# 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

- Practice » CPM syllabus

#### Prior knowledge

- slides
- Syllabus scavenger hunt
- Workshop practice syllabi
- What is mathematics?

### Sept 18

Homework due today

- Practice » In-class assessment

#### Summative assessment

- slides
- Warm up
- Workshop assessments
- ETS Advanced Placement exams: conventions, examples
- Backwards design

### Sept 25

Homework due today

- Readings:
- Practice » Assessment scoring

#### How is mathematics learned?

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

### Oct 2

Homework due today

- Practice » Teaching videos

#### Teaching for understanding

- slides
- Workshop lessons
- Teaching strategies
- Lesson planning

### Oct 9

Homework due today

- Practice »Formative assessment

#### Objectives & Formative assessment

- slides
- Create Learning Targets
- Workshop lesson plans
- Growth vs. Fixed

### Oct 16

Homework due today

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

- Practice » Problem-solving task

#### Problem solving

- slides
- 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? (problems vs. exercises
- 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) ~or~

Surprising truth about motivation (Pink) - America's best teachers get creative (ScienceDaily)
- (optional) Selective attention test (Simons)
- (optional) We don't pay attention to boring things (Medina)

- Practice » Motivation

#### Motivation & engagement

Cognitive engagement

- New groups
- Stories - Three acts of a math story (Meyer, list of tasks), Privileged status of story (Willingham, 2004)
- Manipulatives
- Puzzles - arithmagons, cross-number puzzles, row game, kenken, kakooma, shikaku, zukei, sudoku, Mayan numbers, function operations, connected puzzles
- Games - Derivative block, review quiz, math hombre games list

### Oct 30

Homework due today

- Readings:
- Equality (Carpenter, 2003)
- Five objections to teaching the area model (Tanton, 2017)
- Choose one of the following:
- Developing student's thinking in number and operations (Groth, 2013)
- Number: What is there to know? (National Research Council, 2001)
- K–5 Progression on Number and Operations in Base Ten
- 3–5 Progression on Number and Operations—Fractions
- 6–8 Progression on The Number System; High School, Number
- High School Progression on Quantity

- Practice » Mathematical connections

#### Teaching number and operations

- Assign PS Observations (two weeks to prep problems and scaffolds)
- Issues with number and operations: cross number puzzles?, missing decimals, alternate algorithms, error patterns (aka. buggy algorithms), integer models
- Anticipating mathematics errors

### Nov 6

Homework due today

- Readings:
- Misconceptions in math (Allen, in Canvas)
- Nix the tricks, pick at least two "tricks" to focus on (Cardone)
- Choose one of the following:
- Developing student's thinking in algebraic thinking (Groth, 2013)
- K–5 Progression on Counting and Cardinality and Operations and Algebraic Thinking
- 6–8 Progression on Expressions and Equations
- High School Progression on Algebra
- High School Progression on Functions

- (optional) Against answer getting (Daro)

- Practice » Mathematical connections

#### Teaching algebra

- slides
- Manipulatives: fraction strips, algebra balance, base blocks, algebra tiles, NLVM
- Anticipating mathematics errors

### Nov 13

Homework due today

- Readings:
- When good teaching leads to bad results (Schoenfeld)
- Choose one of the following:
- Developing student's thinking in geometric thinking (Groth, 2013)
- K–5 Progression on Measurement and Data (measurement part)
- K–6 Progression on Geometry
- 7–HS Progression on Geometry

- Practice » Mathematical connections
- Prepare problem and scaffolds for PS observations

#### Teaching geometry & proof

- Measurement: distance, area, surface area, volume
- Manipulatives: geoboards, compasses, protractors, miras, pattern blocks
- Software: GSP, Geogebra
- Puzzles: Zuekei, Shikaku, Area maze
- Vocabulary
- Misconceptions & issues

### Nov 20

Homework due today

- Readings:
- Why we make bad decisions (Gilbert)
- Choose one of the following:
- Developing student's statistical and probabilistic thinking (Groth, 2013)
- K–5 progression on Measurement and Data (data part)
- 6–8 Progression on Statistics and Probability
- High School Progression on Statistics and Probability
- Student's understanding of probability (Shaughnessy, 2003; in Canvas)

- Practice » Mathematical connections

#### Teaching probability & statistics

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

### Nov 27

Homework due today

- Readings
- Designing homework that promotes learning (Weimer, in Canvas)
- Homework: What research says (Cooper, in Canvas) -or-

Benefits of more homework vary across nations, grades (ScienceDaily) - Criticism and ineffective feedback (Heddleston)
- How video games do feedback well (and poorly) (Madigan)
- (optional) Brain Rules in the classroom (Medina)
- (optional) Forget what you know about good study habits [NYTimes]
- (optional) Rules for critique (Berger)

- No practice assignment this week!

#### 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
- Reliability of grading work in mathematics (Starch and Elliot, 1913)
- Failure is a NORMAL part of learning (Andersen/Tae)
- Assessments: The collateral damage of SBG (McMatherson)
- (optional) What if Angry Birds didn't grade with SBG? (Dickson)

- Practice » Math project

#### Grading

- Workshop projects
- Grading: history, different scales, gradebook, rubrics, standards-based grading
- Teaching examples: #grading
- Reminder PS observation

### Dec 11

Homework due today

- Readings (choose three)
- 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)
- Five principles of extraordinary mathematics teaching (Finkel, 2016)
- The most effective teachers turn to their colleagues for advice (while weaker teachers don’t bother) (Busch, 2018)

- Practice » External resources

#### Reflections

- share external resources

### Final exam

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