Innovations in MTH 100E
Kristen Bieda and Raven McCrory, Teacher Education
Steven Wolf, Post-Doc in CREATE for STEM
What is MTH 100E?
A non-credit, on-campus enrichment
seminar (Intermediate Algebra
Workshop) that meets twice a week for
two hours a session
What is MTH 100E?
A non-credit, on-campus enrichment
seminar (Intermediate Algebra
Workshop) that meets twice a week for
two hours a session
Open to students taking MTH 1825, an
online developmental math course using
ALEKS
What is MTH 100E?
A non-credit, on-campus enrichment
seminar (Intermediate Algebra
Workshop) that meets twice a week for
two hours a session
Open to students taking MTH 1825, an
online developmental math course using
ALEKS
~ 10 sections per semester. Enrollment
capped at 20.
What is MTH 100E?
A non-credit, on-campus enrichment seminar
(Intermediate Algebra Workshop) that meets twice
a week for two hours a session
Open to students taking MTH 1825, an online
developmental math course using ALEKS
~ 10 sections per semester. Enrollment capped at
20.
Most taught by undergraduate TAs (some of who
are students taking TE secondary math ed
coursework).
Who takes MTH 100E?
Primarily freshman
Those who do not place into MTH 103 or
higher based on their placement exam
score
Self-selected
Students in the College Admissions
Achievement Program (CAAP)
Who takes MTH 100E?
Approximately 20% intend to pursue
STEM majors
Future mathematics teachers
Approximately 30% are minorities by race
What are the ongoing challenges
in teaching MTH 100E?
Reducing failures and drops; ~30% do
not pass MTH 1825
Students’ attitudes about math and math
courses (Larnell, 2010)
Disparities in achievement levels and
ALEKS performance
Fall 2012: Piloting a new
instructional format for MTH 100E
MTH 100E
Tuesdays
MTH 100E
Thursdays
Fall 2012: Piloting a new
instructional format for MTH 100E
TE 407
student
instructors
MTH 100E
Tuesdays
Coaching
by math
ed GAs
InquiryOriented
Curriculum
& Group
Work
Fall 2012: Piloting a new
instructional format for MTH 100E
MTH 100E
Tuesdays
MTH 100E
Thursdays
Secondary Mathematics Majors as
Instructors
TE 407 is a 5 credit course that includes a microteaching lab
experience
Lab is supervised by graduate TAs who are former secondary
mathematics teachers and mathematics education graduate
students
Beginning in 3rd week of semester, pairs of TE 407 students took
responsibility to plan and enact instruction under supervision of
TAs
Fellow TE 407 peers observed instruction and participated in a
post-lesson discussion with instructors after TE 100E class
Inquiry-oriented curriculum
MTH 100E students need to develop more than just
procedural knowledge. Tasks in lessons were designed
to develop conceptual understanding, problem solving
skills, and reasoning.
Example 1: Simplifying Rational
Expressions
A rational expression is a fraction whose numerator
and/or denominator are1polynomial expressions
x + 34 x + 7
i.e. 3
x+3
x 2 + 5x - 6
What might be some ways students would reason
about these expressions when simplifying them?
Example 1: Simplifying Rational
Expressions
1) Understanding the structure of rational expressions
is a key idea,
3 and
4 x + 7 are portioning a
i.e. that
x+3
x 2 + 5x - 6
whole into different size parts
Example 1: Simplifying Rational
Expressions
1) Understanding the structure of rational expressions
is a key idea,
4 x + 7 are portioning a
3 and
i.e. that
x+3
x 2 + 5x - 6
whole into different size parts
2) Understanding the process/object distinction is a key
idea; i.e. x + 3 describes a process AND is an object
Example 1: Simplifying Rational
Expressions
1) Understanding the structure of rational expressions is a
key idea,
i.e. that
are portioning a
3 and
4x + 7
x+3
x 2 + 5x - 6
whole into different size parts
2) Understanding the process/object distinction is a key
idea; i.e. x + 3 describes a process AND is an object
3) Understanding that simplifying fractions and rational
expressions involves applying the multiplicative identity is
a key idea; i.e. that x * 1 = x for all real numbers x.
College Preparatory Mathematics
10.1.1
Part I: Have students consider what they know about
the number 1.
Part II: Have students consider the claim that anything
divided by itself equals 1. Students are asked to
generate their own algebraic fractions that equal 1.
Part III: Students are asked to simplify 4x and 4 + x
x
Part IV: Students are asked to use what they know
about the number 1 to simplify some given rational
expressions
x
College Preparatory Mathematics
10.1.1 – the MTH 100E lesson
Notice in the clip how the instructors bring out the idea
of how 1 is the multiplicative identify
Notice in the clip how the instructors attempt to get
students to make a connection between simplifying
and using the multiplicative identity
Notice the in-the-moment coaching going on during the
clip when a student provides an answer that the
instructors were not asking for
Reflections from 100E Students
“This is my favorite class this semester.”
Reflections from 100E Students
“This is my favorite class this semester.”
“I found the equations surprisingly easy to
create when usually it’s fairly difficult for
me.”
Reflections from 100E Students
“This is my favorite class this semester.”
“I found the equations surprisingly easy to
create when usually it’s fairly difficult for
me.”
“ This class wasn’t helpful. It’s more for
math majors who want to deeply
understand math. Not people who just
want to know how to solve the problem.”
Reflections from TE 407 students
“I really enjoy the fact that we have a
micro-teaching lab, because being able to
connect what we've talked about in
lecture and put it to use in the classroom
as been really neat to see.”
Reflections from TE 407 students
"The micro teaching lab observation and
discussions about them have helped me
change my ways of thinking what makes
a ‘good’ teacher. How you can question
students to help lead them to the answer
without being too direct. It is still going to
take time before it becomes second
nature but it has definitely had an impact.”
Reflections from TE 407 students
“ I'd say the 5pm meetings on Tuesdays really
help us to unravel all the different aspects of
what is happening in the MTL…. these
meetings help clear up what and why we did, if
it worked, and what we could do differently. I
think the transparency it brings allows us to
better accept changing of our ‘image’ of
teaching from ‘telling’ to ‘student-based
learning’.”
What data do we have?
 Course data:
 ALEKS (homework, assessments, time on task)
 Exams
 Math Placement Exam scores
 Attitude Survey:
 Pre and Post
 Fennema-Sherman Confidence, Effectance, and
Teacher Scales
 Bai Anxiety Scale (MAS-R)
 MTH 100E and PSTs written reflections
Study groups:
Group 1 – Students in MTH 1825 only
(n = 750)
Group 2 – Students in ordinary MTH
100E sections (n = 102)
Group 3 – Students taught by TE 407
students (n = 34)
ALEKS learning model
Assessment
Instruction
0.6
0.4
0.2
1825 only
Reg 100E
Test 100E
0.0
Fraction of students
0.8
1.0
Math Placement Exam (Most recent score)
0
5
10
15
20
Placement Exam Score
25
30
0.6
0.4
0.2
1825 only
Reg 100E
Test 100E
0.0
Fraction of Students
0.8
1.0
ALEKS initial assessment
0
50
100
150
initial assessment score (max = 248)
200
Summary (p-values)
Placement
Exam
ALEKS
initial
Final Exam
ALEKS
final
Group 1 and
Group 2
0.003
0.037
1.000
0.697
Group 1 and
Group 3
0.626
0.077
0.303
0.004
Group 2 and
Group 3
1.000
1.000
0.589
0.328
Take home messages:
Test section doing better on ALEKS
than their peers, especially among
bottom third of students.
100E (in general) seems to help
middle third.
Final Exam and ALEKS assessment
don’t measure the same thing.
Future plans
Look at time on task in ALEKS
Does this correlate with performance
Analyze attitude survey
Factor analysis to create “attitude score”
Interesting question: Do performance gains
persist?
We still have a lot of work to do…
Work with 1 section of MTH 100E for
both class sessions each week
Work on curriculum coherency and
alignment to ALEKS work – give
instructors access to students’ ALEKS
records