Engaging Students in Learning Mathematics

KindergartenSession 2

Pam HutchisonOctober 22, 2015

AGENDA• Guiding Principles for Teaching Math• 8 Math Teaching Practices• Mindset and Mistakes• Review of Daily Math• Math in Focus

Principles to Actions: Ensuring Mathematical Success for All

Assessment

Principles to Actions

Curriculum

Teaching and Learning

Access and Equity Professionalism

Tools and Technology

Effective Teaching and

Learning

Time and time again, research has shown that an effective teacher is the strongest in-school predictor of student achievement. 

6 times the impact of all other factors combined

Mathematics Teaching Practices

• … the profession need to identify “practices at the heart of the work of teaching that are most likely to affect student learning”

• NCTM released “Principles to Actions: Ensuring Mathematical Success for All”

8 Mathematics Teaching Practices

Mathematical Teaching Practices1. Establish mathematics goals to focus

learning. 2. Implement tasks that promote reasoning

and problem solving.3. Use and connect mathematical

representations.4. Facilitate meaningful mathematical

discourse.

Mathematical Teaching Practices5. Pose purposeful questions. 6. Build procedural fluency from conceptual

understanding. 7. Support productive struggle in learning

mathematics. 8. Elicit and use evidence of student

thinking.

MTP’s• Take a few minutes to read over the

descriptions• At your tables discuss,

– How do these practices relate to the SMP and the content standards?

– Which ones do you believe are prevalent at your site?

– What would be your next steps?

Standards for Mathematical Practice1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning

of others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

Connections to SMP’s1. Make sense of problems and persevere in solving them (2,

3, 7)

2. Reason abstractly and quantitatively (2, 3, 4, 5)

3. Construct viable arguments and critique the reasoning of

others (2, 4, 5)

4. Model with mathematics (2, 4, 5)

5. Use appropriate tools strategically (2, 4)

6. Attend to precision (4)

7. Look for and make use of structure (2, 6)

8. Look for and express regularity in repeated reasoning (2, 6)

Mindset

Growth Mindset• A belief system that suggests that one’s

intelligence can be grown or developed with persistence, effort, and a focus on learning

Fixed Mindset• A belief system that suggests that a

person has a predetermined amount of intelligence, skills, or talents

Mistakes and Learning

Michael Jordan1997 Nike commercial• “I’ve missed more than 9,000 shots in my

career. I’ve lost almost 300 games. Twenty-six times I’ve been trusted to take the game winning shot…. and missed. I’ve failed over and over and over again in my life. And that is why I succeed.”

Pete AthansFailures provide information to help us do things differently next time. • “I learned how not to climb the first four

times I tried to summit Everest,” says alpinist Pete Athans, who’s reached the world’s highest peak seven times. “Failure gives you a chance to refine your approach. You’re taking risks more and more intelligently.”

Mindset for Growth• http://mindsetforgrowth.com/

– Growth Mindset: Failure is the most essential step to success

– Famous Failures

Inventions Created by Mistake• We tend to hold inventors in high esteem,

but often their discoveries were the result of an accident or twist of fate. This is true of many everyday items, including the following surprise inventions.

Inventions Created by Mistake1. Penicillin2. The Slinky3. Wheaties4. Post-It Notes5. The Color Mauve6. Plastics7. Saccharin8. Corn Flakes9. Pacemaker

Feedback and Re-Do’s• Keep expectations high and let students

know when they have not met those expectations, then tell them what they need to do to improve.

• Give them time to re-do the work and offer support in the process.

Feedback and Re-Do’s• Circle errors on papers.• Let students know that this means “Look at

this again.”• Provide feedback in writing or in person.

(An X on a paper teaches nothing.)• Allow re-do’s

Feedback and Re-Do’s• Feedback and re-do’s can be an extremely

valuable part of the learning process• We need to allow peer edits and revisions in

math, the same as we do in writing• But it is only valuable if there is something

in place that that will help them learn from their mistakes

A Daily Math Program

Subitizing

Subitizing

Subitizing

Making Tens

Making Tens

Number of the DayNumber of the Day of School• Counting• Counting back• Place Value

– Straws– Ten Frames Chart– Hundred’s Chart (optional)

• Number Bonds

Number of the Day• Today is the 54th day of school

– Let’s count to 54 starting at 42.– Let’s count the number of straws we have so far.

• Groups of 10 – 10, 20, 30, 40, 50• Count on one’s - 51, 52, 53, 54• Add 1 more straw

– Let’s count the number of straws we have now.• Groups of 10 – 10, 20, 30, 40, 50• Count on one’s - 51, 52, 53, 54, 55

– So what is one more than 54?

Number of the DayNumber of the Day on the Calendar • Today is October 22nd

– Let’s count to 22– How many groups of 10 will we need to make

22?– Let’s count – 10, 20– Now how many more?– Let’s count – 21, 22

Random Number of the Day• The number of the day is:

Write “5” or Say “five”– Who can read (or write) the number?– Let’s count to 5– Which of these show 5

Random Number of the Day• The number of the day is: 5

– Let’s count out 5 monkeys.– How many monkey’s did we count?– What’s one more than 5? One less than 5?– What’s two more than 5? Two less than 5?– Number Bonds for 5

Number Bonds – 5

5 5

5 5 5

5

Daily Math, continuedPatterns• Predict the next element in the pattern (shape,

location, etc.)• Identifying the repeating part

Daily Math, continuedWord Problems • All four operations ( +, -, x, ÷)• Start with 4 types of addition/subtraction

problems and basic multiplication/division problems

• Children do not have to have “mastery” with number used on word problems

Add To – Result Unknown• There are three children playing at the park.

Two more children come to the park. How many children are in the park now?

Taken From – Result Unknown• Renee has five toy bears. She loses one at

the park. How many bears does Renee have now?

Put Together/Take Apart – Total Unknown

• In the park, 1 child is at the slide and 2 children are at the swings. How many children are in the park?

Put Together/Take Apart – Both Addends Unknown

• There are 5 children in the park. They are at either the slide or the swings. How many are at the slides and how many are at the swings?

Multiplication• There are 3 beds. Each bed has 2 bears on

it. How many bears are there?

Group Size Unknown• Renee has 6 stuffed bears. She places them

so that there are the same number of bears on each of her two beds. How many bears are on each bed?

Number of Groups Unknown• Renee has 6 stuffed bears. She wants to put

2 bears on each pillow. How many pillows does she need?

Daily Math, continuedGeometry • Plane Shapes: Squares, Circles, Triangles,

Rectangles, Hexagons• Solids: Cubes, Cones, Cylinders, Spheres• Name shape regardless of size or orientation

Daily Math, continuedGraphs and Data• At least once a month – related to things about

the kids• Graphs represent real people and real data• Ask a wide variety of questions related to the

graph

Math in Focus