Learn as you go

"A curriculum written by a teacher who has seen these moments hundreds of times — and built the sequence to stop them from becoming the next thing a student gets wrong."

There is a particular kind of knowledge that early years maths teaching demands, and it isn't found in a syllabus document.

A Foundation student counts a row of ten counters correctly, and then recounts the same row when asked how many? a second time, because the idea that the count holds steady is not yet secure. A Year 1 student writes one hundred and two as 1002, hearing the number and recording each part as it arrives. Another writes "take 3 from 7" as 3 − 7, recording the words in the order they were spoken. A Year 2 student looks at 67 and says the value of the 6 is "six", reading the digit rather than the place. Another rounds 50 to 60, having learned round up as a rule rather than as a decision.

"A Year 1 student writes one hundred and two as 1002, recording each part of the number as they hear it."

These are not random errors and they are not signs that something has gone wrong, they are predictable, and a great many students acquire them quietly along the way because mathematics, taught in the usual way, is genuinely difficult and these are the small slippages that get carried along with the rest of the learning. In a busy classroom they tend to be the moments a teacher might catch in passing — a quick correction, a nod, a redirection — and then the lesson moves on, because there isn't the time to stop and teach into them properly. Without that proper attention these confusions are not resolved, and they compound. The student who writes 1002 for one hundred and two becomes the student who cannot read a four-digit number, and the student who confidently says 6 + 4 = 10 but hesitates on 4 + 6 becomes the student whose number facts never quite stick. Small things, left unaddressed, become large things by Year 3.

"Small things, left unaddressed, become large things by Year 3."

The Y Intercept is built to prevent this from happening in the first place. The sequence does not assume these moments will be caught and corrected on the fly, they are built into the sequence and given the time to allow students to consider the idea, make the error in a low-stakes way, explore the disconnect between what they thought and what is actually true, and form a new connection with the correct meaning. The lesson where a student might draw uneven intervals on a number line is the lesson about even intervals. The lesson where a student might wrongly and silently interpret that a tens rod is probably bigger than ten ones is the lesson about the tens rod and its relationship to the ones block specifically. The lesson where a student might write "take 3 from 7" as 3 − 7 is the lesson about interpreting language and worded stories, and subsequently creating accurate representations as number sentences that genuinely make sense. The misconception is not left to be caught later, it is anticipated and given its proper place in the teaching.

"A student might wrongly and silently interpret that a tens rod is bigger than ten ones blocks. The lesson is built around exactly that."

There is a quiet second benefit to this for the teacher. Because the sequence has been built around these moments, and because each lesson is structured to bring the relevant one to the surface in its proper place, you learn this kind of pedagogical content knowledge yourself as you teach — gradually, in context, lesson by lesson, exactly when you need it. There are no hefty textbooks to work through, and no lengthy professional development sessions where everything is delivered at once and largely out of the context of the concept you are actually teaching that week. The knowing builds as you go, because the curriculum has already done the thinking and is putting the right idea in front of you at the right time.

"No hefty textbooks. No lengthy PD delivered out of context. The knowing builds as you go."

This is mathematical pedagogical content knowledge — the knowing of what to teach, when to teach it, and what students would otherwise do along the way. It cannot be shortcut, and it is built through experience and time spent learning to teach. The Y Intercept has these content knowledge gold nuggets sequenced and written into the lessons, so that every teacher using it inherits the benefit from day one and develops an eye for these moments themselves over the course of teaching the year.

It is, in the end, a curriculum written by a teacher who has seen these moments hundreds of times, and built the sequence to stop them from becoming the next thing a student gets wrong.