Learning and teaching early math

I was delighted to find a textbook called Learning and Teaching Early Math: The Learning Trajectories Approach at an EarlyON drop-in centre. The Esso Family Math program reminded me to talk to A- about math concepts beyond counting, and it was great to learn about math in early childhood education in even more detail.

Subitizing: This is about instantly recognizing small groups without counting them. The key tip was: “Use small number words in everyday interactions as often as you can.” S straight-line arrangements of homogeneous objects are the easiest, then rectangular, then scattered. Presenting different groupings can help kids learn how to add groups up to get a total.

Counting: When A- counts too quickly, she sometimes misses items or double-counts. I can encourage her to focus on accuracy by saying something like, “Slow down and try very hard to count just right.” Pointing, touching, or moving items can help. This is a good time to introduce board games.

Comparing, ordering, and estimating: Number lines are hard to work with. 10-frames might be a good starting point. Estimating can be helped by subitizing and using benchmarks. Games to play: building stairs that are missing a step, matching place settings, asking “Who is older?,” asking “Is it fair?”

Arithmetic: Predict, then count to check. “Counting up to” can lead to subtraction (5, 6, 7, 8). When A- starts doing math in school, it can be good to help her learn how to use her non-writing hand to count as a way of confirming. The textbook had a good breakdown of different types of problems and their difficulty: change-plus, part-part-whole, change minus; a + ? = b; ? + a = b. Showing dot diagrams can help with subitizing and decomposition. (6 = 0 + 6 = 1 + 5 = …) Break apart to make 10. See which numbers can be shown with the same number of fingers raised on each hand.

Spatial thinking: Feely box? Also, talking about patterns, landmarks. Taking pictures of things and their immediate surroundings, then going on a scavenger hunt. Make my picture. Shadows.

Shape: Don’t forget to show different variants instead of just typical triangles, etc. Identify squares as a special type of rectangle. Talk about attributes (points, sides, …). Show distractors. Secret sorting – guess my rule.

Composition and decomposition of shapes: Pre-composer, piece assembler, picture maker, shape composer, substitution composer, shape composite iterator, shape composer with superordinate units. Block & LEGO building: planned, systematic; verbal scaffolding. Agam program? Pattern block: outlines, vertices, matching sides, internal lines.

Geometric measurement: Standard rules are more interesting and meaningful? Teaching kids to line up endpoints. Cut pieces of string to help with indirect measurement. Subskills: iteration, zero point, alignment. Logo programming can be helpful. Talk about bigger, smaller, longer, shorter. Area is hard; try folding/cutting/moving paper. Talk about capacity/volume, angle, finding similar angles.

Patterns: Not just visual patterns (ABAB) – the search for mathematical regularities and structures. Be careful about using = – don’t use it to list objects (John = 8, Marcie = 9), numbering collections (III = 3), strings of calculation (20 + 30 = 50 + 7 = 57 + …). Provide variety (ex: 8 = 12 – 4). Contrast with > and <. All math is a search for patterns, structure, relationships.

How do you know? is a very powerful question. Ask it to get kids reflecting on how they figure things out. Challenging tasks result in better long-term memory. Promote a growth mindset instead of a fixed one. Well-designed computer manipulatives can be worthwhile.


  • Talk about bigger numbers (4-10) for sets of present, visible objects
  • Discuss math while reading
  • Keep fathers involved
  • Talk about geometry and spatial relationships
  • Do puzzles, play math games
  • Cook with kids
  • Have high to very high expectations
  • Don’t worry about base 10 blocks, etc.

The book mentioned that many early educators tend to spend just a little time on math, and may even have a bit of math anxiety themselves. I like math, so it might be good if I handle sneaking in more of it during play time. Based on this, I think I’m going to try:

  • Bringing a die around so that we can use it for subitizing practice and impromptu dice/board games
  • Looking for developmentally-appropriate spatial puzzles at the drop-in centres
  • Using more comparative language (bigger/smaller) when we’re playing with playdough
  • Making up patterns and talking about patterns I see around me (“I noticed that…” “What do you think the next one will be?”)
  • Taking advantage of A-‘s interest in fairness, comparison, etc.