Developing Mathematical Thinking Part 3

This week I presented a training to a group of home based child care providers about developmentally appropriate learning activities for children.  One of the areas we covered was mathematical learning, which you can tell is near and dear to my heart, as this is the third post about it on my blog!  You can see the other posts about developing mathematical thinking here and here.

So what kind of skills are appropriate to teach to young children?  What do they need to know?  Here in Texas we have Texas Essential Knowledge and Skills (TEKS) to guide us.  Depending upon where you live, your state or country may have slightly different guidelines, but here is a link that will let you see the Texas guidelines for infants, toddlers and three year olds, as well as those for prekindergarten through 12th grade. 

Basic skills for preschooler and kindergarteners include counting whole numbers, using patterns, sorting, shape recognition, measurement (longer/shorter, bigger/smaller), making and using graphs, and problem solving. 

Here are some of the ideas and materials that I shared.  There are so many other wonderful materials and ideas available, I strongly recommend Pinterest.com as a great source of ideas, and some of these ideas are ones I have borrowed from other teachers over the years.  Thank you to all the fantastic teachers who generously share their ideas, so we can all benefit from them!

Materials for sorting.  Many things can be sorted more than one way.  I've bought my materials from a lot of different places, and for a lot of different price ranges. 

Here are two examples of super inexpensive sorting materials: erasors, and baby shower decorations from the dollar store.  Note the sorting tray - it's a reused cheese tray.  The erasors are stored in a plastic box that originally came full of rice, and the baby items container came with cookies in it.

Don't forget natural materials!  Do you have oak trees?  Pattern with acorns and leaves.  Live some place stony?  Line rocks up by size.  How about feathers, sticks, pinecones... even seeds from your fruit and veggies.  Look around you, the possibilities are endless, and often free.

Think creatively!  What is my sorting rule for these transportation beads?  Try starting a sort, and let your children try to guess your sorting rule.  They can add one item at a time, and you can tell them if it follows the rule, or not... when they understand the game, let them do the sort, and you take turns guessing their rule. 

This is another inexpensive item, beads.  I've made up patterns with the beads, on fishing line - because that is easy for the kiddos to thread through the beads.  To make this a reusable patterning game, I looped the line several times through the last bead.  The children can add more beads to continue the pattern, and then pull them back off when done, but the base of the pattern stays in place.

Another simple material that you may already have on hand is buttons.  Children love to sort and play with small items!  I went through my button collection and created baggies that work for Venn Diagrams, keeping the buttons and labels in small zipper baggies - so they are easy to change out.
**** Please supervise all children when they are using materials that could be choking hazards! ****

If you can't afford to buy fancy sorting trays, or maybe you just don't have the space to store them, why not create your own on poster board?  I made the giant Venn Diagram poster by tracing a large plastic lid, and the graphing grids with a yard stick and marker.  Super easy!

Graphing is another easy and quick math activity that the children love.  They have to identify their name to put it on the graph, and working with all the names of their classmates helps them learn to read them all.  I made up some generic titles for my graphs, and reuse them with different column headings.  We also reuse the children's name cards, so there is very little to prepare new each time.  Here are some ideas for open ended questions that you can easily change out, and that you could fit with whatever theme you are teaching:

- Which do you prefer _____ or _____ or _____?
- Do you like _____?
- Does your name have _____? (letter __ or  # of letters)
- What is your favorite _____?
- Do you have a ____? (pet / sister / swing set / ___)
- Are you wearing _____? (buttons / zippers / long sleeves / yellow / hair bows / etc.)
- Do you like to _____? (swim / draw / dance / clean up / etc.)
- Are you taller than _____?
- What color are your _____? (eyes / shoes / hair / teddy bear etc.)
- Would you like to _____? (hold a big bug?  climb a mountain?  ride a zebra? etc. )
- Is your arm/leg/shoe longer/shorter/wider than a ______?
- Roll a dice.  What number did you roll?

Don't forget games and puzzles!  Rolling dice, moving the correct number of spaces, taking turns, matching - these all help develop important skills, and the children think they are just "playing". 

Many people who take care of young children have babies as well as toddlers and preschoolers, so they need to offer math learning activities that meet the needs of the older children whilst also being baby safe.  Here are a few possibilities: sort snap lock beads by color or shape, match socks, match clothes pins to a cardboard game board.

Magnetic toys are fun to play with on inexpensive baking trays... dollar store again!

Your materials do not have to be limited to a single use!  These transportation counters are easy to sort by color and shape, but I wanted to incorporate measurement with non-standard units too, so I created measurement mats.  On each mat, I show which piece to measure with, and drew lines equal in length to various numbers of the sorting item.  The children line up the pieces, count them, and then put it away, leaving the items and mats ready for the next child.

Here are some more inexpensive items: buttons, beads, and gems from the dollar store.  There are many ways to sort or use each one.  If you run out of ideas, try challenging the children to help you come up with new ways to use them! 

Remember, mathematics is fun!  I hope you enjoy these, and many other activities with your children.