Designing and teaching courses for 20-30 students (with a ...€¦ · of E ective Teaching Course Design Assessment Classroom Practices What is Course Design? Course design is the

Courses for 20-30students

Benjamin Braun

Three Componentsof EffectiveTeaching

Course Design

Assessment

ClassroomPractices

Designing and teaching courses for 20-30students (with a view toward the MAA

Instructional Practices Guide)

Benjamin Braun

13 September 2016


Benjamin Braun


Course Design

Assessment

ClassroomPractices

Two Caveats

1. This talk reflects aspects of the current vision for theMAA IP Guide, in development.

2. This talk reflects an idealized vision for teaching — onlyon rare occasions does everything I’m going to mentionwork together to our satisfaction.


Benjamin Braun


Course Design

Assessment

ClassroomPractices

Three Components of Effective Teaching

Course Design

Assessment

Classroom Practices


Benjamin Braun


Course Design

Assessment

ClassroomPractices


EffectiveTeaching

CourseDesign

Assessment

ClassroomPractices


Benjamin Braun


Course Design

Assessment

ClassroomPractices


Course Design

Assessment

Classroom Practices


Benjamin Braun


Course Design

Assessment

ClassroomPractices

What is Course Design?

Course design is the process that takes place prior to thestart of a course. When designing courses we must:

I begin by clearly articulating desired student learningoutcomes,

I decide what activities/tasks we will use to guidestudents to reach these outcomes,

I decide the best way for us to assess student learningagainst these outcomes, and

I make clear how the whole will fit together.


Benjamin Braun


Course Design

Assessment

ClassroomPractices

Key Ideas for Course Design

I Psychological domains for student learning

I Student learning outcomes (SLOs)I Psychological aspects of student motivation and beliefs,

e.g.I Stereotype ThreatI MindsetI Attribution Theory

I Frameworks for mathematical proficiency, e.g.I 2015 MAA CUPM Curriculum GuideI 2001 NRC report “Adding It Up” — 5-strand model of

proficiency

I Situational factors, e.g.I course size, classroom environment (tables vs desks etc)I course support (student graders, tutoring resources, etc)

I “Promising” Syllabus


Benjamin Braun


Course Design

Assessment

ClassroomPractices

Psychological DomainsModern psychology provides a basic framework of the humanpsyche with three domains. Our courses must be designed toengage students across all of these domains.

Aside: Many math courses focus primarily on “Intellectual”aspects of student learning. Most active learning andinquiry-based learning techniques engage students across twoor three of these domains.


Benjamin Braun


Course Design

Assessment

ClassroomPractices

Student Learning Outcomes

Every course should have clear Student Learning Outcomes(SLOs) that represent all of the psychological domains andall of the components of a robust framework formathematical proficiency.

For example, at the University of Kentucky, Number Theoryserves as an “intro to proof” course. Our department votedto recommended the following SLOs to faculty teaching thecourse.

Students will deepen their understanding of the followingtopics and improve with regard to the following practices:


Benjamin Braun


Course Design

Assessment

ClassroomPractices

1. Divisibility, Division Algorithm, Euclidean Algorithm

2. Fundamental Theorem of Arithmetic, Infinitude ofPrimes

3. Linear Congruences, Chinese Remainder Theorem

4. Fermat’s Little Theorem, Wilson’s Theorem

5. Direct Proof, Proof by Contradiction, MathematicalInduction

6. Being persistent, Working through perceived failure,Strategic self-questioning

7. Productive collaboration with others, Asking goodquestions

8. Constructing examples and non-examples to investigateand understand new definitions and theorems

9. Reading and understanding existing proofs, Recognizingincorrect proofs

10. Developing and communicating original proofs


Benjamin Braun


Course Design

Assessment

ClassroomPractices


Course Design

Assessment

Classroom Practices


Benjamin Braun


Course Design

Assessment

ClassroomPractices

Key Ideas for Assessment

I Formative and Summative Assessment

I Levels of Cognitive Demand, Cognitive Load Theory,Zones of Proximal Development

I Cognitive Taxonomies, e.g. Bloom’s and variants

I Models for intellectual development, e.g. Perry’s andvariants

I Conceptual and Procedural Understanding


Benjamin Braun


Course Design

Assessment

ClassroomPractices

Formative and Summative Assessment

As described by Carnegie Mellon’s Eberly Center forTeaching Excellence:

I Formative assessment is intended to monitor studentlearning, helping students identify their strengths andweaknesses and target areas that need work. Theseassessments are low- or no-stakes, e.g. incorporated asa required activity during class time or assigning a gradebased only on completion of the task.

I Summative assessment is intended to evaluate studentlearning at the end of an instructional unit.

Note that both types of assessment can be used to assign acourse grade, but formative assessments should generally begraded in a participatory manner rather than in anevaluatory manner.


Benjamin Braun


Course Design

Assessment

ClassroomPractices

Examples of Assessments

Group Projects, Gateway/Mastery Testing, WritingAssignments, Oral Presentations, Online HomeworkSystems, “Clicker” systems, Procedurally-focused problems,Conceptually-focused problems, Service Learning reports,Independent study project reports, Undergraduate researchproject reports, Portfolios, Quizzes and exams, Scaffoldedassignments


Benjamin Braun


Course Design

Assessment

ClassroomPractices

Example of formative writing assignment

Short reflective essays about challenges in the coursepromote development in both the behavioral and emotionaldomains.

I Write several paragraphs on the following topic: whatwas the most challenging aspect for you regarding[TOPIC]? What made this difficult for you? Did youovercome the challenge, or are you still struggling withit?

I This will be graded based on completion, i.e. if youwrite several paragraphs that address these questionsthen you will get full credit for the problem.


Benjamin Braun


Course Design

Assessment

ClassroomPractices

Example of summative writing assignment

To promote critical analysis skills and develop students’reading abilities, have students write a review of selectedreadings from your course text.

I Write a three page critical review of [ASSIGNEDREADING].

I Imagine that you are writing your review for a journalfor undergraduates in mathematics and the sciences.

I You must address the mathematical depth andmathematical style of [ASSIGNED READING] inaddition to other topics.

Short essays graded using a rubric with five criteria: WritingStyle, Arrangement and Development, Editing andConventions, Mathematical Depth, Mathematical Style.


Benjamin Braun


Course Design

Assessment

ClassroomPractices


Course Design

Assessment

Classroom Practices


Benjamin Braun


Course Design

Assessment

ClassroomPractices

Key Ideas for Classroom Practices

I Balancing Direct Instruction and Active Learning

I Inquiry-Based LearningI Inclusive Learning Environments

I Equitable participationI First-generation studentsI Race/gender/socio-economic-status issues

I Mathematical Task SelectionI Individual, small group, whole class

I CommunicationI Reading, writing, presenting, visualizations


Benjamin Braun


Course Design

Assessment

ClassroomPractices

Active Learning

In a given course, an active learning method is a classroomteaching technique in which students complete a task oractivity directly supporting development in

1. one or more student learning outcomes, and

2. one or more psychological domains.

Each course should include a balance of direct instructionand active learning techniques that collectively supportdevelopment across all of our SLOs.


Benjamin Braun


Course Design

Assessment

ClassroomPractices

Example: Think-Pair-Share in a lecture-basedcourse

Technique: Ask students to use Euclid’s proof of theinfinitude of primes to produce as many new prime numbersas possible starting with only the prime 5. Students havethree minutes to compute independently, then three minutesspent comparing their results with one or two of theirneighbors in class, discussing the reason for why their listsare the same or different.


Benjamin Braun


Course Design

Assessment

ClassroomPractices

Example: IBL-style small group activity

Technique: Assign students to small groups. Give eachgroup a theorem with a 15-line proof where each line isseparately cut out and mixed together, where the proof hasone (fixable) error. Students must first collaborativelyreconstruct the proof, then identify and correct the error.


Benjamin Braun


Course Design

Assessment

ClassroomPractices

Three closing comments

1. Start small and plan for gradual change

2. Expect to eventually develop a large toolbox of“teaching moves” that you can pick and choose from

3. As with learning mathematics, plan for productivestruggle as you learn to use new techniques


Benjamin Braun


Course Design

Assessment

ClassroomPractices

Discussion time!

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Designing and teaching courses for 20-30 students (with a ...€¦ · of E ective Teaching Course Design Assessment Classroom Practices What is Course Design? Course design is the