Here is a question we might ask math students: what is this coordinate?

Let’s say a student types in (5, 4), a very thoughtful wrong answer. (“Wrong and brilliant,” one might say.) Here are several ways a computer might react to that wrong answer.

1. “You’re wrong.”

This is the most common way computers respond to a student’s idea. But (5, 4) receives the same feedback as answers like (1000, 1000) or “idk,” even though (5, 4) arguably involves a lot more thought from the student and a lot more of their sense of themselves as a mathematician.

This feedback says all of those ideas are the same kind of wrong.

2. “You’re wrong, but it’s okay.”

The shortcoming of evaluative feedback (these binary judgments of “right” and “wrong”) isn’t just that it isn’t nice enough or that it neglects a student’s emotional state. It’s that it doesn’t attach enough meaning to the student’s thinking. The prime directive of feedback is, per Dylan Wiliam, to “cause more thinking.” Evaluative feedback fails that directive because it doesn’t attach sufficient meaning to a student’s thought to cause more thinking.

3. “You’re wrong, and here’s why.”

It’s tempting to write down a list of all possible reasons a student might have given different wrong answers, and then respond to each one conditionally. For example here, we might program the computer to say, “Did you switch your coordinates?”

Certainly, this makes an attempt at attaching meaning to a student’s thinking that the other examples so far have not. But the meaning is often an expert’s meaning and attaches only loosely to the novice’s. The student may have to work as hard to understand the feedback (the word “coordinate” may be new, for example) as to use it.

4. “Let me see if I understand you here.”

Alternately, we can ask computers to clear their throats a bit and say, “Let me see if I understand you here. Is this what you meant?”

We make no assumption that the student understands what the problem is asking, or that we understand why the student gave their answer. We just attach as much meaning as we can to the student’s thinking in a world that’s familiar to them.

“How can I attach more meaning to a student’s thought?”

This animation, for example, attaches the fact that the relationship to the origin has horizontal and vertical components. We trust students to make sense of what they’re seeing. Then we give them an an opportunity to use that new sense to try again.

This “interpretive” feedback is the kind we use most frequently in our Desmos curriculum, and it’s often easier to build than the evaluative feedback, which requires images, conditionality, and more programming.

Honestly, “programming” isn’t even the right word to describe what we’re doing here.

We’re building worlds. I’m not overstating the matter. Educators build worlds in the same way that game developers and storytellers build worlds.

That world here is called “the coordinate plane,” a world we built in a computer. But even more often, the world we build is a physical or a video classroom, and the question, “How can I attach more meaning to a student’s thought?” is a great question in each of those worlds. Whenever you receive a student’s thought and tell them what interests you about it, or what it makes you wonder, or you ask the class if anyone has any questions about that thought, or you connect it to another student’s thought, you are attaching meaning to that student’s thinking.

Every time you work to attach meaning to student thinking, you help students learn more math and you help them learn about themselves as mathematical thinkers. You help them understand, implicitly, that their thoughts are valuable. And if students become habituated to that feeling, they might just come to understand that they are valuable themselves, as students, as thinkers, and as people.

BTW. If you’d like to learn how to make this kind of feedback, check out this segment on last week’s #DesmosLive. it took four lines of programming using Computation Layer in Desmos Activity Builder.

BTW. I posted this in the form a question on Twitter where it started a lot of discussion. Two people made very popular suggestions for different ways to attach meaning to student thought here.

I wonder if there is option 6, that plots a diff point like, shows the coordinates, and asks if they want to revise their (4,5). This could actually be cool for Ss who plots it correctly the first time as a double check.

— Kristin Gray (@MathMinds) December 10, 2020

Unpopular opinion (apparently) from someone who’s seen many Ss start switching coordinates AFTER they’ve learned slope. Since coordinates represent location, not movement, I’d prefer #4 or better yet, “the meeting of the x&y” pic.twitter.com/mxoz8gM6Sv

— Ms. (Lauren) Beitel (@ms_beitel) December 10, 2020

You can also determine the amount of time we spend with certain groups of people in our lives from childhood to late adulthood. For example, here are graphs of the amount of time we spend with friends and with co-workers.

Fantastic graphs, right? But will students think they’re fantastic? Will they learn from the graphs? How can you effectively introduce your students to the American Time Use Survey?

I use three strategies every time. You can read about them below and experience them in this new free activity from me and my colleagues at Desmos.

First, a meta-strategy:

I don’t allow myself to rest for a second in the false comfort that this is a “real world” context, and per se, interesting to students. Contexts are never “real” or “unreal.” They don’t exist in a vacuum. Contexts become real when teachers invite their students to interact with them in concrete and personal ways.

Here are three invitations I extend to students basically any time I’d like them to experience a graph as real.

1. I invite students to contribute their own data.

The graph represents a group of people’s concrete and personal experiences: time spent with friends, co-workers, and partners. I ask students to contribute their own data so the quantities and relationships become more concrete for them as well.

2. I invite students to sketch their own graph before seeing the actual graph.

This invites students to share their own knowledge about the quantities and relationships. Students have ideas about how many hours people spend with friends throughout their lives. We should invite them to express those ideas with a graph.

I also place their own data from (1) on the graph. This extends an even more personal invitation to students and gives them an anchor for their graphing.

“That’s you on there, friend. Do you think American 15-year-olds spend more or less time with their friends than you? Okay, graph it!”

3. I invite students to reflect.

Jim Coudal called these graphs “Poetry, in data.” So I ask students to tell us which graph is most poetic and why. We’ve built up a lot of steam in the activity, and this question helps release it. It allows us to elicit from students the personal observations that haven’t yet found a home in our activity.

I posted this activity on Twitter and the majority of people said this was the most interesting graph to them.

People wrote:

It is sad to me that once we are old enough to have free time to spend with friends, we spend more time alone.

I wonder if the loneliness is by choice.

Alarming lack of social opportunities for seniors.

There is so much interesting research coming out about the impact of loneliness on people’s health.

How can we change this?

So consider the invitations you extend to students. In many curricula, those invitations are impersonal and abstract. “What is the value of the co-workers graph for a 75-year-old?” That’s a question that invites students to reflect on an adult’s knowledge of graphs and the context.

“What would your data look like? What do you think the graph looks like? Why?” These are questions that invite students to interact with the graph in personal ways, to inhabit the graph as if it were their own.

Featured Comment

Leigh Ann Mahaffie:

As I’m feeling mighty alone personally (even though there are folks in the house) and professionally (electronically just isn’t the same) during the current “Stay at Home” situation, this data definitely evokes some poetry for me.

So it’s been a joy to get to do something more active about that problem than write cranky blog posts, to get to team up with some fantastic teachers, designers, engineers, and funders all continuously interrogating their assumptions about education, design, technology, math, and society, all to create what I think is …

… the very best middle school math curriculum.

This is it.

Call off the search.

You found it.

Read more about the curriculum at the Des-blog, including details about our upcoming pilot.

[extremely Oprah voice] You get a debt of gratitude! You get a debt of gratitude! You get a debt of gratitude!

Aside from my enormous gratitude to the fantastic team I work with daily, I’m especially grateful to two groups:

• The authoring / publishing team at Illustrative Mathematics / Open Up Resources who created and openly licensed a fantastic math curriculum, one which is the foundation of our own work. They dropped a massive gift on the math education community (or a hydrogen bomb from the perspective of the K-12 math publishing industry) and we were extremely happy to pick it up and build on it.
• You. I’m talking about the folks who have been reading this blog, commenting on my posts, critiquing my ideas from day one. Your thoughts and mine are all tied together and run all the way through this curriculum.

This blog has been quieter over the last few years for reasons that are predictable — family, Twitter, the death of blogs, etc. — but also because, for the only time in my career, I haven’t been able to write about my work.

That changes today and I’m very excited to collaborate with you folks once again on the work that matters to me most. It won’t be at its best without you.

Entrepreneurs had a mixed decade in K-16 math education. They accurately read the landscape in at least two ways: a) learning math is enormously challenging for most students, and b) computers are great at a lot of tasks. But they misunderstood why math is challenging to learn and put computers to work on the wrong task.

In a similar retrospective essay, Sal Khan wrote about the three assumptions he and his team got right at Khan Academy in the last decade. The first one was extremely surprising to me.

Teachers are the unwavering center of schooling and we should continue to learn from them every day.

Someone needs to hold my hand and help me understand how teachers are anywhere near the center of Khan Academy, a website that seems especially useful for people who do not have teachers.

Khan Academy tries to take from teachers the jobs of instruction (watch our videos) and assessment (complete our autograded items). It presumably leaves for teachers the job of monitoring and responding to assessment results but their dashboards run on a ten-minute delay, making that task really hard!

Teachers are very obviously peripheral, not central, to the work of Khan Academy and the same is true for much of math education technology in the 2010s. If entrepreneurs and founders are now alert to the unique value of teachers in a student’s math education, let’s hear them articulate that value and let’s see them re-design their tools to support it.

Every new school year, Twitter lights up with caregivers who can’t believe they have to buy their students a calculator that’s wildly underpowered and wildly overpriced relative to other consumer electronics.

The Hustle describes Texas Instruments as having “a near-monopoly on graphing calculators for nearly three decades.” That means that some of the students who purchased TI calculators as college students are now purchasing calculators for their own kids that look, feel, act and (crucially) cost largely the same. Imagine they were purchasing their kid’s first car and the available cars all looked, felt, acted, and cost largely the same as their first car. This cannot go on forever.

As the chief academic officer at Desmos, a competitor of Texas Instruments calculators, I was already familiar with many of The Hustle’s findings. Even still, they illuminated two surprising elements of the Texas Instruments business model.

First, the profit margins.

One analyst placed the cost to produce a TI-84 Plus at around $15-20, meaning TI sells it for a profit margin of nearly 50% – far above the electronics industry’s average margin of 6.7%.

Second, the lobbying.

According to Open Secrets and ProPublica data, Texas Instruments paid lobbyists to hound the Department of Education every year from 2005 to 2009 – right around the time when mobile technology and apps were becoming more of a threat.

Obviously the profits and lobbying are interdependent. Rent-seeking occurs when companies invest profits not into product development but into manipulating regulatory environments to protect market share.

I’m not mad for the sake of Desmos here. What Texas Instruments is doing isn’t sustainable. Consumer tech is getting so good and cheap and our free alternative is getting used so widely that regulations and consumer demand are changing quickly.

Another source told The Hustle that graphing calculator sales have seen a 15% YoY decline in recent years – a trend that free alternatives like Desmos may be at least partially responsible for.

You’ll find our calculators embedded in over half of state-level end-of-course exams in the United States, along with the International Baccalaureate MYP exam, the digital SAT and the digital ACT.

I am mad for the sake of kids and families like this, though.

“It basically sucks,” says Marcus Grant, an 11th grader currently taking a pre-calculus course. “It was really expensive for my family. There are cheaper alternatives available, but my teacher makes [the TI calculator] mandatory and there’s no other option.”

Teachers: it was one thing to require plastic graphing calculators calculators when better and cheaper alternatives weren’t available. But it should offend your conscience to see a private company suck 50% profit margins out of the pockets of struggling families for a product that is, by objective measurements, inferior to and more expensive than its competitors.

BTW. This is a Twitter-thread-turned-blog-post. If you want to know how teachers justified recommending plastic graphing calculators, you can read my mentions.

I spent most of the fall in eighth grade classrooms, watching lots of teachers enact the same set of Desmos lessons in different ways and in different contexts and with different results.

Some classes were high energy, some were low energy.

Some classes seemed to learn a lot, others learned less.

There are lots of important explanations for those differences, of course, many of which have nothing to do with the teachers or students themselves. But it was also interesting to sit in some high energy, high learning classes and palpably feel that these teachers are really, really curious about their students. Curious about them personally, sure, but curious about their thinking in particular.

Students feel that curiosity — “My teacher wants to know what I’m thinking about.” — and I find it easy to attribute some significant amount of those classes’ high energy and high learning to that feeling.

Teachers expressed that curiosity using the snapshotting tool when students recorded their thinking in Desmos. When students recorded their thinking on paper, teachers expressed their curiosity with their cameraphones, taking photos of student work and projecting them up on the board.

You see this on Twitter all the time! Curious teachers share diverse student thinking with other curious teachers.

Making students scratch their heads with our notice and wonder today. It sparked some great conversations! #exceptional #iteachmath pic.twitter.com/uOkcta4ASm

— Teri Beth Shearer (@tbethshearer) January 11, 2019

And that practice creates no fewer than twelve virtuous cycles, a few of which I can quickly describe:

1. When teachers express curiosity about diverse student thinking, students feel that and feel license to express even more diverse kinds of thinking.
2. The more perspectives on an idea a teacher can help students connect, the more students learn about that idea.
3. That all feels great so the teacher becomes more curious about student thinking and consequently re-evaluates her curriculum and instruction to emphasize tasks and pedagogy that are more likely to elicit diverse thinking.
4. The teacher becomes interested in learning more mathematics because the more math you know, the more you’re able to identify and connect diverse student thinking when you see it.

Run that cycle for a few months and you have a different class.

Run that cycle for a few years and you have a different teacher.

Run that cycle across a department and you have a different school.

It starts with your cameraphone.

BTW. If your students’ diverse thinking currently fills you with more anxiety than curiosity, I encourage you “act your way into belief” instead of the reverse. Take two minutes at the end of class to share “My Favorite Whoa,” a photo of student thinking during the day you thought was so interesting and why you thought it was interesting. That’s low commitment with a lot of upside.

BTW. If you already use your cameraphone to express curiosity about student thinking, head to the comments and let us know how you do that. Your colleagues want to know your workflow.

Featured Comments

Daniel Peter uses whiteboards:

Need to be able to put up multiple solutions at the same time so the teacher can use questions to help students create explicit connects between the solutions: similarities/differences, aha (unique, elegant, just plain interesting) and help students make connects to the underlying properties, principles of mathematics. The advantage of paper/vertical whiteboards (or old school individual slates) is I can create the congress or bansho to make those connections explicit through the organization.

Several people use Reflector. Here’s Gretchen Muller:

It turns my phone into a portable document camera. Multiple devices can be shown at a time so I can do compare and contrast between different pieces of work at the same time. I now use it in my work with educators. The first question I always get is “How did you do that?”. I use it both as a live camera so that students can explain from their desk or still pictures from my phone and iPad when I want to compare.

Allison Krasnow describes students using their cameraphones to take pictures of student work:

I received three texts (I use remind.com) this evening with students sending photos of their homework showing where they got confused and asking for help. Them texting me photos of their homework when they are stuck and at home with no one to help them is incredibly powerful.

Here is some personal prejudice: I don’t love online courses.

I love learning in community, even in online communities, but online courses rarely feel like community.

To be clear, by online courses I mean the kind that have been around almost since the start of the internet, the kind that were amplified into the “Future of Education™” in the form of MOOCs, and which continue today in a structure that would be easily recognized by someone defrosted after three decades in cold storage.

These courses are divided into modules. Each module has a resource like a video or a conversation prompt. Students are then told to respond to the resource or prompt in threaded comments. You’re often told to make sure you respond to a couple of other people’s responses. This is community in online courses.

The reality is that your comment falls quickly down a long list as other people comment, a problem that grows in proportion to the number of students in the course. The more people who enroll, the less attention your ideas receive and consequently you’re less interested in contributing your ideas, a negative feedback loop which offers some insight into the question, “Why doesn’t anybody finish these online courses?”

I don’t love online courses but maybe that’s just me. Two years ago, the ShadowCon organizers and myself, created four online courses to extend the community and ideas around four 10-minute talks from the NCTM annual conference. We hosted the courses using some of the most popular online course software.

The talks were really good. The assignments were really good. There’s always room for improvement but the facilitators would have had to quit their day jobs to increase the quality even 10%.

And still retention was terrible. 3% of participants finished the fourth week’s assignment who finished the first week’s.

The organizers and I had two hypotheses:

• The size of the course enrollment inhibited community formation and consequently retention.
• Teachers had to remember another login and website in order to participate in the course, creating friction that decreased retention.

Our Solution

For the following year’s online conference extensions, we wanted smaller groups and we wanted to go to the people, to whatever software they were already using, rather than make the people come to us.

So we used technology that’s even older than online course software, technology that is woven tightly into every teacher’s daily routine: email.

Teachers signed up for the courses. They signed up in affinity groups — coaches, K-5 teachers, or 6-12 teachers.

The assignments and resources they would have received in a forum posting, they received in an email CC’d to two or three other participants, as well as the instructor. They had their conversation in that small group rather than in a massive forum.

Of course this meant that participants wouldn’t see all their classmates’ responses in the massive forum, including potentially helpful insights.

So the role of the instructors in this work wasn’t to respond to every email but rather to keep an eye out for interesting questions and helpful insights from participants. Then they’d preface the next email assignment with a digest of interesting responses from course participants.

The Results

To be clear, the two trials featured different content, different instructors, different participants, and different grouping strategies. They took place in different years and different calendar months in those years. Both courses were free and about math, but there are plenty of variables that confound a direct comparison of the media.

So consider it merely interesting that average course retention was nearly 5x when the medium was email rather than online course software.

It’s also just interesting, and still not dispositive, that the length of the responses in emails were 2x the length of the responses in the online course software.

People wrote more and stuck around longer for email than for the online course software. That says nothing about the quality of their responses, just the quantity. It says nothing about the degree to which participants in either medium were building on each other’s ideas rather than simply speaking their own truth into the void.

But it does make me wonder, again, if large online courses are the right medium for creating an accessible community around important ideas in our field, or in any field.

What do you notice about this data? What does it make you wonder?

Featured Comments

Leigh Notaro:

By the way, the Global Math Department has a similar issue with sign-ups versus attendance. Our attendance rate is typically 5%-10% of those who sign up. Of course, we do have the videos and the transcript of the chat. So, we have made it easy for people to participate in their own time. Partipating in PD by watching a video though is never the same thing as collaborating during a live event – virtually or face-to-face. It’s like learning in a flipped classroom. Sure, you can learn something, but you miss out on the richness of the learning that really can only happen in a face-to-face classroom of collaboration.

William Carey:

At our school now, when we try out new parent-teacher communication methods, we center them in e-mail, not our student information system. It’s more personal and more deeply woven into the teachers’ lives. It affords the opportunity for response and conversation in a way that a form-sent e-mail doesn’t.

Cathy Yenca:

At the risk of sounding cliché or boastful about reaching “that one student”, how does one represent a “data point” like this one within that tiny 3%? For me, it became 100% of the reason and reward for all of the work involved. I know, I know, I’m a sappy teacher :-)

Justin Reich is extremely thoughtful about MOOCs and online education and offered an excellent summary of some recent work.

2018 Oct 5. Definitely check out the perspective of Audrey, who was a participant in the email group and said she wouldn’t participate again.

2018 Oct 12. Rivka Kugelman had a much more positive experience in the email course than Audrey, one which seemed to hinge on her sense that her emails were actually getting read. Both she and Audrey speak to the challenge of cultivating community online.

First, let’s acknowledge that statements of values are often useless. Values are only useful if they help people make hard decisions. Our company values should (a) help educators decide how we’re different from other math edtech companies, (b) help us decide how to spend our limited time in the world. So here is one of our values:

We believe that math class should be social and creative — that students should create mathematics in every form and then share those creations with each other and their teachers.

Many other companies disagree with those values, or at least they spend their limited time in the world acting on different ones. For example, many other companies think it’s sufficient for students to create multiple choice and numerical responses to express their mathematical thinking and to share those responses with a grading algorithm alone.

Our values conflict, and the result is that other companies spend their time optimizing adaptive grading algorithms while we spend our time thinking about ways to provoke mathematical creativity that algorithms can’t grade at all. We may both work in “math edtech” but we are on very different paths, and our path recently led us to a very thorny question:

What should teachers do with all these expressions of mathematical creativity that algorithms can’t grade?

Let’s say we ask students an interesting question about mathematics or we ask them to define a relationship and sketch its graph. That’s good math, but the teacher now has dozens of written answers and sketches that their computers can’t grade.

Other math edtech software offers teachers scarce insight into the ways students think mathematically. We offer teachers abundant insight which is a different kind of problem, and just as serious. We’ve spent months building a solution to this problem of abundance and we likely would have spent years if not for one book:

Mary Kay Stein and Margaret Smith’s Five Practices for Orchestrating Productive Mathematical Discussions.

Smith and Stein describe five teaching practices that promote student learning through summary discussions. Teachers should (1) anticipate ideas students will produce during a task or activity and then (2) monitor student work during class for those ideas and others that weren’t anticipated. Then the teacher should (3) select a subset of those interesting student ideas, (4) sequence the order of their presentation, and then help students (5) connect them.

In our classroom observations of our activities, we noticed teachers struggling to select student ideas because there were so many of them streaming from the students’ heads into the teacher’s dashboard. Sometimes teachers would make a note about an idea they wanted to select later, but when “later” came around, the student had already developed the idea further. So then we saw teachers take screenshots of that idea and paste them into slide software for sequencing. Smith and Stein’s recommendations are already ambitious and our software was not making it easier for teachers to enact them.

So we built “Snapshots.”

If you see interesting ideas at any time during an activity, press the camera icon next to it.

Then go to the “Snapshots” tab.

Sequence the ideas by dragging them into a collection.

Add a comment or a question to help students connect their classmates’ ideas to the main ideas of the lesson.

Then press “Present.”

We tested the tool ourselves during a summer school session in Berkeley, CA, and also with teachers around the country. What we’ve noticed is that students pay much more attention to discussions when the discussion isn’t about a page from the textbook or a worked example from the teacher but about ideas from the students themselves.

It’s the difference between “Let me tell you about a really useful strategy for multiplying two-digit number” and “Let me show you some useful strategies from around the class for multiplying two-digit numbers. They’re all correct. Decide which seems like less work to you.”

Here are some of our other favorite uses from the last month of testing.

Values help us all decide how to spend our limited time in the world, and nobody feels those limits quite like classroom teachers. Teachers frequently, and with good cause, evaluate new ideas and innovations by asking, “Does my class have time for this? What will we have to skip if we do this?”

Your decision to spend your limited class time talking about your ideas, your textbook’s ideas, or your students’ ideas is a loud expression of your values. Students hear it. We hope your students hear how much you value their mathematical creativity, explicitly in your words and implicitly in how you spend your time. You bring those values. We’ll keep working on tools to help you live them out in your classroom every day.

My team at Desmos is hiring!

You should share that link with anyone who might be a good fit for the work. Alternately, if you think you’re a good fit for the work, you should guard that posting with your life, share it with nobody, and start thinking about your cover letter.

Why you should apply is really simple:

Desmos is the best place to do great work in math edtech right now and for the foreseeable future.

Here are six reasons I’m pulling out of muscle memory. I’m not even thinking about them. Ask me in ten minutes and I’ll give you six more just as fast.

• Teachers and students love our work. Check our Twitter feed. Also we just wrapped up a pilot study of 44 teachers using our activities and the results exceeded all of our expectations.
• Desmos folk are enormously talented in their own areas, curious and humble in all the others. So while my team didn’t come to Desmos having studied the same fields as our software developers and product designers (or vice versa) we’re conversationally fluent in each other’s work and humble about the limitations of that fluency. That disposition results in extremely enjoyable and productive collaboration.
• Great work-life balance. Startups are notoriously unfriendly to families but all of the full-time folk on my team have a couple of kids or more. Each one will tell you they love Desmos’s flexibility to do their best work at negotiable hours and locations.
• Everyone at Desmos is really satisfied with how we handle meetings and remote work, according to an internal company survey earlier this month. That’s uncommon.
• Strong financial position. While other edtech companies take on as much venture capital as they can, mortgaging their ability to make important decisions for themselves, Desmos has worked hard to minimize its reliance on outside investment. The result is that my team has had time and freedom to make decisions, first, based on what works for math students and, second, based on what we can sell. (Example: we decided to invest heavily in making our graphing calculator accessible to vision-impaired students because we thought that reducing an impediment to mathematical thinking sounded like a really good idea. Afterwards, we turned that work into contracts with eighteen states with more on the way.)
• Glassdoor reviews that speak for themselves.

We’ve spent several years tuning up our model for math, education, and technology. We studied it over the last three months and various aspects have clicked right into place. Demand is heating up for that work so we’re looking for people to help us build.

So please check out the posting and think about applying or sending it to someone you know.

BTW. If the formatting of the job posting seems atypical, it’s because we spent a lot of time discussing Lever’s blog series on reducing hiring bias. It would be easy to write a list of required credentials based on our mental profile of an ideal candidate. But that mental profile would be extremely susceptible to implicit and explicit biases. Lever received more responses from a more diverse group of candidates when they focused less on their credentials and more on what they’d need to know for the work and what they’d do at different milestones in their first year.

For example, an earlier draft of our posting required “at least five years of teaching experience at grades 6-12,” which isn’t bad as far as credentials go, but we realized it’s really just a proxy for the first four bullets beneath “What you should show up ready to teach anyone on your first day.”

• What a day in the life of a public middle- or high-school teacher looks like in the United States.
• The major challenges of technology integration in US classrooms from the perspective of both students and teachers.
• What separates a great math lesson from a lousy math lesson.
• What separates great classroom technology from lousy classroom technology.

We’re grateful to Lever for opening up their hiring practices to the public.

We also don’t have the assessments to place kids with any precision on the map. The existing measures are not high enough resolution to detect the thing that a kid should learn tomorrow. Our current precision would be like Google Maps trying to steer you home tonight using a GPS system that knows only that your location correlates highly with either Maryland or Virginia.

If you’re anywhere adjacent to digital personalized learning — working at an edtech company, teaching in a personalized learning school, in a romantic relationship with anyone in those two categories — you should read this piece.

Berger closes with an excellent question to guide the next generation of personalized learning:

What did your best teachers and coaches do for you–without the benefit of maps, algorithms, or data–to personalize your learning?

My best teachers knew what I knew. They understood what I understood about whatever I was learning in a way that algorithms in 2018 cannot touch. And they used their knowledge not to suggest the next “learning object” in a sequence but to challenge me in whatever I was learning then.

“Okay you think you know this pretty well. Let me ask you this.”

What’s your answer to Berger’s question?

BTW. It’s always the right time to quote Begle’s Second Law:

Mathematics education is much more complicated than you expected even though you expected it to be more complicated than you expected.

Featured Comment

SueH:

I have come to believe that all learning is personalized not because of what the teacher does but because of what’s happening inside the learner’s brain. Whatever pedagogical choices a teacher makes, it’s the student’s work that causes new neural networks to be created and pre-existing ones to be augmented or strengthened or broken or pruned.

Scott Farrand:

I’ll accept the risk of stating the obvious: my best teachers cared about me, and I felt that. Teaching is an act of love. A teacher who cares about each student is much more likely to, in that instant after a student responds to a question, find the positive value in the response and communicate encouragement to the student, verbally and nonverbally. And students who feel cared for are more likely to have good things going on in their brains, as described by SueH.