Teaching to the Big Ideas - Alberta Regional Professional ...

Teaching to the Big Ideas - Alberta Regional Professional ...

ERLC Presents A 12-Step Program for Student Success in Mathematics With Marian Small A 12-step program for student success Marian Small February 2010

Hello there Just so you know with whom youre talking. Have a look-see! 3 And so I know you Im 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. 4 What led me here Teachers love of lists The existence of other twelve step programs

5 AA twelve steps 1. 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.

6 AA twelve steps 6. 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. 7

AA twelve steps 10. Continue personal inventory and continue to admit wrongs. 11. Prayer and meditation 12. Carry message to others. 8 Our variation

9 Step 1: Recognizing a problem your students might feel in your classroom 10 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 11 Step 2: Deciding you are the one to do something about it

12 A teachers role To your students, math is you- not a book, not algebra, not numbers, not shapes. If things arent working, blaming lazy kids, poor parenting, your principal, your superintendent,

your trustees, the Ministry or the world gets you nowhere. 13 Step 3: Becoming self-aware without condemning yourself 14

Be kind We want students to honestly face their learning struggles without making them feel awful. We owe ourselves the same kindness. 15 Think to yourself

What do I do as a teacher that is really great? Will somebody share here? 16 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? 17 Think to yourself When colleagues seem not to connect with me. Is it because: A Im so good; theyre jealous

B Im so bad that they dont want the association. C We teach different grades or subjects. D Our philosophical approaches are just too different? 18 Step 4: Looking for a sponsor working with other teachers

19 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? 20 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.

21 Value of interaction We teach students about the value of working in groups, teamwork, etc., so we need to practise it. Its about really hearing what someone else does and why and being forced to tell someone else

what you do and why. 22 If you dont have to talk to someone about what you are doing, you often dont notice some of the things youre not doing or realize alternatives you could be doing.

23 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. 24 So how come that doesnt work for division? (Why isnt 300 50 = 600 25?) It is only then that you realize that there were some glaring omissions in what you had told your

students. 25 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?

26 8x6 xxxxxx xxxxxx xxxxxx xxxxxx

xxxxxx xxxxxx xxxxxx xxxxxx 27

82 xx xx xx xx 44 xxxx

Not enough stuff and too many sharers 28 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. 29 Ratio table 3.2 80 32 800

8 200 4 100 30

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 its 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. 31 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.

32 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 . 33

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. 34 Step 6: Teaching through problem solving

35 What does it mean? You dont teach a whole bunch of techniques so that kids can solve problems of a certain type. (They arent problems if the kid knows the type they are anyway.)

36 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. 37

What does it look like? In Grade 4, I might ask my students something like: I used 43 sticks to make triangles, squares and hexagons. What did I make? 38

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 39

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? 40

What does it look like? In Grade 6, I might ask my students something like: A parallelogram has an area of 32 cm2. What might its dimensions be? 41 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? 42 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. 43 What does it look like? In Grade 9, I might ask my students something

like: Without using a protractor, how do you know that these line segments on a geoboard are perpendicular? 44 What does it look like? Look at the rises and runs. 45

Step 7: Planning ahead what to ask and, as much as possible, how to respond, but with a willingness to change. 46 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. 47 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? 48 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 49 So what might you ask.. Describe a situation where you might divide 50 by

4. Now describe a situation where you are forming groups but you would not divide. 50 Or Jennifer said that you cant divide 50 by 4 since if

you try to make equal groups it doesnt work. What would you say to Jennifer? 51 Or Tell how dividing is related to multiplying. 52

Or Alicia says that 45 9 9 9 9 9 = 0 describes a division. Do you agree? Explain. 53 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? 54 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. 55

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

56 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? 57

Step 8: Recognizing that different students need different treatment. 58 Recognizing differences recognizing student talents and interests. 59

Recognizing differences You could provide choice in consolidation (or practice) or choice in instruction. 60 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.. 61 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. 62

Multiplication Task 1: Task 2: A hotel has 24 A hotel has 24

windows on a floor. There are 19 floors. How many windows are there? windows on a floor. There are 9 floors. How many windows are there?

63 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? 64

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.

65 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.

66 Step 9: Responding to individual students. 67 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. 68 Giving feedback The best feedback you can give is personal; it

picks up specifically on what the student has said. 69 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?

70 Giving feedback Suppose a Grade 5 student says that 6/4 is not a fraction since fractions are parts of wholes and that isnt. What would you say? Can someone share?

71 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?

72 Step 10: Making what you teach your own. 73 Too many teachers.. tell me that they are asking a question that makes

no sense to them just because its 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 dont see you comfortable, its very unlikely they can be. 74 Step 11: Relaxing

75 Uptight is bad. Too many teachers are obsessed with wording, with following instructions that are peripheral,. 76

For example You ask students to pace off the length of the classroom. One student does the width instead. Who cares? 77 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. 78 Step 12: Staying the course and carrying the message if youre up for it.

79 Persistence Persistence is the key. You have to try. You have to try more than once. 80

Taking initiative You can be the leader as well as a follower and encourage others. 81 So. If you want a checklist, If not, there is a bigger picture here. I actually

think that the three big issues Ive 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. 82

Teaching is constantly staying up to date, conferring and talking over cases, and considering the individual welfare of each of our patients/clients

83 Thank You You can download this presentation on my website: www.onetwoinfinity.ca Look for: West Webinar Your feedback is valuable to us: please click the link in the chat box and complete the electronic survey

84

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