A presentation I made to show how I support students in writing in math.

1. Problems of the Week

2. For many of
us, math was just
another course we
book with a huge
book to lug
around.

3. Text
But in fact math
is an amazing
collection of human
achievement

4. So, is math
one or the
other, or
something else
completely?
Math = Science ?
or
Math = Religion ?

5. For you personally, Math is primarily
an art,
a language,
a science,
a tool,
a way of life,
a distant memory,
a nightmare,
or something else entirely?

6. How about
this idea?
Math is an exquisite
expression of
human culture.

7. Who is glenn kenyon in 2009?

8. Who is glenn kenyon in 2009?
48% of my life as a teacher

9. Who is glenn kenyon in 2009?
48% of my life as a teacher
about 4,100 days with students
or
about 25,000 hours

10. Who is glenn kenyon in 2009?
48% of my life as a teacher
about 4,100 days with students
or
about 25,000 hours
bilingual teacher for 82%

11. Who is glenn kenyon in 2009?
48% of my life as a teacher
Math specialist for 18% about 4,100 days with students
or
of professional life
about 25,000 hours
bilingual teacher for 82%

12. Who is glenn kenyon in 2009?
48% of my life as a teacher
Math specialist for 18% about 4,100 days with students
or
of professional life
about 25,000 hours
bilingual teacher for 82%
28% in kinder/first,

13. Who is glenn kenyon in 2009?
48% of my life as a teacher
Math specialist for 18% about 4,100 days with students
or
of professional life
about 25,000 hours
bilingual teacher for 82%
28% in kinder/first,
54% in 4/5

14. Who is glenn kenyon in 2009?
48% of my life as a teacher
Math specialist for 18% about 4,100 days with students
or
of professional life
about 25,000 hours
bilingual teacher for 82%
28% in kinder/first,
54% in 4/5
18% in Middle School

15. Who is glenn kenyon in 2009?
48% of my life as a teacher
Math specialist for 18% about 4,100 days with students
or
of professional life
about 25,000 hours
bilingual teacher for 82%
28% in kinder/first,
54% in 4/5
18% in Middle School
I’ve worked with a little over
1,800 students and their families

16. Who is glenn kenyon in 2009?
48% of my life as a teacher
Math specialist for 18% about 4,100 days with students
or
of professional life
about 25,000 hours
bilingual teacher for 82%
28% in kinder/first,
54% in 4/5
18% in Middle School
I’ve worked with a little over
1,800 students and their families
The San Francisco School Teacher. 50% students of color.
50% from public elementary schools. 40% on scholarships.

17. I think the camel might be
a good symbol for me as a
teacher. Methodical, self sufficient,
agile over difficult terrain, good
over the long haul.
I trace my own thoughts about
how to teach systematic problem
solving to my students to this
camel. This represents a problem
I encountered in my homework
while studying for my Masters in
Math Education. The each week
we were assigned problems to
solve and write about. They were
called “Problems of the Week”.
This process had a profound
impact on my practice because I
encountered not only fascinating
problems, but also was required
to write about it and share with
my classmates.

18. Balanced Math Program!
Problem!
Solving!
Math encompasses all these and
this is the sweet spot. Technology!
Skills! Concepts!

19. At first, I just
set my students on a
Camila Camel problem with little
guidelines. it. There is a
freshness when you have to
create your own structures, but
Camila Camel's harvest, worth its weight there is also a certain fatigue. I
also feel it my role to be more a
in gold, consists of 3000 bananas. more explicit model for my
students. So here is how I
The market place where the stash can be simplified the problem
solving strategy.
cashed in is 1000 miles away.
However, Camila must walk to the market,
and can only carry up to 1000 bananas at
a time.
Furthermore, being a camel, Camila eats
one banana during each and every mile
she walks (so Camila can never walk
anywhere without bananas).
How many bananas can Camila get to the
market?

20. Wait,
something is
missing!
I noticed that my 4th and 5th
graders really struggled with
writing about their thinking in
math. They could write the
answer in a sentence, and the
could tell me a little about how
they solved it, but it was not a
very satisfying explanation. Other
students and their families really
did not know how to approach
problems without clear algorithms
and were clearly stymied.
I wanted to persist with these
more complex problems, but I
also saw that just as I was doing
in language arts or social studies,
I needed to provide my students
with some schemas or outlines to
help them organize their
thoughts.

21. Problem of the Week Essay Organizer
1.
So I
2.
created a
Introduction
quadrant Strategies/Procedure
outline for (reword the problem)
them to
(how to solve this problem)
collect
their
thoughts in
essay form. Relevant Information
Dead ends?
4.
3.
Solution (s) Reflection
(What was difficult/surprising)

22. The
problem
solving
structure
and essay
come from
this
amazing
book.
George Polya
Stanford
1944

23. Original Version
The
problem 1944
solving
structure
and essay
come from
this
amazing
book.
George Polya
Stanford
1944

24. 4 Principles of Problem Solving
1st Principle
Understand the Problem
2nd Principle
Devise a Plan
3rd Principle
Carry Out the Plan
4th Principle
Review / Extend

25. 4 Principles of Problem Solving
1st Principle
Understand the Problem
A problem well-stated is a problem half-solved.
-John Dewey

26. 4 Principles of Problem Solving
2nd Principle
Devise a Plan
When you’re prepared, you are more confident.
When you have a strategy, you’re more comfortable.

27. 4 Principles of Problem Solving
3rd Principle
Carry Out the Plan
I think and think for months and years.
99 times, the conclusion is false.
The hundredth time, I am right.
-Albert Einstein

28. 4 Principles of Problem Solving
4th Principle
Review / Extend
Knowledge of self is the mother of all knowledge
- Kahlil Gibran

29. http://mathforum.org/

30. Ken Johnson
Ted Herr
Judy Kysh

31. With your partner, revisit the Camel Problem
Focus on Intro, Plan and Reflection
Camila Camel's harvest, worth its weight
in gold, consists of 3000 bananas.
The market place where the stash can be
cashed in is 1000 miles away.
However, Camila must walk to the market,
and can only carry up to 1000 bananas at
a time.
Furthermore, being a camel, Camila eats
one banana during each and every mile
she walks (so Camila can never walk
anywhere without bananas).
How many bananas can Camila get to the
market?

32. Introduce

33. Introduce

34. Introduce Plan
Here is a partial
Guess & Check
Orderly Lists
Solve an equation
Draw a diagram
Solve a simpler
problem
Eliminate

35. Reflect
What, if anything, did this problem teach you?
• What was interesting/intriguing about
this problem?
• How did this problem challenge you?
• How did you manage your time?
• What might you do differently next time?

36. Solve

37. Solve
This problem has many good answers
(between 400 and 500 bananas)
And one best answer
(533 1/3 bananas)

38. Student Work

39. comment:
comment:
comment:
comment:

40. The title of this P.O.W. is Verdania: A Math Oddesy, Chapter 3: Sailing. This P.O.W. is
SAMPLE A
about two radar stations that both send out a signal at the same time and both hit a
target. One station is 90 miles away from the target and the other station is 75 miles
away from the target, forming a triangle. I will assume that both stations are on land. The
problem is to find out where the target is. The key math concepts in this P.O.W. are the
Pythagorean theorem and logic.
The first step I took towards solving this P.O.W. was, I read the problem over about 4
times and still didn’t understand it until I realized that it gave me 2 sides of a possible
triangle. One side was 90 miles and the other is 75 miles so, 90 squared is 8,100 and 75
squared is 5,625. 8,100+5,625 is 13,725 and the approximate square root of 13,725 is
117.15 this being how far the two stations are apart. This strategy only works if this is a
right triangle that I just created. The next thing I did was, I divided the triangle into two
separate triangles by drawing a line from where the 90 degree angle is to about half-way
through the hypotenuse. One triangles side lengths were now, 90, 58.6 (half of 117.15),
and ?. The other triangles side lengths were now, 75, 58.6 and ?. To find the ? of the first
triangle: 90 squared (8,100) minus 58 squared (3,431) is 4,669. The square root of 4,669
is 68.33, this being how many miles away from shore the target is.
My solution to this problem is that the target is 68.33 miles from shore if the two
stations are 117.15 miles apart. I know that there are many, many other answers
depending on how far apart the two stations are and mine is just one. I think my answer
is correct because I revised it everyday for 3 days and I checked it over with my dad, it
also makes sense.
I found this P.O.W. relatively difficult because I have never been in the situation where I
not only need to find the answer, I need to find the problem. Next time I will manage my
time better, and get the essay done sooner. I ranin to a problem while I was writing the
essay and that was that I didn’t really understand the question, next time, I’ll make sure
that I understand the question before trying to answer it.

42. Read and evaluate the
Sample Essays B and C
When finished, compare your evaluations
of one of the essays with your partner
Were there major discrepancies in your
evaluations? Why?

43. Issues I consider with student writing:

44. Issues I consider with student writing:
• Student time management.

45. Issues I consider with student writing:
• Student time management.
• Student struggles with saliency.

46. Issues I consider with student writing:
• Student time management.
• Student struggles with saliency.
• Student dependence on peers’ work.

47. Issues I consider with student writing:
• Student time management.
• Student struggles with saliency.
• Student dependence on peers’ work.
• Resistance to describe failed attempts.

48. Issues I consider with student writing:
• Student time management.
• Student struggles with saliency.
• Student dependence on peers’ work.
• Resistance to describe failed attempts.
• Issues with logic:
“my solution is correct because I checked with
“______” and they got the same answer”.

49. Issues I consider with student writing:
• Student time management.
• Student struggles with saliency.
• Student dependence on peers’ work.
• Resistance to describe failed attempts.
• Issues with logic:
“my solution is correct because I checked with
“______” and they got the same answer”.
• Superficial reflections: “manage time better”.

50. Issues I consider with my teaching practice:

51. Issues I consider with my teaching practice:
• What are reasonable expectations for written work?

52. Issues I consider with my teaching practice:
• What are reasonable expectations for written work?
• How can I use rubric for more POSITIVE feedback?

53. Issues I consider with my teaching practice:
• What are reasonable expectations for written work?
• How can I use rubric for more POSITIVE feedback?
• How can I provoke more sincere student reflection?

54. Issues I consider with my teaching practice:
• What are reasonable expectations for written work?
• How can I use rubric for more POSITIVE feedback?
• How can I provoke more sincere student reflection?
• Does the outline allow sufficient creative thought?

55. Issues I consider with my teaching practice:
• What are reasonable expectations for written work?
• How can I use rubric for more POSITIVE feedback?
• How can I provoke more sincere student reflection?
• Does the outline allow sufficient creative thought?
• How can I promote process over product more effectively?

56. Issues I consider with my teaching practice:
• What are reasonable expectations for written work?
• How can I use rubric for more POSITIVE feedback?
• How can I provoke more sincere student reflection?
• Does the outline allow sufficient creative thought?
• How can I promote process over product more effectively?
Do these questions resonate in your own practice?
How do you deal with them?

57. How this activity can be adapted to other
classroom settings:
* Being succinct in restating the introduction. Language teacher could give math problems to
practice summarizing.
* In prompt breakdown: students need the same skills in essay prompt understanding.
*Use writing to solidify knowledge of content, metacognitive, sometimes we forget to do this in
English class. Reflection on how it went.
* Unpack the use of quotes in writing: “I picked it because it really shows what I am thinking”
Unpacking faulty logic.
* Helping kids not to compartmentalize: use math problems in English class. Writing a poem
about math.
*What do students value, how they value it, what is the most important thing to them: is the
camel problem about enjoying the journey or getting the most $$$ or maybe hoard them.
* Give ELL students comfortable in math, perhaps this would give them a window into
expanding their language use (especially in elementary school)
* Notion of critical inquiry: using students’ abilities of making meaning of the problem of their
own. Writing is often about document, vs generating ideas, transformative. How human beings
in all civilizations use math to make sense of things. Examination of Silk Road.
*Make a plan, reflect on problem on words, or crosswords.
* Talking with partners makes us smarter. Together