Problem Emergence, Problem Solving, and Mathematics in Family Life

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Problem Emergence, Problem Solving, and
Mathematics in Family Life

• Shelley Goldman, Lee Martin, Roy Pea, Angela
  Booker, Kristen Pilner Blair
• Stanford University

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Outline

• Overview
• Families in our sample
• Analysis
• General findings
• Example cases
• Games
• Home improvement
• Conclusions

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Goals

• Identify contexts, activities, and resources
  involved in learning and using mathematics in
  families.
• Investigate the family as a cultural context for
  learning and doing math.
• Identify and design for points of synergy between
  math in the home and math and school.

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Method

• Two-hour interview in the familys home
• Questions focus on everyday activities
• Designed to solicit narratives
• e.g., Have you decorated or made any
  improvements to the inside or outside of your
  home? What are they? Can you describe what you
  did? When you do it? A favorite story about it?
  Who do you do it with? Where?
• In addition, two standard activities
• Math in a minute stories
• Cell phone plan selection task

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Families in our sample

• Every family has a middle-school child
• Family is defined by the participants
• 19 families interviewed so far
• 67 individual participants

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Analysis
40 hours of video
Content-log
Develop codes

• Problem solving
• Emotions
• Division of labor
• Home-school connections

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Analysis tools
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Analysis
40 hours of video
Content-log
Develop codes
Enter into Problem Database

• Problem solving
• Emotions
• Division of labor
• Home-school connections

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Problem Database

• All problem solving events involving math entered
  into a database
• 264 problem events in our database
• Further coded for
• Activity category
• Participants
• Mediating tools
• Type of math involved

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Analysis tools
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General Findings

• Mathematical problem solving in families is
  different than problem solving at school
• Math in families is organized by problems, not
  the other way around
• Great variety of problem solving and types of
  math
• Generation of an inventory of math found in
  various activities

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Activity x Math Inventory
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(No Transcript)
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Activity Domain 1 Games

• 17 problems coded in Games category
• Type of math
• Arithmetic (10)
• Probability (6) highest of all activities
• Logic (3) highest of all activities
• 9 of 19 families have at least one instance

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Games Example 1

• Family AP Mother, Father, 7th grade girl, and
  3rd grade girl
• Younger Daughter Theres a lot of games on
  NeoPets so, when you play them, you, youll, what
  you, if you press send score, you-, how much,
  points you got it will go to your, um, bank,
  well, it will go to the top so you can spend it,
  but if you dont, you go to shop, and you go to
  the bank, and you deposit it.
• Older Daughter And, um, the more money you have,
  theres like levels to go up, and, if you have a
  lot of money in your account, then you can earn
  more interest, but if you have like, five
  NeoPoints, you probably get like one interest a
  day.

Mother So it kind of shows them the deposit,
shows them the interest, and it shows them that,
you know, in order to take care of something they
will have to pay some money to feed them.
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Games Example 2

• Family AF Mother, Father, 6th grade girl
• Daughter When you play a game, you can only send
  three scores in, like, send three scores in to
  get NeoPoints per day, otherwise you could just
  keep playing the same game So, um, you have to
  figure out which scores to send, and you have to
  kind of figure out, well, if this score is a
  hundred, and the next score is go, is more
  likely higher or lower, or whatever, so you need
  to know which score to send in.
• Father Oh, yeah.
• Interviewer And how do, how do you know

Daughter Well I usually think, like, whats the
average sort of score, that I get. Say it was
thirty or something, Id think, if I got, five, I
probably wouldnt send it. If I got over fifty
Id send it.
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Games in Two Families

• Example 1 (Family AP)
• Daughters explanation involves the concept of
  interest rate
• Both parents are bankers
• The girls each have a toy ATM piggy bank
• Their mother lets them help her write checks and
  work the real ATM
• Example 2 (Family AF)
• Daughters explanation involves the concept of an
  average value within a distribution of likely
  values
• Father and daughter have worked on making games
  before, and have discussed chance and expected
  value

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Games in Two Families

• Games provide a context for engaging with
  mathematical content within the family
• On the surface, the girls in the two families
  engage in the same activity
• The NeoPets game means something very different
  to the two families
• Goal of the activity is flexible, as are the
  means of achieving it
• The math involved in playing the game and the way
  that the game gets talked about in the family are
  consistent with broader trends seen in the
  families

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Activity Domain 2 Home Improvement

• 38 problems coded in Home Improvement category
• Type of math
• Measurement (34) highest of all activities
• Arithmetic (16)
• Geometry (10) highest of all activities
• 11 of 19 families have at least one instance

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Home Improvement Case 1

• Family AK Mother, Older Daughter, Younger
  Daughter (8th grade)
• Interviewer Did you use any tools, visualize to
  make these decisions? How did you actually do
  it?
• Older Daughter We were trying to figure out. We
  had this space between the tub and the toilet and
  how much space do you need for your knees. So we
  would just take the tape measureso we wanted
  particularly the bench by the dining table. So
  we literally took the tape measure and sat down
  and measured our knees for the bathroom.

What are our options. You draw those on paper
then you them you actually show up and you sit on
the toilet. How many inches do I need if the tub
comes to here will I be able to sit down. We
will, but if we sell the house to someone else,
they wont. So it was kind of a back and forth.
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Home Improvement Case 1

• Interviewer So you used your bodytape measure
  and plans drawn scale or free form?
• Older Daughter I did both I actually got on my
  computer and found some grid to work with to get
  more of the proportions. I mostly draw free form
  on paper to give the contractor an idea, OK this
  is what I decided, the tub is going to go here,
  and I draw the inches. But I actually got on my
  computer and found some grid to work with to get
  more of the proportions. I didnt have a ruler in
  my whole room so couldnt even just like measure
  a piece of paper and do it all myself I had to do
  it all online.
• Interviewer How did you find it?
• Older Daughter I googled graph paper.

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Home Improvement Case 2

• Father There was an outhouse in the yard. First
  I planned what I was going to do to make all of
  these three things fit into such a small place.
  And she didnt believe I could do it. She thought
  the only thing Im going to have is a Jacuzzi.
  Then I designed it myself because the architect
  guy, he couldnt design it.
• Mother He had never built a sauna.
• Father See it was a triangle. See that place was
  a triangle. So I made a pentagon steam room.
  Because his room is right there too in the corner
  so I had to give him a concept too.
• Mother What happened, there were two closets,
  Js and Ys closets are together. There were two
  closets and then the wall. So we break the
  closets out so there is a walkthrough hallway
  from inside the house rather than going outside
  the house and coming back from outside
• Interviewer So you knocked out the closets and
• Father Made a hallway.
• I made a pentagon steam room

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(No Transcript)
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Home Improvement in Two Families

• Home improvement provides a context for math
  engagement
• Interplay between precision and general concept
  of a solution
• Visualization important in both problems
• Drawings and gesture
• Math content scale, conversions, applications of
  formulas, measurement, geometry, spatial
  visualization
• Tool use bodies, rulers, scale grids, sketches,
  physical models, formulas
• Solving the problem resulted in high levels of
  satisfaction and pride

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Conclusions About Problem Solving in the Family

• Families learn and do math in the context of a
  variety of activities that are important in their
  lives.
• The math itself is organized by the problems
  people have to solve, not the other way around.
• The problems to be solved are in combination with
  the resources at hand.
• Problem solving is with orientation and reference
  to historical, current and projected trends,
  frames and events
• Math problems at home have different features
  than math problems at school.

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Informal vs. School Problem Solving