Where Is My Child on the Counting Learning Progression?
When I first began teaching, I spent hours creating lessons designed to perfectly teach the day’s objective. Without fail, over and over, a large portion of my students still struggled to grasp the content. I couldn’t understand why the lesson was working perfectly for some of my students and falling short for others. They were all trying equally hard, so what was going on?
What was going on was that I was using a one-size-fits all approach to my instruction. I was teaching all 25 students the exact same lesson in the exact same way. I quickly learned that mathematical concepts develop along a continuum. If some of my students were missing key pieces of relevant knowledge from early grades, they wouldn’t be ready for the content I was delivering.
To address this, I began researching the relevant content from earlier grades and ensuring that I was targeting multiple levels of these learning progressions in my lessons—thus more effectively reaching the various needs of my students.
As a parent, research-based learning progressions provide a window into how my children’s thinking has already developed and where they’ll go next. It allows me to make sure I am providing the appropriate supports as they learn.
The learning progression for counting found in John Van de Walle’s book Teaching Student-Centered Mathematics is a great learning trajectory for parents because it clearly maps out how children’s knowledge of counting progresses as they learn.
Counting Learning Progression:
Precounter: Here the child has no verbal counting ability. A young child looking at three balls will answer “ball” when asked how many. The child does not associate a number word with a quantity.
Reciter: This child verbally counts using number words, but not always in the right order. Sometimes they say more numbers than they have objects to count, skip objects, or repeat the same number.
Corresponder: A child at this level can make a one-to-one correspondence with numbers and objects, stating one number per object. If asked “How many?” at the end of the count, they may have to recount to answer.
Counter: This student can accurately count objects in an organized display (in a line, for example) and can answer “How many?” accurately by giving the last number counted (this is called cardinality). They may be able to write the matching numeral and may be able to say the number just after or before a number by counting up from 1.
Producer: A student at this level can count out objects to a certain number. If asked to give you five blocks, they can show you that amount.
Counter and Producer: A child who combines the two previous levels can count out objects, tell how many are in a group, remember which objects are counted and which are not, and respond to random arrangements. They begin to separate tens and ones, like 23 is 20 and 3 more.
Counter Backwards: A child at this level can count backward by removing objects one by one or just verbally as in a “countdown.”
Counter from Any Number: This child can count up starting from numbers other than one. They are able to immediately state the number before and after a given number.
Skip Counter: Here the child can skip-count with understanding by a group of a given number—tens, fives, twos, etc.
Progression quoted directly from source text
Source: Counting trajectory is found on page 114 of John Van de Walle’s Teaching Student-Centered Mathematics, vol 1. Van de Walle’s counting trajectory is based on the research of Clements and Samara in their 2014 publication: Learning and teaching early math: The learning trajectories approach