correct or best answer.
Which pair results in an even number
when added?
A. 1 and 4
B. 1 and 5
C. 2 and 9
D. 3 and 7
Instead of this:
Which pair results in an even number
when added?
A. 1 and 4
B. 1 and 5
C. 2 and 7
D. 3 and 8

• Make sure that the four response options are
independent. Response options should not represent
subsets of other options.
Which is correct arranged from LEAST to
GREATEST?
A. 1, 2, 3, 4
B. 2, 4, 5, -7
C. A digits added with 1
D. B digits subtracted with 0.5
Instead of this:
Which is correct arranged from LEAST to
GREATEST?
A. 1, 2, 3, 4
B. 2, 4, 5, -7
C. 3, -3, 5, -5
D. 7, 5, -5, -7

• Make sure that the grammatical structure of all
response options “fit” the stem. Inconsistent grammar can
provide clues to the key or eliminate incorrect response options.
What are three-sided polygons called?
A. Box
B. Cube
C. Rectangle
D. Triangles
Instead of this:
What are three-sided polygons called?
A. Boxes
B. Cubes
C. Rectangles
D. Triangles

•Make sure all (or sets) of the response options are
parallel in length, level of complexity, and
grammatical structure.
•Avoid the tendency to include more details or
qualifications in the correct response, thus making it
stand out.
•If the best options are not parallel in length, please
order the options short to long if at all possible.

• Do not use words or phrases in the stem that are repeated in one
of the response options and, therefore, act as a clue to the
correct response.
What angle is like a straight line?
A. Acute angle
B. Obtuse angle
C. Right angle
D. Straight angle
Instead of this:
What angle measures 180°?
A. Acute angle
B. Obtuse angle
C. Right angle
D. Straight angle

• Do NOT use “none of these” and “all of these” as response
options.
Which of the following will result to an
odd number?
A. 7 + 12
B. 15 – 3
C. All of these
D. None of these
Instead of this:
Which of the following will result to an
odd number?
A. 7 + 12
B. 15 – 3
C. 20 x 0
D. 55 ÷ 5

• Arrange the response options in a logical order if this
makes sense and saves the student time in reading the options
(e.g., years in chronological order, numbers from least to
greatest).
What is the sum of the largest even and
odd numbers less than 20?
A. 40
B. 31
C. 37
D. 39
Instead of this:
What is the sum of the largest even and
odd numbers less than 20?
A. 31
B. 37
C. 39
D. 40

• Avoid writing items where students can work
backwards from the response options to find the
correct answer. In such cases, a constructed-response item
may be more appropriate than a multiple-choice item.
Which number when subtracted with 12
will result to an odd number less than 9?
A. 17
B. 18
C. 21
D. 25
Instead of this:
Which numbers when subtracted with
12 will result to an odd number less
than 9 but more than 5?
Answer: _____________________

Plausibility of Distracters
•Use plausible distracters (incorrect response options)
that are based on likely student errors or
misconceptions.
•If there are no plausible errors or misconceptions,
still make the options “reasonable.”
•Avoid the use of “trick” distracters.

Multiple-choice Item Review Checklist

Writing Constructed-response Items
and Scoring Guides
(following TIMSS 2021 Item Writing Process and Guidelines)

Writing Constructed-response Items and Scoring Guides
For some desired outcomes of mathematics and science education,
constructed-response items provide more valid measures of
achievement than do multiple-choice items.
Constructed-response items usually require students to give a
numerical result, provide a short explanation or description given in
one or two phrases or sentences, complete a table, or, provide a
sketch.
It is essential that each constructed-response item and its
scoring guide be developed together.

Constructed-response items should be used when it is desirable
that the student be required to think of an answer without the
possibility of being cued by an option in a multiple-choice item.
If too few plausible distracters are available for a multiple-choice item,
it may be better framed as a constructed-response item.

Care in writing constructed-response items is especially important for
two reasons.
First, if the task is not well specified
students may interpret the task in
different ways and respond to
different questions.
Second, a constructed-response
item may carry more score
points than a multiple-choice
item.

Guidelines for Writing Constructed-response Items
Write questions in language appropriate to the age and
experience of the target population. If students are uncertain
about what they are to do the difficulty of the item will increase, and
this may be falsely attributed to lack of student proficiency.
Joe knows that the cost of an air pod can
buy three ear buds. He was able to buy
two air pods for P10,000.00. How much
will be his savings if he instead bought
two ear buds?
Instead of this:
Joe knows that a sign pen can buy three
ordinary ball pens. He was able to buy
two sign pens for P60.00. How much will
he save if he instead bought two
ordinary ball pens?

Make what is expected of students as clear as possible without
compromising the intent of the item.
Use words such as “explain” or “describe” to focus students on the task
rather than “fuzzy” words such as “discuss” or “comment” that can lead
to wide variation in the content of responses.
3 – 3 = 0
3 – 2 = 1
3 – 1 = 2
3 – 0 = 3
Give you personal comment on the next line of
the pattern given.
Instead of this:
3 – 3 = 0
3 – 2 = 1
3 – 1 = 2
3 – 0 = 3
Explain what would be the next line of the
pattern.

Students should be able to complete the task in the time
allocated for each constructed-response item, that is, 1–3 minutes.
Kim is packing eggs into boxes. Each box
holds 6 eggs. She has 125 and a half
dozens of eggs. What is the smallest
number of boxes she needs to pack all
the eggs? What if each boxes hold 4 eggs
only, how many more boxes will she
need?
Instead of this:
Kim is packing eggs into boxes. Each box
holds 6 eggs. She has 94 eggs. What is
the smallest number of boxes she needs
to pack all the eggs?

Select real life problem settings that are likely to be “real” to students
at the target grade levels, and that involve quantities that are realistic
for the situations.
Si Mario gitagaan sa iyang inahan og
P1,000.00 kay siya ang gitahasan
pagpamalit sa mercado sa ilang pagkaun
sa sunod semana. Nakapalit si Mario og
karne bali og P540.00, utanon bali og
P145.45 ug prutas bali’g P123.45. Pila
ang nahibilin nga kwarta ni Mario?
Instead of this:
Si Mario gitagan sa iyang mama og
P50.00 para palit og duha ka putos nga
asin ug isa ka pakete nga gatas. Tag-
P5.00 ang putos sa asin ug tag-P10.00
ang gatas. Pila ang sukli ni Mario?

Avoid asking questions that could give rise to answers that cannot be
scored strictly in terms of accuracy of mathematical or scientific
understanding
Write the complete value of π.
Instead of this:
Write the value of π till the
thousandths place.

Write an appropriate answer to the question in terms of the language,
knowledge, and skills that a good student at the target grade could be
expected to possess
Produce a scoring guide

Guidelines for Writing Scoring Guides
1-point constructed-response
items
are scored as correct (1 score
point) or
incorrect (0 score points).
2-point constructed-
response items
are scored as fully correct
(2 score points),
partially correct (1 score point),
or incorrect (0 score points).
Constructed-response items need scoring guides with well-
defined categories for allocating score points

Guidelines for Writing Scoring Guides

Test Construction following TIMSS Guidelines
The progression of topics/competencies is the
basis for item placement rather than the type of
item or its cognitive domain.
To Illustrate:
1. C1 - MC – Knowing
2. C1 - MC – Applying
3. C2 - CR – Reasoning
4. C2 - MC – Applying
5. C3 - CR – Knowing
As for lay-outing, test items are encoded in two
columns, with a line separating these columns.
As to the font, TIMSS used Cambria Math 12

GRASPS Model
in Constructing Authentic
Performance Tasks

Performance Task
•A performance task is any learning activity or
assessment that asks students to perform to
demonstrate their knowledge, understanding and
proficiency.
•Performance tasks yield a tangible product (or
project) and/or performance that serve as evidence
of learning.

GRASPS Model in Constructing Authentic Performance Tasks
The GRASPS model
outlines the elements
of an effective and
authentic performance
task intended to
provide learners with
experiences found in
the real world.
G – Goal
R – Role
A – Audience
S – Situation
P – Product/ Performance/Purpose
S – Standards and Criteria for Success

GRASPS Model in Constructing Authentic Performance Tasks
GOAL
Provide a statement of the task; establish the goal, problem, challenge, or obstacle in the task
ROLE
Define the role/state the job of the students in the task.
AUDIENCE
Identify the audience in the context of a scenario
SITUATION
Set the context/setting/background of the scenario
PRODUCT/PERFORMANCE/PURPOSE
Clarify what the student will create or perform and why they will create or perform it
STANDARDS AND CRITERIA FOR SUCCESS
Provide students of a clear picture of success; identify standards of success through rubrics

Standard and Criteria for Success
A rubric is a learning and
assessment tool that is used to
evaluate written outputs,
products, or performance-based
tasks.
A rubric is scoring guide that
articulates the expectations the
expectations and describes the
levels of quality expected from a
learner
(DO 31, s. 2020, p. 20)
Four Essential Features of Rubrics
(Stevens & Levi, 2013)
A task description or a
descriptive title
A scale (or scoring)
Components and criteria
Description of performance quality
(performance descriptor)

Rubrics
A rubric can be analytic or holistic.
An analytic rubric articulates
different dimensions of
performance and provides rating
for each criterion or dimension.
A holistic rubric describes the
overall characteristics of a
performance and provides a single
score.
In developing a rubric, it should be emphasized that higher points
could be given for a certain level of mastery depending on the
complexity of the question.

Rubrics

Sample Performance Task using GRASPS
Goal
Your task is to create an MS Excel spreadsheet survey by surveying the class as
to which was their favorite vegetable that is planted in the Gulayan sa Paaralan.
Role
You are a survey taker and you need to obtain your data by surveying your
classmates on their favorite vegetable that is currently planted in the Gulayan sa
Paaralan.
Audience
You are letting your classmates and the school GPP Coordinator which vegetable
is their favorite and thus should be planted in higher quantity than others.
Situation
The challenge involves gathering data and then displaying these data in a MS
Excel spreadsheet.
Product &
Performance
You will create a MS Excel spreadsheet using the data you obtained and share it
in a letter addressed to the School GPP Coordinator.
Success
Indicators
The letter to the School GPP Coordinator is correctly written and contains
accurate data displayed in cells and also displayed in a chart.
(See attached rubric for reference)

Success Indicator (Scoring Rubric)
Letter with Spreadsheet Attachment Rubric
This rubric is designed to evaluate a letter with MS spreadsheet attachment based on the accuracy of data in
MS Excel spreadsheet, appropriateness of graph/s of the data and correctness of the letter written.
Dimension Exceed Expectations
(3)
Meet Expectations
(2)
Did not Meet
Expectations (1)
Accuracy of Data
presented in MS
Excel
All data needed are presented
correctly and accurately with
uniformity in lay-outing.
All data needed are presented
correctly but lay-outing
needs improvement.
Data are lacking and lay-
outing needs major
improvement.
Appropriateness of
Graph/s of the Data
Graphs clearly showed the
data gathered and in
appropriate formatting.
Data presented in the
graph/s are lacking and
missing.
No/Incorrect graphs were
used.
Correctness of the
Letter Written
The letter contains the
complete findings and
recommendation of the
survey conducted and has no
grammatical and spelling
errors and follows proper
letter formatting.
The letter contains the
complete findings and
recommendation of the
survey conducted but has
grammatical and spelling
errors.
Letter submitted did not
contain the relevant findings
and recommendations of the
survey.

General Characteristics of a Good Performance Tasks
It heeds the application of knowledge and skills, and not just recall
and/or recognition of a concept.
It is not limited to a single correct answer.
It should be contextualized based on real-life problems.
It should provide proof of the learners’ understanding through transfer.
It should be multi-faceted and multiprocedural.
It should be integrative with other learning areas and with 21st century skills.
It should have a clear and well-established scoring rubrics/
guidelines with relevant criteria.

Application/
Outputs Required

Output/s Required
Summative Test for Mathematics, Quarter 1-4
with at least 1 performance task with rubric
Grade Level
Multiple Choice
Items
Constructed-
Response Items
Total
Items
Math 1 8 2 10
Math 2 10 5 15
Math 3 15 5 20
Math 4 30 10 40
Math 5 30 10 40
Math 6 25 15 40

Output/s Required
Summative Test for Mathematics, Quarter 1-4
Formatting Guidelines
•Paper size: A4
•Margins: 0.5” all sides
•Columns: One column for Heading to the Instructions/Directions; Two
columns for the Test Items and separated by a vertical line.
•Font and Size: Cambria Math 16 for Grade 1; Cambria Math 14 for Grades 2-3;
Cambria Math 12 for Grades 4-6
•Alignment: Justify
•Line spacing: 1.0; There should be one line space before each item.
•Page Number: Lower Right portion of the page
•Organization: Written Works then Performance Task/s using GRASPS Model
•File Name: ST_MathX_QX_Qualci# Ex: ST_Math1_Q1_Qualci1

Output/s Required
Summative Test for
Mathematics,
Quarter 1-4
Table of Specifications
(TOS)

Assessing-Learning-in-Math-Classrooms.pptx

Recommended

Recommended

More Related Content

Similar to Assessing-Learning-in-Math-Classrooms.pptx

Similar to Assessing-Learning-in-Math-Classrooms.pptx (20)

More from CarmehlynBalogbog

More from CarmehlynBalogbog (10)

Recently uploaded

Recently uploaded (20)

Assessing-Learning-in-Math-Classrooms.pptx

Editor's Notes