17. Session No. 5
SANNYVAL R. ESTABILLO
Learning Facilitator
LEARNING
MATHEMATICS
THROUGH INQUIRY
DIVISION TRAINING-
WORKSHOP ON 21ST
CENTURY TEACHING IN
MATHEMATICS
August 16-18, 2022
18. TERMINAL OBJECTIVE
At the end of the session, the participants
are expected to integrate in their lessons the
four levels of inquiry such as confirmation,
structured, guided, and open.
19. ENABLING OBJECTIVES
Identify four levels of inquiry
Construct math prompt based on the level of
inquiry
Model inquiry by asking leading questions
20. WHAT IS IT THAT ALL KIDS HAVE IN
COMMON?
What is it that all kids have in common?
21. 2 COMMON WAYS
TO TEACH MATH
You don’t know?
Let me tell you!
You don’t understand?
Let me explain to you!
TELL
EXPLAI
N
INQUIRY-BASED
LEARNING
2 Common ways to teach Math
22. MATH INQUIRY
MATH INQUIRY is a model of learning that encourages students to regulate
their own activity while exploring a prompt (an equation, statement or diagram).
It involve the class in questioning, conjecturing, generalizing and proving and,
when required, in listening to an explanation.
Students learn to take responsibility for directing the lesson with the teacher
acting as the arbiter of legitimate mathematical knowledge and activity.
23. WHY IS MATH INQUIRY IMPORTANT?
MATH INQUIRY establishes a culture of curiosity,
collaboration and openness in the classroom.
Students meet new concepts and procedures when they are
necessary, meaningful and connected – necessary to make
progress on a line of inquiry, meaningful in the context of
the inquiry and connected to other concepts and
procedures in the field of inquiry.
24. LEARNING MATHEMATICS THROUGH
INQUIRY
LEARNERS:
Ask questions
Design and implement method to
investigate
Analyze, interpret, and synthesize
results of investigation
Construct new understanding
Apply new knowledge
INQUISI
TIVE
MIND
TEACHERS:
Facilitate learning
Model inquiry by asking
leading questions
Scaffold
LEARNING MATHEMATICS THROUGH INQUIRYR
26. TASK # 1A: NUMBER PROMPT
Fill each box with a different digit 1, 2, 3, or 4 to
get the biggest product.
Describe the pattern in the placement of the digits
that gives the biggest product.
Make a conjecture based on the pattern.
Test your conjecture with other sets of four digits.
X
TASK # 1A NUMBER PROMPT
X
27. TASK # 1A: NUMBER PROMPT
Fill each box with a different digit 1, 2, 3, or 4 to
get the biggest product.
Describe the pattern in the placement of the digits
that gives the biggest product.
Make a conjecture based on the pattern.
Test your conjecture with other sets of four digits.
X
TASK # 1A NUMBER PROMPT
X
3
3
2
3
1
3
4
3
1, 2 8 44
28. TASK # 1B: NUMBER PROMPT
Fill each box with a different digit 1, 2, 3, or 4 to get the
biggest product.
Try filling the boxes with different combinations of the digits
1, 2, 3, and 4. Then, find the combination that gives the
biggest product.
Describe the pattern in the placement of the digits that gives
the biggest product.
How would the pattern change if one of the digits is 0?
X
TASK # 1B NUMBER PROMPT
X
29. TASK # 1B: NUMBER PROMPT
Fill each box with a different digit 1, 2, 3, or 4 to get the
biggest product.
Try filling the boxes with different combinations of the digits
1, 2, 3, and 4. Then, find the combination that gives the
biggest product.
Describe the pattern in the placement of the digits that gives
the biggest product.
How would the pattern change if one of the digits is 0?
X
TASK # 1B NUMBER PROMPT
X
4
3
1
3
3 2
1,3 2 2
30. FOUR LEVELS OF INQUIRY IN
MATHEMATICS
Adapted from Rezba, R. J., Auldridge, T. & Rhea, L. (1999). Teaching & learning the basic science
skills. Available online at www.pen.k12.va.us/VDOE/insruction/TLBSSGuide.doc .
Level 1
CONFIRMATION
Level 2
STRUCTURED
Level 3
GUIDED
Level 4
OPEN
Question
Method
Answer
Given by the teacher
Not given by the teacher
Given by the teacher
X Not given by the teacher
FOUR LEVELS OF INQUIRY IN MATHEMATICS
31. INQUIRY PROMPT ANALYSIS
Fill each box with a different digit 1, 2, 3, or 4 to get
the biggest product.
What is the pattern in the placement of the digits that
gives the biggest product?
What did the teacher do?
X
Question Method Answer
GUIDED INQUIRY
INQUIRY PROMT ANALYSISy
X X
X
32. INQUIRY PROMPT ANALYSIS
Fill each box with a different digit 1, 2, 3, or 4 to get
the biggest product.
What is the pattern in the placement of the digits
that gives the biggest product?
Try filling the boxes with different combinations of
the digits 1, 2, 3, and 4. Then, find the combination
that gives the biggest product.
What did the teacher do?
X
Question Method Answer
STRUCTURED
INQUIRY
INQUIRY PROMT ANALYSISy
X
33. INQUIRY PROMPT ANALYSIS
Fill each box with a different digit 1, 2, 3, or 4 to get
the biggest product.
What is the pattern in the placement of the digits
that gives the biggest product?
Try filling the boxes with different combinations of
the digits 1, 2, 3, and 4. Then, find the combination
that gives the biggest product.
The combination is 41 x 32. Check if this product is
the biggest.
What did the teacher do?
Question Method Answer
X
INQUIRY PROMT ANALYSISy
X
CONFIRMATION
INQUIRY
