Education ∪ Math ∪ Technology

Month: July 2026 (page 1 of 1)

Feedback in Digital Learning Systems

There are three different ways the word learning is used, and all of them are important. Educational technology companies usually pick one of these forms of learning to focus on, but to be effective, their products really need to do all three. The feedback systems built into their products need to find ways to support all three learning scenarios.

  • Learning as the introduction to ideas
    This is the most commonly way of understanding learning. A learner doesn’t know something and they are exposed to information that gives them new insight about the world.1 This exposure may take the form of explicit instruction or it could be as part of a guided discovery. Learning is measured by student performance on tasks completed closely related to the ideas to which a student was exposed. Improving learning is focused on either improving instructional delivery or on improving student performance on follow-up tasks.
  • Learning as the activity
    Sometimes learning is defined as the activity students do that results in their engagement and some measurement of performance, and this activity does not include being introduced to new information. For example, students who complete a worksheet can be said to be in the act of learning. Learning is measured by how much students participate and complete work. Improving learning centers around improving engagement with the activity.
  • Learning as long-term change
    Graham Nuthall, author of the Hidden Lives of Learners2, defined learning as the longterm change in what students know, believe, and can do. With this model of learning, students can be exposed to new information, complete activities, and not learn anything because the ideas didn’t stick. Learning is measured by longterm assessments measuring knowledge and skills gained over months and years. Improving learning centers around long-range strategies and finding ways for learners to remember ideas they have learned more robustly.

If one is designing a digital learning experience, all three of these ways of understanding learning need to be addressed. Ideas need to be introduced to students, students have to complete activities, and long term changes in what students know, believe, and can do should be measured.

Most educational technology solutions focus on introducing ideas to students or engaging students in activities and sometimes both. Very few products focus on ensuring students have changed in the longterm, where ironically, accountability for schools focuses nearly entirely on this aspect of learning.

Feedback while introducing ideas

When introducing ideas to students, it is an excellent practice to frequently check to see if students understand an idea. It is even better practice to check how students understand a new idea! One can then adjust instruction based on the feedback to the instructor. Ideally, this results in short cycles of introducing a small amount of information to students, engaging students in an opportunity to demonstrate their understanding, gathering evidence of that performance, and adjusting instruction.3

The image shows a circle demonstrating a cycle with four different stages.
Introduce a small amount of information.
Check how students understand the information.
Gather feedback from student performance.
Adjust instruction accordingly.
A useful instructional cycle

Here the feedback is mostly to the instructor and they make decisions about how to adjust their instruction that result in new information (e.g. feedback on learning) being given to learners.

Most educational technology products are not this deliberate in how they introduce information to students, and even the ones that include small incremental steps when introducing information do not consistently change their instruction as a result of a cycle like this.

Further, the information provided to instructors about student performance is generally unhelpful. Knowing that children have completed this activity or that activity (information typically provided in educational technology products) is less helpful than knowing what kinds of mistakes students were making and how to support students (information never provided in educational technology products). The lowest hanging fruit in reporting is completion data, but the closer the data is to the actual work students did, the more likely it is to be helpful. Imagine a product that takes all student work from activity and synthesizes it into the three to five most commonly used ways of thinking students had during the activity and then suggests activities instructors can do.

Feedback during activities

Key among the strategies educational technology companies have promised over the years is personalized feedback to students. Unfortunately, few products on the market deliver on this promise. If your product contains digital explanations, showing them an explanation of why they are wrong after they get an answer incorrect is the digital equivalent of reteaching by talking louder and slower. It doesn’t work. Feedback in those moments should depend on the thinking children have done, and few products include robust enough student testing in their development lifecycle to be able to create the feedback opportunities that actually work.

An alternative way of presenting feedback to students is to select a different task for them to work on. Perhaps a student is having trouble with 102 – 94 and you want them to think about this problem differently. A teacher would know that a related problem in the moment can be transformative and ask that child to try solving 100 – 94. If this is still a struggle for the child, they can try 100 – 95 first, then go back to 100 – 94, and then go back to the original problem of 102 – 94. To mitigate this struggle in the first place, one could reverse this sequence of problems, but then one might not know if the scaffolding led the child to the idea of changing 102 – 94 to 102 – 100 + 100 – 94 or if the child can do this independently. Using tasks to provide feedback is one of the more powerful instructional moves a teacher can make and most educational technology products do not even attempt to use it.

Feedback during long-term learning

Durable long-term learning is really about supporting students with revisiting ideas they to which they have already been exposed. Our brains are designed to ruthlessly trim ideas from active recall that we do not use frequently. This means, if there are things we want to remember, we either need to make the experience of learning them extremely memorable, or we need to spend effort thinking about those ideas again periodically.

No educational technology products on the market today deliberately and systematically offers students opportunities to revisit ideas over time. Every product assumes that once children have demonstrated proficiency with an idea that this proficiency is stable and unchanging. This is demonstrably false! We all know that learners forget things over time.

Spaced opportunities to revisit ideas learned is in the best interest of learners. Educational technology has the ability to track what students have demonstrated proficiency in, and to keep track of the hundreds of ideas that students should revisit and at what intervals they should come back. There is very solid evidence that spaced, interleaved repetition and practice lead to long term changes in memory.

Conclusion

There is a need for educational technology to be better than it is. More deliberate systems and focus on improving feedback in a product is one way nearly every product on the market can improve. They need to move beyond simplistic models of learning (the student completed an activity so therefore they “know it”) to models that include all three ways of understanding learning.

We need an education system

Our current “system” of education is actually hodgepodge of different competing organizations layered on top of each other. It’s not actually a system at all.

If you compared our system for professional learning to a relay race where each organization in a teacher’s career should pass the baton of learning to the next organization, it’s instead like a race with people running in different directions and there’s no baton in sight.

The education relay race

Our system for student learning is slightly better, if only because students tend to stay within the same school for a number of years and schools tend to be a bit better about internal consistency across year levels. Still, in most schools what a child knows about a topic from the year before is almost always lost by the time the related topics come up in the following year. In fact, despite the fact schools collect mountains of information on each child in a year, most of it is discarded before the following year. Remember, every worksheet a child does contains information about their performance at a moment in time.

Our systems for connecting educator learning to student learning are at best aspirational, with almost no schools anywhere linking the two. When was the last time you heard in a staff meeting, “We see students need support with ____ so we need to learn ____”? It’s just not done. In the best schools, teachers get autonomy to decide what to learn based on reflecting on their work with students, and in the worst, educator professional learning is neither professional nor does it result in learning.

We need a stable set of goals for students, so that we can measure student progress toward those goals and make decisions from that information. We need agreement on the relative importance of those goals, so that we stop shifting goalposts year after year. We need to create our system by working up from student learning and not down from ministries of education, so that every link in the chain of the system is built carefully based on evidence of impact.

Observing Math Classrooms

Now that I’ve been coaching math teachers again, I have been in a lot more classrooms and doing classroom observations again.

In a past iteration as a math coach4 , I created this checklist of things5 to look for explicitly when observing teachers. The goal at the time was to be able to have our team have a clear list of observable behaviours so that we could measure whether our professional learning work was landing with teachers. With 8 instructional coaches and 30 schools in our project, we needed something that would work at scale.

A checklist of different behaviours one can observe in a math classroom broken into 4 different categories: student to student, student to mathematics, teacher to student, and teacher to mathematics.
Available in a larger size

We created curricular resources for teachers, ran workshops for teachers to teach them how to use the curricular resources (via modeling, rehearsals, and dialogue), and then coached the teacher leads at the schools. We would then observe teachers in their classrooms and teacher leads in their meetings, so that we could learn whether our work was landing. Over time, we iterated and improved our approach as we learned from what we did.

As an individual coach though, my goals for lesson observations are tied to the coaching work I do with teachers. The teacher I’m coaching and I decide together what I should focus on when observing them, and I spend much more time learning alongside the teacher instead of just sitting back and passively observing their classrooms.

I’ve since been heavily influenced by Elham Kazemi’s (et al.6) Learning Together so that instead of trying to transmit what I know to the teachers I work with, I work with teachers to try out different strategies to see what works with these students in this context, focused heavily on instructional goals informed by our conversations, data we have collected, and the goals of the school. I still do typical coaching ‘moves’ such as modeling instruction, observations, and leading team meetings, but these are in service of our shared learning.

Neither of these approaches are better than the other. They are meant to serve different types of structures and sets of resources available. But both are meant to serve the main goal — the learning of teachers in service of student learning. One’s strategy for coaching should match the available resources one has and the goals one has for that coaching.

I like Graham Nuthall’s definition of learning as ‘long-term changes in what learners know, believe, and can do.’ From this definition, we can see that one cannot directly observe student or teacher learning from a single lesson observation; all one can observe in learners are behaviours that are likely to lead to learning. Lesson observations therefore also have to be paired with collection of other kinds of data, including student performance data collected over the long term, and data about changes in teacher practice that are sustained.

Either approach therefore will require a longer term view. It’s hard to see if long term changes are making an impact as well, as one needs both a control year (how much did students change this year) and a treatment year (under this new strategy, how much did students change). You also need time to see if the strategies you and teachers learn stick, since you are learners too! My recommendation is to make sure to study the impact of your work and repeatedly iterate on both your coaching approach and the teaching strategies your team tries, until you see the results you want.

School Culture and Math Teaching

School culture trumps great teaching, or it can.

When teachers try to teach the way they think is best, they do so while navigating the culture of the school and community where they work. What is considered excellent teaching is dependent on both the school culture and the dominant culture the students come from7.

Our personal set of values informs how we teach, and the set of values a school community values informs what they consider good teaching. Consequently, comparing your personal values to the lived (rather than the espoused 8) values of a school is a good way of figuring out whether you are a good fit for a school.

If you are an educator considering transitioning to a new school, here are some questions you can ask to see if your set of values will mesh well with the school’s culture.

  • What level of technology is expected in your teaching?
  • How much flexibility do educators have in selecting their curricular resources?
  • When one enters a classroom and everything is going smoothly, what does one see?
  • How does the school support students with behaviour?
  • What support exists at the school for students with special needs?
  • What supports exist for teachers?

The answer to these questions will speak to what the school values, and you can use the answers to help yourself determine if you are a good fit for the school culture.