ERLC Presents …

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ERLC Presents…

A 12-Step Program for Student Success in Mathematics

With Marian Small

A 12-step program for student success

Marian SmallFebruary 2010

Hello there• Just so you know with whom you’re talking….

• Have a look-see!

And so I know you…• I’m curious as to what division you are in. Could

you let me know?

• A for Division 1

• B for Division 2.

• C for Division 3.

• D for Division 4.

What led me here• Teachers’ love of lists

• The existence of other “twelve step” programs

AA twelve steps1. Admit life out of control

2. Admit greater power could restore you.

3. Decide to turn to a higher power.

4. Make a personal inventory.

5. Admit the problem to self and another.

AA twelve steps6. Be ready to remove defects.

7. Ask for help in removing shortcomings.

8. Be willing to make amends to those harmed.

9. Make the amends.

AA twelve steps10. Continue personal inventory and continue to

admit wrongs.

11. Prayer and meditation

12. Carry message to others.

Our variation

• Step 1: Recognizing a problem your students might feel in your classroom

What do you see as the biggest problem?

A Not enough academic success

B Not enough confidence

C Not enough engagement

D Not enough joy

• Step 2: Deciding you are the one to do something about it

A teacher’s role• To your students, math is “you”- not a book, not

algebra, not numbers, not shapes.

• If things aren’t working, blaming lazy kids, poor parenting, your principal, your superintendent, your trustees, the Ministry or the world gets you nowhere.

• Step 3: Becoming self-aware without condemning yourself

Be kind• We want students to honestly face their learning

struggles without making them feel awful. We owe ourselves the same kindness.

Think to yourself• What do I do as a teacher that is really great?

Will somebody share here?

Think to yourself• Which kids seem not to connect with me? Why

might that be?

• Which colleagues seem not to connect with me? Why might that be?

Think to yourselfWhen colleagues seem not to connect with me…. Is it

because:

A I’m so good; they’re jealous

B I’m so bad that they don’t want the association.

C We teach different grades or subjects.

D Our philosophical approaches are just too different?

• Step 4: Looking for a “sponsor”– working with other teachers

What makes us change?• If our ideas are “confronted” either through

personal interactions or through reading.

• Where do we find our sponsor? It might be a colleague, an administrator, a coach, a consultant,…

Can someone share one experience where such an interaction made them a better teacher?

• Step 5: Gaining better insight into what and how you are teaching by talking (to your sponsor and others) and reflecting and/or by reading and reflecting.

Value of interaction• We teach students about the value of working in

groups, teamwork, etc., so we need to practise it.

• It’s about really hearing what someone else does and why and being forced to tell someone else what you do and why.

• If you don’t have to talk to someone about what you are doing, you often don’t notice some of the things you’re not doing or realize alternatives you could be doing.

For example…• You are teaching your students about half/double,

i.e. if you multiply two numbers, you can halve one and double the other (e.g. 18 x 25 = 9 x 50)

• You say it works since you are doing the opposite to each number.

• I (a colleague) come along and ask….

• So how come that doesn’t work for division? (Why isn’t 300 ÷ 50 = 600 ÷ 25?)

• It is only then that you realize that there were some glaring omissions in what you had told your students.

Would you:

A Just clarify by saying it only works for x

B Explain why it only works for x using examples

C Explain why it only works for x using reasoning

D Ask kids to figure out why it only works for x?

x x x x x x x x x x x x

8 ÷ 2

x x x x x x x x

4 ÷ 4

x x x x Not enough stuff and too many sharers

Or…• You are teaching students how to solve

proportions. Lots of students struggle when solving a proportion such as 4/x = 3.2/80.

• You talk to another teacher to get an idea, e.g.

Ratio table

3.2 32 8 4

80 800 200 100

Or…• You are teaching students how to calculate the

mean of 58, 57, 55, 70 and 68.

• You never realized, until you talked to someone else, you could think of each number in terms of 60, so it’s really the mean of:

60 – 2, 60 – 3, 60 – 5, 60 + 10 and 60 + 8, so you could calculate the mean of -2, -3, -5, +10 and +8 and just add 60.

• In addition, a conversation with other teachers can help you clarify what your learning goals can or should be, different pedagogical approaches you could take, or missed opportunities.

What to read?• Our math teaching benefits by reading math-

specific material. Whether they are books and articles that give us more insight into the math content we teach or pedagogical approaches ….

What to read?• Whether they are books and articles that are

research based or that are personal reflections….

• Whether they are in print or on the internet….

• Step 6: Teaching through problem solving

What does it mean?• You don’t teach a whole bunch of techniques so

that kids can solve “problems” of a certain type. (They aren’t problems if the kid knows the type they are anyway.)

What does it mean?• Instead you present the problem and let kids try.

The problems are not random; you make a professional judgment about where your students need to and can go.

What does it look like?• In Grade 4, I might ask my students something

• I used 43 sticks to make triangles, squares and hexagons. What did I make?

What does it look like?43 sticks to make triangles, squares and hexagons.

Choose which answer might be reasonable:

A: all triangles

B: all squares

C: 5 hexagons and some squares

D: 3 hexagons and some squares and triangles

What does it look like?• Or, more specifically….

• A) How many of each shape might I have made?

• B) How do you know that at least one shape was a triangle?

like: A parallelogram has an area of 32 cm2. What might its dimensions be?

What should I ask now?A: Could the parallelogram be really long?

B: Could the height be 4?

C: Could the height be just a little less than the base length?

D: What do you know about the parallelogram?

What should I ask now?A: Could the parallelogram be really long?

B: Could the height be 4?

C: Could the height be just a little less than the base length?

D: What do you know about the parallelogram?

Someone explain their choice.

like: Without using a protractor, how do you know that these line segments on a geoboard are perpendicular?

What does it look like?• Look at the rises and runs.

• Step 7: Planning ahead what to ask and, as much as possible, how to respond, but with a willingness to change.

Planning questions• When you write a lesson plan, you could be

thinking about the questions you should ask that bring out the big idea and that ensure that all students’ needs are addressed.

For example…• You are teaching a grade 4 lesson on dividing two-

digit numbers by one-digit numbers, e.g. 78 by 6.

• What do you think are the one or two most important ideas you want students to walk away with?

Is it…A That division describes the equal groups when you

divide up a whole.

B That you can accomplish division by thinking about subtraction or multiplication.

C That you should estimate before you calculate

D The procedure for dividing

So what might you ask..• Describe a situation where you might divide 50 by

• Now describe a situation where you are forming groups but you would not divide.

Or…• Jennifer said that you can’t divide 50 by 4 since if

you try to make equal groups it doesn’t work. What would you say to Jennifer?

Or…• Tell how dividing is related to multiplying.

Or…• Alicia says that 45 – 9 – 9 – 9 – 9 – 9 = 0 describes

a division. Do you agree? Explain.

Grade 8 example• You are teaching students to solve linear

equations with integer solutions, using a variety of strategies (e.g. 2n + 1 = 17).

• What are the most important things you want students to know?

Maybe…• That an equation is a statement of balance.

• That the equation has many “equivalent” forms, e.g. 2n + 1 = 17 is equivalent to 2n = 16 or 2n + 2 = 18 or….

• That solving an equation is finding the “simplest” equivalent form.

So you could plan to ask…• Which of these equations do you think are

most alike? Why do you think that?

3n - 1 = 17

36 – 6n = 0

3n – 4 = 20

18 – n = 2n

Or…• Give three equations equivalent to (with exactly

the same solutions as) 10 – n = 6.

• Kylie said that if 8 + 4 = x + 5, then x = 12. Do you agree? Explain why you agree or disagree.

• Lenee said that 5 + n = 12 is just the equation n = 7 “in disguise”. Do you agree? Explain why you agree or disagree.

Which did you like best? Can someone share?

• Step 8: Recognizing that different students need different “treatment.”

Recognizing differences• recognizing student talents and interests.

Recognizing differences• You could provide choice in consolidation (or

practice) or choice in instruction.

Recognizing differences• For example, if you have students who really like

to “debate”, then include as one of the assignment choices the opportunity to debate. A student could take the pro or con side on “You never really need to learn how to divide if you know how to multiply.”.

Recognizing differences• In an instructional situation, you could provide

alternate activities for students who need those alternatives.

• For example, if you wanted lots of students to multiply two 2-digit numbers, but some are really not ready, you could provide these alternatives.

MultiplicationTask 1:

• A hotel has 24 windows on a floor. There are 19 floors. How many windows are there?

Task 2:

• A hotel has 24 windows on a floor. There are 9 floors. How many windows are there?

Some common questions• Is the number of windows more than 240? How do

you know?

• How would you estimate the number of windows?

• How could you use manipulatives or a diagram to model the problem?

• How could you use mental math to solve the problem?

Or…• Or you could ask more open-ended questions. For

example, in grade 3, when working on addition of 3-digit numbers, you could say:

• Create an addition problem where you add a number greater than 30 to 38. Solve your problem.

Too many …• teachers believe that whatever way they think is

clearest is clearest to everyone.

• parents believe that whatever way they remember is the right way.

• Step 9: Responding to individual students.

Ensuring praise• Every child needs genuine praise.

• You need to be assigning tasks where students can succeed so you can praise.

• Praise works best when the tasks allow for unique responses.

Giving feedback• The best feedback you can give is personal; it

picks up specifically on what the student has said.

Giving feedback• Suppose a Grade 1 student says that 15 – 8 is less

than 15 – 10 since 8 is less than 10.

Will someone share?

Giving feedback• Suppose a Grade 5 student says that 6/4 is not a

fraction since fractions are parts of wholes and that isn’t. What would you say?

Can someone share?

Giving feedback• Suppose a Grade 9 student says that -4 - (-3) =

7 since two negatives make a positive. What would you say?

Can someone share?

• Step 10: Making what you teach your own.

Too many teachers..• tell me that they are asking a question that makes

no sense to them just because it’s in the book.

• What you do has to make sense to you. Ultimately you are responsible for the instruction in the class– if the students don’t see you comfortable, it’s very unlikely they can be.

• Step 11: Relaxing

Uptight is bad.• Too many teachers are “obsessed” with wording,

with following instructions that are peripheral,….

For example…• You ask students to pace off the length of the

classroom. One student does the width instead.

• Who cares?

Uptight is bad.• If we could relax a bit and go with the flow,

classrooms would be more pleasant environments, students would take more risks, and there would be much less stress all around.

• Step 12: Staying the course and carrying the message if you’re up for it.

Persistence• Persistence is the key.

• You have to try.

• You have to try more than once.

Taking initiative• You can be the leader as well as a follower and

encourage others.

So….• If you want a checklist,…

• If not, there is a bigger picture here. I actually think that the three big issues I’ve addressed are the need to take responsibility for your instruction, the need to work collaboratively, and the need to really think hard about what you do.

Teaching is…• constantly staying up to date,

• conferring and talking over “cases”, and

• considering the individual welfare of each of our “patients/clients”

Thank You• You can download this presentation on my

website:

www.onetwoinfinity.ca

Look for: West Webinar

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