This document provides strategies for incorporating rigor into a mathematics classroom using Bloom's Taxonomy. It discusses understanding the curriculum and standards, using questioning techniques to check for understanding at higher levels of thinking, allowing mistakes to promote learning, and pacing instruction to ensure deep conceptual understanding of mathematical concepts. The goal is to challenge students with authentic problem-solving that requires critical thinking, collaboration, and applying knowledge in new situations.

1. How to Get the Best Out of
Your Students in a Rigorous
Mathematics Classroom
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Sources:
Lead4Ward STAAR 3D and Bloom’s Taxonomy

2. Know Your Curriculum
Make sure that you fully understand your curriculum, the vertical
alignment and how to intervene when necessary.
Once you do, it is time to bring the rigor up like you never have
before. We will be discussing how to incorporate Bloom’s
Taxonomy and rigorous strategies to ensure you are teaching to a
higher level where students are actively and consistently proving
their deep conceptual understanding of core academic concepts.
Source: Lead4Ward STAAR 3D Sept. 19, 2012 2

3. 7 Ways to RENEW
Instruction
O Talk with Students
O Ask great questions
O Check for understanding
O Learn from mistakes
O Wait time
O Pace instruction
O Teach for transfer
Source: Lead4Ward STAAR 3D Sept. 19, 2012 3

4. Talk With Students
O Nuh uh!!
O No way!
O How’d you do that?
O Prove it!
Source: Lead4Ward STAAR 3D Sept. 19, 2012 4

5. Ask Great Questions
O Bloom’s Taxonomy
O That student’s themselves can answer
O Try to intrigue them
O Expand the answer from correct to
“complete”
O “Why” or “How”
Source: Lead4Ward STAAR 3D Sept. 19, 2012 5

6. Bloom’s Taxonomy
Sept. 19, 2012 6

7. Knowledge Levels
Learn terms
Facts
Methods
Procedures
Concepts
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 7

8. Knowledge Verbs
Draw, Recognize
Count, Group
Reproduce
Memorize
State
Tabulate
Identify
Point
Follow Directions
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 8

9. Knowledge Tasks
 Identify different place
values
 State the mode, mean,
median, and range
from your set of data.
 Reproduce a circle
using a compass?
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 9

10. Understand Levels
Terms
Facts
Methods
Procedures
Concepts
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 10

11. Understand Verbs
Change
Classify
Convert, Estimate,
Interpret, Measure,
Put in Order, Show,
Suggest,
Express in other terms
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 11

12. Understand Tasks
 Classify polygons by
regularity, concavity and
line symmetry.
 Explain how to convert
between fractions,
decimals, and percents.
 What is your
interpretation of the data
expressed on the graph?
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 12

13. Apply Levels
O Practice theory,
solve problems,
use
O Information in the
new situations
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 13

14. Apply Verbs
Calculate, Compute,
Construct,
Demonstrate,
Derive, Graph,
Manipulate,
Operate,
Practice, Prove,
Solve
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 14

15. Apply Tasks
 Calculate the percent
of a given whole?
 Solve for the area of a
rectangle by using
A= l x w.
 What information do
you consider when
graphing data derived
from a survey?
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 15

16. Analyze Levels
Analyze structure,
recognize
assumptions,
breaking down
material into parts
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 16

17. Analyze Verbs
Break down,
Deduce, Diagram,
Distinguish,
Formulate, Group,
Order, Separate,
Simplify,
Sort
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 17

18. Analyze Tasks
 What methods can be
used to compare and
order fractions?
 Analyze the relationship
between variables on a
graph.
 What factors do you
consider when
formulating a plan for
problem solving?
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 18

19. Evaluate Levels
Set standards,
Judge with
purpose, accept or
reject on basis of
criteria
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 19

20. Evaluate Verbs
Appraise, Choose,
Compare, Conclude,
Decide, Describe,
Evaluate, Justify,
Measure, Validate
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 20

21. Evaluate Tasks
 Evaluate the
expression after
changing the order of
operations.
 Describe how to solve
a problem using the 4
step method.
 Justify your reason for
choosing the strategy
selected.
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 21

22. Create Levels
Putting information
together into a new
and creative way.
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 22

23. Create Verbs
Construct, Create,
Derive, Develop,
Document,
Generate,
Integrate, Plan,
Predict, Prepare,
Propose, Specify,
Tell
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 23

24. Create Tasks
 Describe some patterns
that you recognized in
the construction of
Pascal’s Triangle.
 What kind of table can
you create that
represents change in
temperature?
 What prediction can you
make from this graph?
http://montemath.com/bloomstaxonomyformath.pdf Sept. 19, 2012 24

25. Bloom’s Activity Discussion
Give examples of how a perimeter lesson
might look at each level of Bloom’s
Taxonomy.
O Knowledge
O Understand
O Apply
O Analyze
O Evaluate
O Create
Sept. 19, 2012 25

26. Check for Understanding
O Focus should be more on the extended
response of the student, rather than the
question itself
O Tickets out the door
O Think-pair-share
O CBAs
Source: Lead4Ward STAAR 3D Sept. 19, 2012 26

27. Allow Students to Learn
from Their Mistakes
“Great teachers allow students to fail just enough so
they can discuss and learn from it.” ~ Ervin Knezek
Procedural Errors
Application Errors
Conceptual Errors
Source: Lead4Ward STAAR 3D Sept. 19, 2012 27

28. Wait Time
O Wait Time 1 – when you
allow time for the first
responder to answer.
O Wait Time 2 – when you
allow time for slower
processors to think
about the question, the
first answer and
piggyback on that
response.
Source: Lead4Ward STAAR 3D Sept. 19, 2012 28

29. Pace Instruction
O Know your concepts
and give
O Right amount of time
O Right amount of
instruction
Source: Lead4Ward STAAR 3D Sept. 19, 2012 29

30. Teach for Transfer
“Are we giving tricycle problems to students who
are responsible for taking a motorcycle test?” ~
Ervin Knezek – Lead4Ward
Source: Lead4Ward STAAR 3D Sept. 19, 2012 30

31. Rigor in the classroom
O Develop a set of best management
practices
O Develop strategies for establishing
instructional goals
O Document progress toward these goals
O Assess rigor in the classroom
http://edge.ascd.org/_Seven-Myths-About-Rigor/blog/3235457/127586.html Sept. 19, 2012 31

32. Components of Rigor
O Content acquisition
O Critical thinking
O Relevance
O Integration
O Application of concepts
O Long term retention
O Responsibility
Sept. 19, 2012 32

33. Rigor Is… Rigor Is Not…
 More effort
 For every student
 Quality
 Messy and Free Ranging
 All levels of Bloom’s
 Intentional
 Builds Self Regulation
 Risky (Uncertainty)
 Challenging
 Relevant
 Relative
http://edge.ascd.org/_Seven-Myths-About-Rigor/blog/3235457/127586.html Sept. 19, 2012 33

34. Strategies
O Interactive Journals
O Multiple Representations
O Problem-solving
O Collaboration
O Wait Time
O Vocabulary
Sept. 19, 2012 34

35. Authentic Problem Solving
O Students actively explore, research and solve complex
problems to develop a deep understanding of core
academic concepts.
O Increasing rigor means time and opportunity for students
to consistently think critically about their content.
O Students analyze, collaborate, connect, identify patterns,
evaluate outcomes, speculate on possibilities and
assess value.
Sept. 19, 2012 35

36. AfterMATHs
O Clear expectations
O Higher test scores
O Improved math skills
O Higher ordered thinking skills
Sept. 19, 2012 36