MR:PP Workshop #1
Kritzer & Pagliaro
October 10, 2009

 High School: 6th/5th gr.
 Middle School: 4th/3rd gr.
 Elementary School: 2nd/3rd gr.
 Pre-school aged: substantially behind in foundational mathematics concepts
Consistent over the past 30 years !
(Allen, 1995; Ansell & Pagliaro, 2006; Kritzer, 2007; Leybaert & Van Cutsem, 2002; Marschark
& Everhart, 1999; Nunes & Moreno, 1998; Stanwick, Oddy, & Roper, 2005; Traxler, 2000)

 Math skills at the time of school entry are a strong predictor of later achievement
 Family interaction and the home environment are important predictors of later academic success in content areas such as mathematics
(Allen, 1995; Ansell & Pagliaro, 2006; Kritzer, 2007; Leybaert & Van Cutsem, 2002; Marschark
& Everhart, 1999; Nunes & Moreno, 1998; Stanwick, Oddy, & Roper, 2005; Traxler, 2000)

Math Dev.
Language
My child
Stimulus
Mediation

Math Dev.
Language
My child
Stimulus
Mediation

Math Dev.
Language
My child

Math Dev.
Language
My child

• Making information accessible & easy to understand to another individual
• Guidance through questioning
• Modeling how to learn and seek information

• Creating Learning Environments
(Intentionality/Reciprocity)
– Encourage engagement with the environment
• Ex. Initiating communication, responding, focusing attention
• Connecting Learning Environments
(Transcendence/Meaning)
– Make connections; demonstrate curiosity
• Ex. Questioning, explaining, comparing, referring to time
• Creating Lifelong Learners
(Competence/Regulation of Behavior)
– Encourage self-control & self-esteem; reinforce positive learning behaviors; deter impulsivity
• Ex. Planning, praising, prudency
Miles & Huberman, 1994; Feuerstein & Rand,1997

• Maintain visual attention while communicating with your child
• Discuss things in context (e.g., discuss where toys belong as you help your child put them away)
• Take advantage of what your child is doing naturally (e.g., match toys)

High Math Ability Group
While driving to a party.
Child: How far is it?
Mom: About 40 minutes.
Where do they live? Do you remember the town?
Low Math Ability Group
Mom gives child an Ice
Pop.
Mom: The paper from the ice goes in the trash.
Child: (teasing) I’ll put it under the bed.
[no response]

High Math Ability Group
Adult: You don’t eat at
6, that’s late. Get home around 4:30, you eat around 5.
Child: No, yesterday we ate at 6, remember? We had pizza.
Adult: Oh, you’re right, yesterday was different.
Low Math Ability Group
Child tells mom that she wants her Easter candy.
Mom gets two Easter baskets off the entertainment center and gives them to the child.

– Daily routines
– Helping around the house
– Categorization
– Sequencing

• Daily routines
– Wake up on school days
– Brushing teeth
– Bed time
– Meals
– Saturday/Sunday mornings (What’s different?)
• Helping around the house
– Sorting laundry/matching socks
– Putting away groceries, toys

• Categorization/grouping
– Same, different; Intersection – by two aspects
• By physical characteristic
• By function
• By concept
• Explicit or implicit “rule”
• Sequencing/ordering
– First, second, third, next, last
– Smallest to biggest, etc.

• Language helps children to sort. When they have a label for a category they begin to search for things that match that label.
Children learn:
First - names for objects
Then - names for properties (color, etc.)
Then - names for numbers
• Categorization give a reason to count (e.g., count the bears)
(Carey, 1982; Mix, Huttenlocher, Levine, 2002; Mix & Waxman, 1999;
Nelson, 1973; Smith & Sera, 1992)

• Time
• In/out
• Together/with
• Same/different
• Sequence/order
– First, second, third, next, last
• Category/group
• Color
(blue, green, etc.)
• Shape
– Circle, triangle, square, rectangle, rhombus
• Texture
– Smooth, rough, bumpy, soft, hard
• Function
– Play, eat, work, use

• Match perceptually- by characteristics that are observable (e.g., match socks that are the same)
• Group perceptually- by characteristics that are observable (e.g., color, shape)
• Sort by characteristics that are not directly observable (e.g., function, number)
• Consider more than one characteristic simultaneously; and/or consider an implicit relationship
(Adapted from: Phillips & Phillips, 1996)

• Sample activity: Matching
• When?
– During play, household chores
• What do I need?
– Socks, mittens, any group of items to be matched (1 to 1; or 1 to many)
• How? What do I do?
– Give child group of items to be matched
– Say: find the socks that are the same. Put them together.
– Say: here are all of your action figures, what else goes in this group?

• Sample Activity: Is it or isn’t it?*
– When: During play, cleaning up, etc.
– What do I need: A junk drawer, toy box, etc.
– How? What do I do?
• Put all things on floor or table.
• Decide on observable characteristics to sort by (Ex: soft, hard, blue, has wheels, etc.)
– Ask child: Can you find something soft? Is there anything here that has wheels?
– Ask child: Find EVERYTHING soft-
• Discuss each item child selects, sort and re-sort
• Decide on non-observable characteristics to sort by (Ex: everything that mommy uses, find everything used for cooking, etc.)

• Sample Activity: Junk Drawer Jumbalya*
– When: During play, while cleaning up
– What do I need: 10-20 things from toy box or junk drawer
– How? What do I do?
• SHARED CHARACTERISTIC
– Say: That was just sorted as “red” – now it is in the “soft” pile- can
something be red and soft? OR
• ABSTRACT AND IMPLICIT
– Say: I’m looking at all of these things to see if I can find two that go together
– Separate items that go together. Say: Why do these things go
together? [accept all reasonable answers]
– If child can’t come up with it, add another member to your group.
Say: This belongs in this group too.
– If child doesn’t know- tell him/her. Together, find more things that fit that group- Think “out loud” as you sort
– Gradually move on to unobservable characteristics

• Laundry
– Matching socks- Say: Find all of the socks that go together.
– Sorting loads- Choose characteristic of laundry load (ex: darks). Say: We need to wash all of the dark things- which things are dark in color?
– Sorting by person- Say: We need to put the clothes away.
Find all of mommy’s things and put them together. Find all of daddy’s things, put them together, etc.
– Sorting by location- Choose a non-observable, implicit (“in my head”) characteristic to sort by-(ex: items that go in a specific drawer). Say: I put all of these things together- do you know why? What else goes in this group?

• Grocery shopping*
– Decide on characteristic to sort by (ex: frozen, canned goods, etc.) Say: Find everything that goes in the freezer.
Put it on the table over here.
– Decide on non-observable characteristic to sort by. Say:
Find mommy’s favorite foods; find YOUR favorite foods.
– Decide on non-observable, implicit characteristic to sort by
(ex: items that belong on a certain shelf). Say: Here are two things that go together. Can you find anything else that goes in this group?

• Sequencing is related to ordering or seriating
– More difficult than comparing- several decisions must be made (e.g., to sort by length the “middle” of 3 items must be bigger than one and smaller than the other- child must understand that an item can be “bigger” and “smaller” simultaneously).-
– In terms of sequence- an event happens before one step and after another- all abstract terms
• Trajectory
– Things placed in random order
– Use of trial and error
– Systematic ordering
(Copeland, 1984; Sperry-Smith, 2006)

• Watch for opportunities when the child lines things up or is playing with items that can be aligned- “Let’s put these ___ in order from smallest to biggest. This ___ is smallest so it’s first, this ___ is bigger, so it goes next, this ___is the biggest. It goes last.”


Emphasize the importance of order. For example, “When you brush your teeth the first thing you do is ____ next you ____”
– emphasize the importance of order- “Can you put your toothbrush in your mouth BEFORE you put on the toothpaste?
No…”
Talk out sequence- Think aloud and involve your child in the process- For example, when heating up a can of soup- “What should I do first? I need to open the can…”

• Identify daily routines in your household
– Take pictures of your child engaging in each step of a routine
- post as a visual reminder and aid for discussion
• Post a weekly schedule in an accessible location
(e.g., on the refrigerator)- talk about what you are doing “today” “tomorrow” what you did
“yesterday”
• Use sequencing language to discussing what is done during routines

• Sample activity: Shoes in a Row*
– When?
• Play
– What do I need?
• shoes
– How? What do I do?
• Gather shoes from family members
• Say: “look at these shoes! What a mess! I am going to fix them.”
• As you sort the shoes, talk about what you are doing: “I’m putting
Daddy’s shoe with Daddy’s other shoe.”
• Involve your child. Comment on how s/he arranges the shoes. For example, “You put Daddy’s shoe next to mommy’s shoe, etc.)
• Leave the shoes as your child arranged them. Have him/her explain the arrangement to another person.

• Barron, M. (1995). Ready, Set, Count, 60 playful math activities for you and your child
to share. John Wiley & Sons: New York.

• Videotapes
– You make 8 videotapes
• 2 videos of you and your child cooking/meal time;
• 2 videos of you and your child at bedtime;
• 1 video of you and your child doing the categorization/sequencing activity;
• 1 video of you and your child taking a trip (to the store or to a friend’s house, etc.);
• 1 video of you and your child at a cultural event (Deaf event, birthday party, etc.);
• 1 video of you and your child doing something else – your choice (reading a story, gardening, bath time, etc.).

• Activity

• Laundry
– Matching socks- Say: Find all of the socks that go together.
– Sorting loads- Choose characteristic of laundry load (ex: darks). Say: We need to wash all of the dark things- which things are dark in color?
– Sorting by person- Say: We need to put the clothes away.
Find all of mommy’s things and put them together. Find all of daddy’s things, put them together, etc.
– Sorting by location- Choose a non-observable, implicit (“in my head”) characteristic to sort by-(ex: items that go in a specific drawer). Say: I put all of these things together- do you know why? What else goes in this group?

• Grocery shopping *
– Decide on characteristic to sort by (ex: frozen, canned goods, etc.) Say: Find everything that goes in the freezer.
Put it on the table over here.
– Decide on non-observable characteristic to sort by. Say:
Find mommy’s favorite foods; find YOUR favorite foods.
– Decide on non-observable, implicit characteristic to sort by
(ex: items that belong on a certain shelf). Say: Here are two things that go together. Can you find anything else that goes in this group?

• Daily Log/Reflection
– On wiki page, you write about what your child did that day that you consider to be math or related to math
– You comment on how your child is developing his/her math skills – the progress/advances that you notice
• Wiki Discussions
– On wiki page, you write about the success and challenges that you experience as you try to apply what you learned in the workshop.
– You share ideas with other parents and problem solve
– You ask questions and get advice from other parents and staff
– You get support between workshops

• When: November 21 st
• Time: 9:30-3:30
• Where: KSD