Innovations in MTH 100E Kristen Bieda and Raven McCrory, Teacher Education Steven Wolf, Post-Doc in CREATE for STEM

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). What is MTH 100E?

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 MTH 100E Tuesdays TE 407 student instructors Inquiry- Oriented Curriculum & Group Work Coaching by math ed GAs

Fall 2012: Piloting a new instructional format for MTH 100E MTH 100E Thursdays MTH 100E Tuesdays

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 3 rd 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 are polynomial expressions i.e. 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, i.e. that and are portioning a whole into different size parts

Example 1: Simplifying Rational Expressions 1) Understanding the structure of rational expressions is a key idea, i.e. that and are portioning a 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 and are portioning a 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 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 and Part IV: Students are asked to use what they know about the number 1 to simplify some given rational expressions

College Preparatory Mathematics – 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 AssessmentInstruction

Summary (p-values) Placement Exam ALEKS initial Final ExamALEKS final Group 1 and Group Group 1 and Group Group 2 and Group

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