Friday, March 11, 2016

Family Math

I promised that I would give you a glimpse of what family math looks like around here.  I know folks are wondering "Is this method sustainable?  Will you really be able to cover all of the things you need to cover for a range of different ages and abilities of children in a whole-group setting?"  So here is the answer: "I don't know!"

I really haven't done this long enough to know if there are cases where this model will prove more challenging.  But I have definitely seen many beautiful aspects of this approach.  Let me share with you a few anecdotes and then a few observations.


  • We did a review of the concept of place value using play money - hundreds, tens and ones - over the course of a few days.  The children practiced exchanging between hundreds and tens and between tens and ones.  We experimented with what happens when you add, subtract or divide a three digit number, and which order (hundreds, tens, ones vs. ones, tens, hundreds) makes the most sense for each process.  My ten, nine, eight and six year olds were all in participation.  The older three have definitely mastered the concepts of regrouping and their application to the three operations we examined.  The six year old showed a clear understanding of place value, but not as great a fluency with "regrouping" and didn't apply it to the operations.  That's OK.  She's learned some and become familiar with the concept.  She'll have plenty more exposure to it in future.
  • I realized that, though my six-year-old can tell time fairly well, she was having trouble taking into consideration the movement of the hour hand as the minute hand makes its way around the entire clock face.  I planned to take a moment during math time to talk about this with her, but since the older children were sitting nearby, the conversation turned into a discussion of percentages and proportions with the older children when one of them said,  "So, if the minute hand has gone 25% of the way around the clock, then the hour hand should have also moved 25% of the way between two numbers ..."  This reminded us why it is that we refer to times as "a quarter past" or "a quarter til" and we also talked about the reason (historically) that the minute hand is larger than the hour hand.  We also discussed that situations like this illustrate the usefulness of percentages, because they allow us to make comparisons between the parts of two different-sized things.
  • We are now studying Geometry.  Sometimes we read one of the Sir Cumference books.  All of the children (except the baby who still takes a morning nap) sit and listen as I read.  We have also done some hands-on activities.  The oldest four participate and the younger two (ages 4 and 3) go back and forth between being engaged and doing their own thing nearby.  For example, as we explored perimeter and area, we used Blokus pieces to make rectangles of different sizes and to calculate the perimeter and area in the pretend units of a Blokus (B) and a square Blokus (B2).

  • In pretty much every other subject, my approach has been to teach the older kids and let the younger ones listen in and glean whatever they are able.  Why not math?  It can't hurt, right?
  • If math is a conversation, then each person can engage at the level to which he is able.  Older children can bring more complex ideas to the table and younger ones can pick up on the simpler aspects of what we're learning.  Math really isn't as compartmentalized as we tend to think - there is so much overlap and interconnectedness.  And making connections between previous learning and current learning is a huge piece of what education is all about.
  • Math as a conversation easily overflows to other times of the day (like lunchtime) because we've all been a part of the discussion, not just Mama and one kid.
  • When other children are getting a concept and one is not ... Do I stay on that topic and approach it from a different angle to see if I can make it clear?  Do I determine that that one child just isn't developmentally ready, and move on, figuring that she'll grasp it later on another pass when she is ready?  Do I find a chunk of time to work individually with her on that topic?  From where I sit right now, it seems like any of the above would be a viable option.  I know how to track what has been mastered and what hasn't.  So if not everyone is on top of a concept, it doesn't have to stop us from moving forward and doing the next thing as a group.
Have you ever explored math in a multi-age group?  What worked for you?  What did you like or dislike about that approach?  In reading over the descriptions above, what questions come to mind?  What is concerning about that approach?  What is attractive about it?  I'd love to hear your thoughts!

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