# Innovations in MTH 100E

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Innovations in MTH 100E

Innovations in MTH 100EKristen Bieda and Raven McCrory, Teacher EducationSteven Wolf, Post-Doc in CREATE for STEMA 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 raceWhat 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 performanceFall 2012: Piloting a new instructional format for MTH 100EMTH 100ETuesdaysMTH 100EThursdaysFall 2012: Piloting a new instructional format for MTH 100EMTH 100ETuesdaysTE 407 student instructorsInquiry-Oriented Curriculum & Group WorkCoaching by math ed GAsFall 2012: Piloting a new instructional format for MTH 100EMTH 100EThursdaysMTH 100E TuesdaysSecondary Mathematics Majors as InstructorsTE 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 classInquiry-oriented curriculumMTH 100E students need to develop more than just procedural knowledge. Tasks in lessons were designed to develop conceptual understanding, problem solving skills, and reasoning.

Have audience actually do a part of a task in groups that was used that was especially well-received by MTH 100E students (approx. 20 minutes)13Example 1: Simplifying Rational ExpressionsA rational expression is a fraction whose numerator and/or denominator are polynomial expressionsi.e.

What might be some ways students would reason about these expressions when simplifying them?

14Example 1: Simplifying Rational Expressions1) Understanding the structure of rational expressions is a key idea, i.e. that and are portioning a

whole into different size parts

15Example 1: Simplifying Rational Expressions1) 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

16Example 1: Simplifying Rational Expressions1) 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.

17College Preparatory Mathematics 10.1.1Part 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

18College Preparatory Mathematics 10.1.1 the MTH 100E lessonNotice 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 for19Reflections from 100E StudentsThis is my favorite class this semester.20Reflections from 100E StudentsThis is my favorite class this semester.I found the equations surprisingly easy to create when usually its fairly difficult for me.21Reflections from 100E StudentsThis is my favorite class this semester.I found the equations surprisingly easy to create when usually its fairly difficult for me. This class wasnt helpful. Its more for math majors who want to deeply understand math. Not people who just want to know how to solve the problem.22Reflections from TE 407 studentsI 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. 23Reflections 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.24Reflections 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.

25What data do we have?Course data:ALEKS (homework, assessments, time on task)ExamsMath Placement Exam scoresAttitude Survey:Pre and PostFennema-Sherman Confidence, Effectance, and Teacher ScalesBai 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)27ALEKS learning model

AssessmentInstructionBegin with Assessment (30 item)Assessment informs ALEKS choice of learning modulesCompleting modules brings about a new assessmentNew assessment repeats process

Self-paced 28

Group 1 and Group 2 are distinct (p=0.003) [Group 1 has a higher mean]Group 1 and Group 3 are not distinct (p=0.626)Group 2 and Group 3 are not distinct (p=1.000)

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)

(Welsh t-test with Bonferroni Correction)29

Group 1 and Group 2 are distinct (p=0.037) [Group 1 has a higher mean]Group 1 and Group 3 are distinct (p=0.077) [Group 1 has a higher mean]Group 2 and Group 3 are not distinct (p=1.000)

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)

(Welsh t-test with Bonferroni Correction)30

Group 1 and Group 2 are not distinct (p=0.697)Group 1 and Group 3 are not distinct (p=1.000)Group 2 and Group 3 are not distinct (p=1.000)

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)

(Welsh t-test with Bonferroni Correction)31

Group 1 and Group 2 are not distinct (p=1.000)Group 1 and Group 3 are not distinct (p=0.303)Group 2 and Group 3 are not distinct (p=0.589)

(Welsh t-test with Bonferroni Correction)32Summary (p-values)Placement ExamALEKS initialFinal ExamALEKS finalGroup 1 and Group 20.0030.0371.0000.697Group 1 and Group 30.6260.0770.3030.004Group 2 and Group 31.0001.0000.5890.328Group 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)

33Take 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 dont measure the same thing.Future plansLook at time on task in ALEKSDoes this correlate with performanceAnalyze attitude surveyFactor analysis to create attitude score

Interesting question: Do performance gains persist?Note lack of attrition in test sections35We still have a lot of work to doWork with 1 section of MTH 100E for both class sessions each weekWork on curriculum c

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