# Teaching Mathematics, grades 5-12

## Calendar

This is a tentative schedule that may be changed based on the needs of the students, the needs of the instructor, or any apocalyptic events that may occur during the semester.

### Sept 11

Homework due today

- Readings:
- A mathematician's lament (Lockhart, p. 1-16)
- Ch 1. What is math? (Boaler)
- Global perspective on mathematics education (Groth, 2013, p. 12-18)
- (optional video) Breaking the cycle (Zager)
- (optional) The real worlds (Ani, 2014)

- Practice » CPM syllabus

#### Prior knowledge

- Syllabus game
- Workshop practice syllabi
- compare grading overview via large white boards (typical math class: 33% exams, 33% individual, 33% listening)
- defend policies against being gamed
- review pacing calendars for flexibility and projects/papers
- discuss syllabus and decisions

- What is mathematics? Noun or verb? Maybe it is an
**adjective**, a type of thinking(?)- Toolkit - skills for unknown future
- Modeling - language of abstraction for science, engineering
- Problem solving - "Mathematics consists of problems and their solutions" (Paul Halmos)
- Art - cultural/creative activity worth doing for its own sake (proof, concepts)

### Sept 18

Homework due today

- Readings:
- Strands of mathematical proficiency (Kilpatrick, Swafford, & Findell, 2001)

- Practice » In-class assessment

#### Summative assessment

- Warm up
- Workshop assessments ~take test, report time to take (multiple by 4 or 5 to find student time), classify as concept, procedure, math reasoning, or PS
- ETS Advanced Placement exams: conventions, examples
- Backwards design

### Sept 25

Homework due today

- Readings:
- Learning with understanding (NAP, 2002) -or-

Key psychological ideas and research findings (Groth, 2013, pg. 27-46) - Three rules on mindsets (Pink) -or-

Myth of being bad at math (Boaler) -or-

Low floor, high ceiling (Boaler) - Mindsets graphic (Holmes)
- (optional) Mindsets quiz

- Learning with understanding (NAP, 2002) -or-
- Practice » Assessment scoring

#### How is mathematics learned?

- Workshop scoring guides
- What do we remember? (fear as motivation?)
- "The best learning begins with …" ~a problem

### Oct 2

Homework due today

- Readings:
- Never say what a kid can say (Reinhart)
- Choose two subsections from pages 29-52 (
*Principles to actions*, 2014) - Ch 3. A vision for a better future (Boaler, 2015)
- math instructional practices (Andersen)
- (optional) Learning through problem solving (Scammell)

- Practice » Teaching videos

#### Teaching for understanding

- Workshop lessons
- What is the teacher doing?
- What are the students doing?
- The hard parts

- Teaching strategies
- Lecture (aka. instruction)
- Interactive lecture - clickers
- Group work
- Project/inquiry based
- Formative assessment based
- One-on-one

- Lesson planning

### Oct 9

Homework due today

- Readings:
- Establish goals to focus learning (
*Principles to actions*, 2014, p. 12-17) - Elicit and use evidence of student thinking (
*Principles to actions*, 2014, p. 53-58) - Assessment for learning (
*What's math got to do with It?*, p. 98-105) - New forms of testing that encourage learning (Boaler, 2015, p. 84-94)
- (optional) Planning chapters, not lessons (Daro)

- Establish goals to focus learning (
- Practice »Formative assessment

#### Objectives & Formative assessment

- Create lesson objectives
- Teaching strategy: Framing the question / Questions / Feedback
- Growth vs. Fixed ~fixed: comparing yourself to others; growth: comparing yourself to yourself
- CCSS-M: Practice standards

### Oct 16

Homework due today

- Readings:
- Implement tasks that promote problem solving (
*Principles to actions*, 2014, p. 17-24) - CCSS math practice standards
- Math class needs a makeover (Meyer)
- Design of tasks (Boaler in D2L)

- Implement tasks that promote problem solving (
- Practice » Problem-solving task
- Practice » Professional lesson plan

#### Problem solving

- Workshop problems
- What important mathematics concepts/skills does the problem promote?
- What background knowledge would students need to be able to solve this problem?
- Would students find the problem interesting? Why or why not?
- Classify the problem based on Stein's criteria for cognitive demand. Provide reasons for your classification.
- Memorization
- Procedures w/o connections
- Procedures w/ connections
- Doing mathematics

- What other aspect of the problem should be considered?

- Examples ~darts, camels and bananas
- What is a problem? ~vs. exercise
- Scaffolding while maintaining high expectations

### Oct 23

Homework due today

- Readings (choose four):
- Motivation, not IQ, matters most for learning new math skills (Blue)
- Puzzle of motivation (Pink)
- We don't pay attention to boring things (Medina)
- America's best teachers get creative (ScienceDaily)
- Breaking the cycle (Zager)
- (optional) Selective attention test (Simons)
- (optional) math hombre games list

- Practice » Professional lesson plan (returned)

#### Motivation & engagement

- What are barriers to learning math?
- War on attention
- Difficulty
- Cognitive engagement
- Stories - Boy who cried wolf (why tell story? just tell moral instead)
- Toys
- Puzzles - arithmagons, row game, kenken, kakooma, shikaku, sudoku, Mayan numbers, function operations
- Games - Derivative block, pubquiz

- PS example?
- Three acts of a math story (Meyer, list of tasks)

### Oct 30

### Nov 6

Homework due today

- Readings:
- Equality (Carpenter)
- Misconceptions in math (Allen, in D2L)
- Nix the tricks (Cardone, pick at least two "tricks" to focus on)
- (optional) Against answer getting (Daro)

- Practice » CCSSM Progressions

#### Teaching algebra

- Assign PS Observations
- Error patterns, base system & operations, alternate algorithms
- Manipulatives: fraction strips, algebra balance, base blocks, algebra tiles, NLVM
- Extra teacher examples:
- Anticipating mathematics errors

### Nov 13

Homework due today

- Readings:
- Van Heile exerpt (Groth, in D2L)
- When good teaching leads to bad results (Schoenfeld)
- Notion of proof (video, in D2L)
- (optional) Notion of proof (Boaler and Humphries, in D2L)

- Practice » CCSSM Progressions
- Practice » prepare for PS observations (problem & scaffolds)

#### Teaching geometry & proof

- Manipulatives: geoboards, compasses, protractors, miras, pattern blocks,
- Software: GSP, Geogebra
- Vocabulary
- Misconceptions & issues

### Nov 20

Homework due today

- Readings:
- Student's understanding of probability (Shaughnessy, 2003; in D2L)
- Why we make bad decisions (Gilbert)

- Practice » Review two stats lessons
- Practice » CCSSM Progressions

#### Teaching probability & statistics

- Outcome generator
- Law of large numbers
- Comparing distributions
- Misconceptions & issues

### Nov 27

Homework due today

- Readings
- Criticism and ineffective feedback (Heddleston)
- Designing homework that promotes learning (Weimer, in D2L)
- Homework: What research says (Cooper, in D2L)
- Benefits of more homework vary across nations, grades -- sciencedaily (ScienceDaily)
- (optional) Brain Rules in the classroom (Medina)
- (optional) Forget what you know about good study habits [NYTimes]

- Practice » CCSSM Practice standards

#### Homework and practice

- CCSS practice structure
- Elaboration on 6-8 practices
- Practice and forgetting
- Teaching examples: Exit slips as practice — Warm-up routine

### Dec 4

Homework due today

- Readings
- What if Angry Birds didn't grade with SBG? (Dickson)
- Failure is a NORMAL part of learning (Andersen/Tae)
- Assessments: The collateral damage of SBG (McMatherson)

- Practice » Math project

#### Grading

- Workshop assessments
- History
- Different scales
- Gradebook & rubrics
- Standards-based grading
- Teaching examples: #grading
- Reminder PS observation

### Dec 11

Homework due today (incomplete)

- Readings
- The flip: End of love affair (Wright, 2012)
- Forget what you know about good study habits (Carey, 2010)
- The door problem (England, 2014)
- Want to close the achievement gap? (Darling-Hammond, 2014)

- Writing assignment (open)
- Practice » External resources

#### Reflections

- discuss external resources

### Final exam

- Reports from PS observations
- Exit slip ~What does it mean to think like a math teacher? (6 words or less?)