1. Finding (and Avoiding)
Our Blind Spots
Deb Poese
Director, School of Education; Professor,
Mathematics
Montgomery College
debra.poese@montgomerycollege.edu
AFACCT 2012 Conference
Montgomery College- Rockville
Session 7.12 1:50 pm
January 6, 2012
1

2. Why Are We Here?
2

3. Source of Image:
Maths4life, Improving learning in mathematics: challenges and strategies by Malcolm Swan
Retrieved online from http://www.maths4life.org/content.asp?CategoryID=1068
3

4. Agenda
Considering “Blind Spots”
Some Examples
Related Teaching Theory
An Application
Questions/Evaluation

5. What is a Blind Spot?
Jot down the first thing that comes to mind.
Turn to a partner and discuss your thought.
What ideas are out there?
5

6. Try out your “Blind Spot”
 Participants were provided with an index card
marked as below:
A O X
6

7. Try out your “Blind Spot”
 Hold your card in your left hand, with the X on
the right side
 Cover your right eye with your right hand, and
focus on the X
 Move the card slowly toward your face until the
O disappears (but A remains)
 Now, flip the card horizontally and repeat,
covering your left eye and still focusing on the X
7

8. Expert Blind Spots
An expert blind spot occurs when someone
skilled in an area overestimates the ease of
learning its formalisms or jargon or
underestimates learners’ informal
understanding of its key ideas. As a result,
too little attention is paid to linking formal
…understanding to informal reasoning….
Bransford, Brown and Hocking, How Students Learn, p. 355
8

9. An Example: Multiplication
 3 X 4 = 12
 3 X 7 = 21
 7 X 5 = 35
Memorizing these facts is not really any different
than memorizing what is below:
 Carl Dennis lives on Allen Brian Avenue
 Carl Gary lives on Brian Allen Avenue
 Gary Edward lives on Carl Edward Avenue
Sousa, page 43

10. Another Example
Which of these problems is most difficult for a beginning
algebra student?
1. Solve for x: x*6 + 66 = 81.9
OR
2. Starting with some number, if I multiply it by 6 and
then add 66, I get 81.9. What number did I start
with?
OR
10

11. Another Example
3. When Ted got home from his waiter job, he
multiplied his hourly wage by the 6 hours he
worked that day. Then he added the $66 he made
in tips and found he had earned $81.90. How
much does Ted make per hour?
11

12. And the Answer is….
 Most math teachers (from pre-service to
higher ed) believe #3 is most difficult.
 The research showed that student
responses were
1. 43% correct
2. 62% correct
3. 66% correct
Koedinger and Nathan, 2004
12

13. At Your Tables:
 Share a time when you were part of an EBS
moment, either as the teacher or as the
student.
 What more effective strategies might have
been used?
 Why would it be helpful to know about
EBS?

14. Teaching Styles
Dimension Options
Information Concrete vs Abstract
Presentation Visual vs Verbal
Organization Deductive vs Inductive
Participation Active vs Passive
Perspective Sequential vs Global
Felder/Silverman, p. 675

15. What About in STEM Fields?
Dimension Options
Information Concrete vs Abstract
Presentation Visual vs Verbal
Organization Deductive vs Inductive
Participation Active vs Passive
Perspective Sequential vs Global
Felder/Silverman, p. 675

16. What About in STEM Fields?
Dimension Options
Information Concrete vs Abstract
Presentation Visual vs Verbal
Organization Deductive vs Inductive
Participation Active vs Passive
Perspective Sequential vs Global
Landis, page 126

17. Visual vs Verbal?? Really?
Visual is NOT just something you show; it
must involve charts, graphs, diagrams.
(Writing on a board is generally verbal,
not visual.)
Visual Example: Expansion of (a + b)2
http://illuminations.nctm.org/ActivityDetail.a
17

18. Inductive Vs Deductive
Inductive Reasoning
Inductive reasoning is based on observation. People
using inductive reasoning find a pattern in a
collection of specific observations and draw a
general conclusion based on that pattern.
Deductive Reasoning
Deductive reasoning is based on laws or general
principles. People using deductive reasoning apply
a general principle to a specific example.
18

19. Inductive Vs Deductive
“Induction is the natural human learning
style .”
“Deduction is the natural human teaching
style , at least for technical subjects at the college
level. Stating the governing principles and
working down to the applications is an efficient
and elegant way to organize and present material
that is already understood .”
Felder/Silverman, p. 677

20. Classical Deductive Approach
Def: The point-slope form of a line is a
common and useful form of the equation of a
line. If a line passes through the point ( x 0 ,
y 0 ) and has a slope of m, then the equation
of the line can be written
20

21. Classical Deductive Approach
1. Use this formula to find the equation of
the line through the point (2,3) with
slope -4.
2. Find the equation of the line through
the points (1,3) and (-1, 4).
3. Oops, out of time, do the word
problems for homework!
21

22. An Inductive Example
In late summer, the outside
temperature in degrees
Fahrenheit can be
predicted based on how
fast the crickets are
chirping!
# Chirps °F
40 50
Some summer interns 60 55
working for a biology 100 65
teacher recorded this data: 160 80
22

23. An Inductive Example:
What questions can we
ask and answer about
this situation?
23

24. Rehearsal
 Find one or two other participants
who teach similar content/courses.
 Together, identify a content piece
that you might typically present in a
deductive way.
 Sketch out a plan for teaching that
same idea using induction followed
by deductive practice.
24

25. Questions?