You can have active learning in online math classes, if you know how to do it.

1. Aha Moments!
Active Learning in Online Math
Maria H. Andersen, Ph.D.
Westminster College, SLC
CEO, Coursetune

2. Three Categories of
Active Learning
• Discussion Activities
• Synchronous Sessions
• Individual Active Learning

3. Dreaded Discussion Posts

4. Initial Posts
Whenever possible,
choose discussion
topics that will force
every initial post to be
unique.

5. Replies
To avoid “conga line
replies” assign specific
tasks for each reply.

6. Smaller Groups
The more
“sameness” to the
initial posts or
responses, the
smaller the group
size needs to be.

7. Build in a little
flexibility
• Make a post or two
yourself (extras for replies)
• Tell a group they need to
each complete one of 4
tasks with no repeats.
• Choices for replies

8. And build in a
little rigidity
• Initial posts must be on time
• No repeats (the faster you
post, the easier this is)
• Subject lines – tell them
what you want!

9. 1. Reformat the
Q&A Discussion
Board
Initial Post: Students must post a question about a concept
they are struggling with (not a specific problem) … I don’t
understand why ...
Subject Line: It helps tremendously if students are
prompted to write a catchy subject line (so they can be
drawn in to posts to respond).
Reply: Attempt to answer two other questions OR clarify
what the question is about with an example (graph,
equation, or scenario) that illustrates the question.

10. 2. Group Problem Set
Post the same problem
set for each group (equal
to number of students)
and randomly assign each
student to a problem on
the problem set.
Initial post: Every student
is responsible for writing
up the solution to one
problem (with all steps)
and posting it (with
appropriate subject line).

11. 2. Group Problem Set
Replies: Every student is
responsible for verifying
two problems and
showing how to check
them. Each student must
show two different ways
to check. For example,
one check using plug-in
the answer and one check
using a graph.

12. 3. Elaborate on a Problem
You: Post a problem with
solution to each small group.
Reply 1: Each students must
add an elaboration to the
problem.
Reply 2: Each student must
take someone else’s
elaboration a step further.
For variation, try posting a
problem and an incorrect
solution to really get some
conversation going.
See: Elaborations for Creative
Thinking in STEM

13. What is an
elaboration?
Graph it
Solve it another way
Find something you weren’t
asked to find
Change a number and see what
affect that has on the problem

14. I thought we
should try
this concept.
So here’s your discussion post. Once you set it
down, others in your group can write on it.

15. Do an
elaboration
on this
problem.

16. Now
elaborate
on another
students’
work.

17. How do
students share
graphs on a
discussion
board?
Photo from a Smartphone
CamScanner App to PDF
Desmos Share by URL

20. 4. Data to
Predictions (A-
B-C-A activity)
A – Start a thread,
choose a graph, declare
the variables, and make
a table of data to go with
the graph.
B - Choose a function or
function(s) to represent
the data and find the
appropriate model.
C - Write up the
variables, domain and
range, the function, and
two predictions from the
data.
A – Checks the work of B
and C on their own post.

23. GraphsInTheWorld

24. 5. Write the Test
You: Start a new thread for
every learning objective
covered on the test.
Initial post: Each student
writes a possible test
question (this produces x
questions). You can
randomly assign these or
let the students self-select.
Replies: Each student
provides solutions to two
test questions (this will
produce repeats on most
questions - but should help
to validate that answers are
correct).

25. Graph Show and Tell
Initial Post: Each student draws or shares a graph
of a relevant function in Desmos. They should
label key points that might be hard to determine
just by looking at the graph. No function should
be written.
Reply 1: Find the function and post it on another
graph.
Reply 2: Explain how to get from graph to
answer on another post.

26. 6. Vocabulary Challenge
You: Post a list of vocabulary
words that can be used in the
context of a particular kind of
problem and solution.
Initial Post: Each student
should write a paragraph
explaining how to solve a
problem they make up using all
the vocabulary words on the
list, but without giving away
what the problem is!
Sidenote: Have the students
turn in the actual problem and
paragraph to you separately for
easy grading.
Reply: Guess the problem on
another post.
Use Small Groups: 3-4 students

27. 7. Application Dissection
(D-E-A-R)
You start the initial threads with X application
problems (best if groups have X-1 students).
Over 4 days, each step is performed on
different problems by different students. A
student cannot do all the DEARS steps for one
problem.
Dissect - dissect the words in the problem to
declare the variables and all known and unknown
values in the problem.
Equations - write equations and draw tables and
diagrams that help explain the problem.
Algebra - solve the problem algebraically (if possible) or with technology.
Reasonable - check the problem for reasonableness.

28. 8. Student Graders
You: Post a test problem
with a number of points.
Initial Group Activity:
Define a rubric for grading
the problem.
During the Week: Release
a written-out solution
each day. The group has
to decide how to grade it.
Best in groups of 3 so
there is not too much
“me too”-ing.

29. I thought we
should try
this concept.
So here’s your discussion post. Once you set it
down, others in your group can write on it.

30. How will you grade this problem?

31. Tuesday’s
Problem

32. Wednesday’s Problem

33. Thursday’s
Problem

34. 9. Math Demonstrations
You: Assign a general problem with
assigned variations for each student.
Initial Post: Each student has to record
themselves solving the problem (this is
much easier than it used to be).
Replies: Each student needs to peer
review two other problems for
correctness of math and correctness of
vocabulary.
To make the peer reviews more solid, some of
the grade should be based on whether the peer reviewing
student correctly ascertains the correctness of the problem
they are reviewing.

36. Give students a
“practice
video” to make
sure they can
record and
upload.

37. Group Data Share
In online classes where data sets for projects come in handy, you can use a
shareable spreadsheet or survey tool to collect data for several things at once.
Students could propose data to collect in a prior discussion post.
Here are a few examples:
• Age and number of jobs held
• Hand size and foot size (specify unit of measure)
• Number of coffee mugs in your house vs number of regular-sized plates in your
house
• Time spent on smart phone in social activities in a day
• Number of contacts in your LinkedIn account, friends in your Facebook account,
number of people you follow (or who follow you) on Instagram or Twitter

38. Synchronous Sessions

39. Don’t do it if you’re
going to Lecture.
Just. Don’t.

40. Decent Synchronous Video Technology

41. Scheduling
Early in the week and later in the evening.
Get it in the schedule of classes or warn students 4 weeks in advance.

42. Make it “mandatory”
Honestly, if any student misses I
email them and let them know
they can watch the video, work the
problems, and email me their
notes for full credit.

43. 10. Synchronous
Problem Practice
Be prepared with a list of 10 problems or
so that you can easily project to the
screen, write on a document camera, or
write in OneNote.
Try to pick problems that really poke at
concepts and will take no more than 2-3
minutes.
Project a problem, then ask the students
to try the problem on their own, enter it
into the chat, and hold on pressing enter.
Ask for the answers all at once.

44. It’s not going to
be like a face-
to-face class.

45. 3, 2, 1,
press enter

46. 11. Kahoot
Kahoot games work in synchronous
sessions so long as you project the
questions on your screen share.
(Remember they only get the
answer screen on their phones)
Example Kahoot: College Algebra:
Functions - concept questions
about functions and function
notation
Create a Kahoot:
https://create.kahoot.it

47. 12. Synchronous Elaborations
You: Post a problem
with solution to each
small group.
Each students must
work out an
elaboration to the
problem.
--- Hold for answers ---
3, 2, 1 – Press Enter
Discuss!

48. 13. Synchronous
Grade-the-work
You: Post a test problem
with a number of points.
Initial Group Dicussion:
Define a rubric for grading
the problem.
You: Post a written-out
response. Ask students to
decide on the points
given and why.
--- Hold the answers ---
3, 2, 1 – Press Enter
Discuss.
Repeat.

49. 14. Desmos Polygraph Activities
The Desmos
Polygraph activities
lend themselves well
to a synchronous
session since students
are automatically
paired as they finish a
game. These are great
for practicing with
vocabulary of
functions and graphs.
https://teacher.desmos.com/

51. Asynchronous
Active Learning
Just because they are alone,
doesn’t mean it can’t be active and
exploratory!

52. 15. Sorting Activities
“Sorting” objects into
collections is a very exploratory
/ active mind activity. Provide
some kind of handout where
the students can cut out the
pieces and sort them in various
ways. Sort graphs, sequences,
data sets, functions, word
problems, etc.
Provide some guidance for
sorting – questions requiring a
sort or questions about a sort.
For example, why have you
sorted the way you did?
They can take pictures of their
results and write about their
thinking.

53. 16. Desmos Activities that can be done alone – and are active!

54. 17. Look around, you’ll find other digital activities you like.

55. https://www.explodingdots.org/

56. https://davidwees.com/graphgame/

57. https://ncase.me/crowds/

58. If you think online
learning in math is
only video lectures
and problem sets.
Please think again.
It doesn’t have to be.

59. Contact Info
Slides at:
Maria Andersen, Ph.D.
Westminster College, Salt Lake City
Email: busynessgirl@gmail.com
Twitter: @busynessgirl
Instagram: GraphsInTheWorld
Facebook: GraphsInTheWorld