Helen Burnhburn@highline.edu

Fostering Student Attributes in the Mathematics Classroom: Promising Practices

Helen Burn, Ph.D.Instructor, Department of MathematicsDirector, Curriculum Research Group

Highline Community College

Goals of this Session

• Share the attributes

• Focus session on your interests IDEASGeneral discussion of what the attributes “are.”

Share predominant approaches to fostering the attributes developed as part of 2010 College Spark SAMS grant Specific results of Highline’s project

Student Attributes

• Demonstrates intellectual engagement• Takes responsibility for own learning• Perseveres when faced with time-consuming or complex

tasks• Pays attention to detail

Attributes were created by a team of faculty as part of the College Readiness Standards work in 2006-2008.

http://www.transitionmathproject.org/standards/index.asp

SAMS: Student Attributes for Math Success

Grant Wiki http://studentattributes.wetpaint.com/

Highline Community CollegeRenton School DistrictOlympic College w/ Olympic School DistrictYakima Valley Community College w/ Toppenish School DistrictSeattle School District5 grants of $10,000 each

Learning Outcomes Examples

• Math 81: Introduction to Algebra

Describe her/his reasoning on a task, including sources of confusion or errors [Pays attention to detail, Takes responsibility for own learning]

• Math 91: Essentials of Intermediate Algebra

Describe her/his level of understanding before a formal assessment as well as steps she/he will take to improve [Demonstrates intellectual engagement, Takes responsibility for own learning]

Learning Outcomes Examples

• Math& 146: Introduction to Statistics

Examine and evaluate a statistical process and its results including recognizing when arguments are valid and invalid based on how data was collected and statistical processes used. [Persevere through time-consuming tasks]

Intellectual Engagement (n=9)

Perceives mathematics as a way of understanding… (n=6)Actively explores new ideas, posing questions, .. . . (n=4)Recognizes patterns . . . (n=7)Appreciates abstraction and generalization. . . (n=3)Is willing to take risks and be challenged . . . (n=6)Contributes and benefits from group problem solving (n=7)

TASKS mentioned: A natural part of their teaching (n=7)Gives harder problems, typically in groups (n=5)Group work (n=7)

“Harder Problem” Examples

• Factor by grouping

• Graph the triangle with vertices (-2, 1), (-6, -8), (-11, 5). Show that this is a right triangle.

232232 1548417696

“Taking Risks” Examples

• Assign students numbers and choose them at random to show homework on the board. Or have students volunteer.

• Make student work public using ELMO technology

• Use open-ended tasks that ask students to engage in a concept without prior instruction.

Takes Responsibility for Learning (n=7)

Attends nearly every class session . . . (n=5)Conscientiously prepares work assigned for class (n=3)Examines and learns from errors, seeks help . . . (n=5)Takes advantage of resources. . . (n=6)Sets aside necessary time . . . (n=4)

TASKS mentioned (n=8): Speaks to it (n=5)Encourages attendance (n=3): Board presentations, attendance in grade, quiz at beginning of class

Takes Responsibility for Learning

TASKS mentioned (n=8): Encourage preparation (n=5): Prereading assignment, reading guides, provide daily schedule, group quizzes, boardwork

Creates online resources and expects engagement (n=4): Post notes online, web-based videos, homework, Angel postings

Examines and learns from errors (n=5): Collect HW and expect students to review; provide key to exams, board presentations, error analysis/partial credit request, retesting scheme, students grading each others’ quizzes

Example Tasks

• Frequent quizzes at the beginning of the class. Tardy students do not have additional time. . . [Encourages attendance]

• Provide detailed answers for each test. If class does poorly on test, an announced make-up quiz will be given within a week that consists of two or more randomly selected questions similar to the test. If student obtains full points on the make-up, half the difference is added to the original score [Takes responsibility, learns from errors]

• Partial credit requests on exams

Perseveres Through Time Consuming Tasks (n=8)

Willing to work on challenging problems (n=7)Successfully completes complex, multi-step tasks (n=5)Recognizes unproductive approach (n=3)Is convinced that efforts is important to success (n=4)

TASKS mentioned (n=8)Projects (n=3), only in stats and Math 95More advanced problems, critical thinking problems (n=5)Speak to importance of effort. Stressed in class or through Dweck video (n=2)

Pays Attention to Detail (n=4)

Correctly follows all parts of oral and written directions without needing additional reminders (n=3)

Makes few notational errors . . . (n=3)

TASKS mentioned (n=3)Points out common errors; uses metacognitive language (n=2)Expects details in answers or points deducted (n=1)Just expects it

Example Tasks

I require calculus students to “write the answer (to a word problem) in a complete sentence, including units. “Be precise in the inclusion or exclusion of the descriptor ‘limit as x approaches a.” . . . Points will be deducted if the details are omitted.

The Future of Student Attributes?

As written, they are murky. The “categories” are not clear, nor is their theoretical rationale.

• Metacognition• Study Skills• Habits of Mind• College Knowledge At Highline, we recognize that effective teaching requires

that we build SA systematically, rather than haphazardly, into our teaching.

Weekly Checklist (Diana Lee a la Atul Gawande)

WEEK ONE• First Day - Review Syllabus, show logging into MML, introduction to a

notebook organization system• Midweek – Taking Personal Responsibility (before, during, after class)• Midweek – Have students bring notebooks and tabs and set them up• End of Week – Review again Personal Responsibility (before, during,

after class) and review logging into MML . . .

WEEK THREE• Monday (during exam) do a notebook check (organization, inclusion,

forms filled out)• Day after exam – Student fill out self-reflection (concepts understood and

study effectiveness)• End of week – Time management (what does it mean to study

effectively?)

Adding it Up, NRC (2001)

• Conceptual understanding• Procedural Fluency• Strategic Competence• Adaptive Reasoning: (Capacity for logical thought, reflection, explanation, and justification)• Productive Disposition (Habitual inclination to see mathematics

as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy

How Students Learn: Mathematics in the Classroom, NRC (2005).

Principle 1: Teachers Must Engage Students’ PreconceptionsPrinciple 2: Understanding Requires Factual Knowledge and Conceptual FrameworksPrinciple 3: A Metacognitive Approach Enables Student Self-Monitoring.

• Emphasis on debugging problems• Internal and External Dialogue as Support for Metacognition• Seeking and Giving Help

Carnegie Foundation (2009)

Psychosocial Theories to Inform a New Generation of Student Support Structures for Learning Mathematics, Fong & Asera (2010) http://www.carnegiefoundation.org/sites/default/files/elibrary/psychosocial_theories.pdf

“The goal of this paper is to explore theories from psychology that could inform a new generation of student support committed to increasing student motivation and academic success” (p. 2)

• Bandura’s Theory of Self-Efficacy• Motivational Processes (Goal Orientation, Self-Regulation)• The Social Environment (Stereotype Threat)• Grit, Resilience, and Self-Discipline• Theory to Practice: AYD

The Students and Professors Misunderstand One Another College Fear Factor: How

Students and Faculty Misundersatnd One Another. Cox (2009)

• Imposter Syndrome• Advising Needs• College Cultural Capital (Bourdieu)• College Expectations

Redefining College Readiness (Conley, 2007)

http://www.aypf.org/documents/RedefiningCollegeReadiness.pdf

• Key Cognitive Strategies (open mindedness, analysis, reasoning, etc)

• Academic Knowledge and Skills (writing, research, core academics)

• Academic Behaviors (study skills, self monitoring)

• Contextual Skills and Awareness (advising, resources, etc.)

My Framing of Student Attributes

• Understands college norms and values (intellectual engagement,

taking responsibility for learning, actively exploring questions, taking risks,

complexity)

• Prerequisite Knowledge and Skills (writing, research, core academics)

• Metacognitive Skills (self monitoring, self regulation, attn to detail)

• Campus navigation skills (registration/advising, how to approach

faculty, netiquette skills, available resources, etc.)

Helen BurnHighline Community CollegeCurriculum Research Group

hburn@highline.eduwww.CurriculumResearchGroup.org