Walk this Way! Active Learning Strategies for Math Instruction: To promote student learning and engagement in an active learning environment, and make math more meaningful, hands-on activities can be incorporated into the traditional lectures. The presenter shared some active learning strategies and activities to be incorporated into the math classrooms to promote student engagement and learning.

1. Walk This Way:
Active Learning Strategies
for Math Instruction
Supawan King, Ph.D.
Harford Community College
Section 1.9, 9:00-10:00, 1/5/2017
AFACCT 2017

4. Student Engagement
Was identified in 1996 as a latest “buzzword” in
education circles.
Occurs when students psychological investment in
learning.
Refers to a “student willingness, need, desire and
compulsion to participate in, and be successful in, the
learning process promoting higher level thinking for
enduring understanding”
-Alma Bella Agua

6. Engaging Students in Learning Process
Research has demonstrated that engaging
students in the learning process:
• increases their attention and focus,
• motivates them to practice higher-level critical
thinking skills and promotes meaningful
learning experiences.

7. Active Learning is generally defined as
any instructional method that engages
students in the learning process.
~Benjamin Braun~
Active Learning is often contrasted
to the traditional lecture where
students passively receive
information from the instructor.

8. Why is Active Learning important?
• The amount of information retained by
students declines substantially after ten
minutes (Thomas, 1972).
• Numerous researchers and national reports:

9. • All genuine learning is active, not passive. It is
a process of discovery in which the student is
the main agent, not the teacher. (Adler, 1982)
• Students learn what they care about and
remember what they understand. (Ericksen,
1984)

10. • Learning is not a spectator sport. Students do
not learn much just by sitting in class listening
to teachers, memorizing pre-packaged
assignments, and spitting out answers. They
must talk about what they are learning, write
about it, relate it to past experiences, apply it
to their daily lives. They must make what they
learn part of themselves. (Chickering and
Gamson, 1987)

11. • The sort of teaching we propose requires that
we encourage active learning and that we
become knowledgeable about the ways in
which our students hear, understand,
interpret, and integrate ideas. (AAC Task
Group on General Education, 1988, p. 25)
• One must learn by doing the thing, for though
you think you know it-- you have no certainty
until you try. (Sophocles, 5th c. B.C.)

12. Active Learning Increases Student Performance in
Science, Engineering, and Mathematics
The President’s Council of Advisors on Science and Technology has
called for a 33% increase in the number of science, technology,
engineering, and mathematics (STEM) bachelor’s degrees completed
per year and recommended adoption of empirically validated teaching
practices as critical to achieving that goal. The studies analyzed here
document that active learning leads to increases in
examination performance that would raise
average grades by a half a letter, and that
failure rates under traditional lecturing increase
by 55% over the rates observed under active
learning. The analysis supports theory claiming that calls to
increase the number of students receiving STEM degrees could be
answered, at least in part, by abandoning traditional lecturing in favor
of active learning. – Freeman, et al.

13. Common obstacles or barriers
1. Cannot cover as much course content in the
time available
2. Take too much pre-class preparation
3. Large class sizes
4. Being good lecturers – no reason to change!
5. Lack of materials or equipment needed to
support active learning approaches
6. Students resist non-lecture approaches

14. Common obstacles or barriers
(continued)…
1.Find other ways such as reading, writing assignments, group work on
quizzes, etc.
2.Takes more time than that needed to “recycle old lectures”, not necessary
take more time that that needed to create thorough and thoughtful new
lectures.
3.Large class can be divided into small group discussion, etc.
4.Teaching does not equal learning : this can be seen clearly in the painful
disparity between what we think we have effectively taught, and what
students indicate they have learned on the examination papers that we
grade.
5.certainly not all. For example, asking students to summarize in writing the
material they have read or to form pairs to evaluate statements or
assertions does not require any equipment.
6.With explicit instruction in how to actively participate and learn in less-
traditional modes, students soon come to favor the new approaches.

15. Also
7. Too risky !!!

16. Possible Risks
Students will not Faculty will not
• Participate actively
• Learn sufficient
course content
• Use higher order
thinking skills
• Enjoy the
experience
• Feel in control of the class
• Feel self-confident
• Possesses the needed skills
• Be viewed by others as
teaching in an established
fashion

17. Lower Risk Activities Higher Risk Activities
• Pause Procedure
• Short writes
• Thumps up/down response
• Surveys/Questionnaires
• Formative (ungraded)
quizzes
• Think-Pair-Share
• Brainstorming
• Pairs/group develop an
outline of the lecture
• Structured group discussion
(specific questions
provided)
• Group discussion (no structure)
• Guided lecture
• Individual/group presentations
• Pairs/groups develop
applications related to lecture
content
• Pairs/groups write test questions
related to lecture material
• Students analyze a problem,
poem, photography, etc.
• Students work a problem then
evaluate each others’ work
• Role plays illustrating a concept
from lecture
• Responsive lecture

18. Which One ! ! ! !

20. Mathematics is beautiful.
Teach math in context with the real
world applications incorporated.
Motivate and support students in
their attempt to learn math.

22. I have tried these with my classes!
MATLAB = TOO MUCH
MATHEMATICA = GOOD FOR CERTAIN CLASSES
Math Articles: read and shared with the class = WENT
WELL BUT TIME WAS AN ISSUE
Group Projects on a given scenario: solved and wrote
report = WENT WELL, GETTING BETTER
WITH TIME ISSUE
IN-CLASS GROUP WORK = MY WINNER 

23. You can successfully overcome each of
obstacles or barriers, and reduce the
possibility of failure, by
gradually incorporating teaching strategies
that increase student activity level and
instructor risk into your regular teaching style.
Choose what is appropriate for you within the
context of your discipline!

24. Active Learning: Things to consider
Set Clear
Expectations
Design Effective
Evaluation
strategies
Provide
Helpful
Feedback

25. Active and Supportive Learning Environment
Students working in small groups
Instructor Watching
Visiting
Listening
Assisting

26. • Work in small group – some students are shy
• Students do amazing things.
• Sometimes they get off a workable track but colleagues and teachers bring
them along.
• Students make mistakes, but learning from mistakes is an important part of
learning [BrownEtAl2014].
• Indeed, we do it all the time ourselves and call it conjecture and research. -
See more at: http://blogs.ams.org/matheducation/2016/06/27/learning-
mathematics-in-context-with-modeling-and-
technology/#sthash.rbIA1PyW.dpuf
• Indeed, Dina Yagodich, of Frederick Community College, says that
throughout the semester her students refer to a first day of class activity on
death and immigration modeling with simulations using m&m candies
[Winkel2014], an indication of the importance and meaning of a modeling
first approach to teaching. - See more at:
http://blogs.ams.org/matheducation/2016/06/27/learning-mathematics-in-
context-with-modeling-and-technology/#sthash.rbIA1PyW.dpuf

27. WORKING IN SMALL GROUPS
• Applying this method in the lecture hall this
automatically made the course more engaging,
encouraged more discussion and allowed students to
interact with one another (Ebert-May, Brewer, Allred,
1997).
• As students are engaged in the material, they are
learning the concepts, communicating mathematically,
and when teaching the material to others they have
effectively learned the material.

28. WORKING IN SMALL GROUPS
• Another benefit of small group exercise is the carry over effect, if
students worked together inside the classroom, sometimes this
would lead to collaborations and discussions outside the
classroom as well (Rosenthal, 1995).
• Write Mathematics: Writing is another way to communicate ones`
understanding of mathematical ideas. “Written assignments are
known to be a good way to encourage students to think about
what they are learning, to remember more, and to see course
material in a larger context. They have been advocated across the
curriculum including mathematics (Connolly and Vilandi, 1989 as
cited in Rosenthal’s 1997).”

29. 29

30. Collaborative Assignments
(CA’s)

31. The majority of students do not learn mathematics by simply
sitting in a classroom, listening to a teacher, recording notes,
memorizing assignments and regurgitating answers. Rather,
they must read mathematics, reflect on it, talk about it, write
about it, and relate it to their prior knowledge. Simply put, they
must be actively engaged in the process of constructing their
mathematical knowledge.

33. 33

34. 34

35. 35

36. Sample of Lab Activities
Activities Objectives Math course
Walk This Way Linear Equation
Piecewise-defined Function
Rate of Change
Area between curves
College Algebra
PreCalculus
Calculus
The Way the Ball
Bounces
Quadratic Function
Rate of Change
Derivative
Chill Out Exponential Function
Newton’s Law of Cooling

37. Materials
Motion Detector
Temperature probe
TI-Nspire Handheld Calculator
Data Collection Interface

38. 38

39. Walk This Way

40. The Way the Ball Bounces

41. Calculus I – Honors Fall 2016
75% were male.

42. How do you see yourself as a math student?
a. Very weak b. Weak c .Average d. Strong e. Very strong
Survey I 0.0% 0.0% 8.3% 75.0% 16.7%
Survey II 0.0% 16.7% 16.7% 41.7% 25.0%
0%
20%
40%
60%
80%

43. Do you think your grade in this class reflects
your true understanding of math?
Survey I Survey II
a. Yes 58.3% 75.0%
b. No 41.7% 25.0%
0%
20%
40%
60%
80%

44. Survey I Survey II
a. Yes 100.0% 100.0%
b. No 0.0% 0.0%
0%
20%
40%
60%
80%
100%
Do you think HW helps you learn math?

45. In this class, do you think you receive too
much HW, just enough, or not enough?
a. Too much
HW
b. Just enough
HW
c. Not enough
HW
Survey I 0.0% 91.7% 8.3%
Survey II 54.5% 36.4% 9.1%
0%
20%
40%
60%
80%
100%

46. Thinking about how you learn math, what type of
learning activities would you suggest to your
instructor?
Survey I
 More examples that we can workout on our own in class
 More group assignments
 Hands-on activities on real world applications
 Just a whole sheet of problems with given example at the
top
 More labs
 I learn best when I know a real world applications
Survey II
 More in-class examples so we can try out what we learned
 More group assignments.
 Hands-on activities (as we are doing)
 No labs, more classwork

47. When you are learning about a new topic in
math, does it help you to:
a. Talk
about it
b. Think
about it
c. Write
about it
d. Other
Survey I 45.5% 22.7% 27.3% 4.5%
Survey II 31.3% 25.0% 37.5% 6.3%
0%
10%
20%
30%
40%
50%
Other:
 Visualize the problem and see
the work for it
 Practice problems on the
subject
 Learn what was happening in
the subject
 describe every step in details

48. Do you think lab activities help you learn math?
a. Yes b. No c. Somewhat
Survey I 66.7% 33.3% 0.0%
Survey II 75.0% 8.3% 16.7%
0%
20%
40%
60%
80%

49. Comments - YES
It allows us to apply the skills we learn.
It helps connect class time to real life situations and other subjects.
They are easier to reference in memory, easier to remember an action
rather than notes.
Connects to the real world.
It helps put what we learned into the lab and better understand it.
It made me better understand the application of the math we do in class.
Numbers are meaningless unless applied. Labs help us see the relation.
I learn the application which helps me think about how to do the
problem.
A hands-on idea of how it works helps.
Helps me apply it to real life.

50. Comments – No/Somewhat
No, it is a real world application but not necessary
to understand math.
No, they were applications of Physics more than
applications of math.
Not too much, more science involved rather than
math.
It’s usually really simple math.
Not exactly, it is more based on Physics.

51. SUMMARY
Some of major characteristics associated with active learning
strategies:
1. Students are involved in more than passive listening
2. Students are engaged in activities (e.g., reading, discussing,
writing)
3. Student motivation is increased (especially for adult
learners)
4. Students can receive immediate feedback from their
instructor
5. Students are involved in higher order critical thinking skills
(analysis, synthesis, evaluation).

52. Behaviors promoting student learning
(Gorham, 1988)
1. Appropriate use of humor
2. Praising student performance
3. Engaging student outside of the classroom
4. Appropriate level of self-disclosure
5. Encouraging students to talk
6. Asking questions about student viewpoints or feelings
7. Following up on topics raised by students even if not
directly related material
8. Referring to ”our” class and what “we” are doing.

53. Conclusion
 Active learning involves students in doing things and thinking
about the things they are doing.
 Creating an active learning environment in a mathematics
course might take more work on the instructor side to be
creative on how to present mathematical concepts.
 The tasks you assign for group work should challenge students
to analyze phenomena, solve problems, apply theories,
exercise judgment, or perform some combination of these
activities.

54. Conclusion
 Clearly written instructions are vital to the success of this kind
of exercise, which means the teacher must analyze the task
carefully and break it down into its component parts. During
the exercise, the teacher moves from group to group,
answering questions, clarifying instructions, giving advice, and
observing the group process.

55. » Supawan King, Ph.D. sking@harford.edu
» STEM Division, Harford Community College, Bel Air, MD
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