Tisha Jones, Enrichment for All
ROUNDING UP: SEASON 2 | EPISODE 5
At their best, programs with titles such as “gifted and talented” seek to provide enrichment to a subset of learners. That said, these initiatives can have unintended consequences, sending messages about which students are (or are not) capable doers of mathematics. What if there was a way educators could offer problems that extend grade-level learning to each and every student. Today, we’ll explore the concept of horizontal enrichment with Tisha Jones, MLC’s senior manager of assessment.
Tisha Jones is the senior manager of assessment at The Math Learning Center and a dedicated educator with more than 11 years of experience teaching elementary students. Early in her career, she discovered her passion for teaching elementary math and has since worked to develop better methods of teaching math to children. She strongly believes that all children can learn and enjoy math.
Mike Wallus: At their best, programs with titles such as “gifted and talented” seek to provide enrichment to a subset of learners. That said, these initiatives sometimes have unintended consequences, sending messages about which students are, or are not, capable doers of mathematics. What if there was a way educators could offer problems that extend grade-level learning to each and every student? Today we'll explore the concept of horizontal enrichment with Tisha Jones, MLC's senior manager of assessment.
Well, thanks for joining us, Tisha. I am excited to explore this idea of horizontal enrichment.
Tisha Jones: I am excited to be here and talk about it.
Mike: So, we're using the term “horizontal enrichment,” and I think we should define the term and talk about, what do we mean when we say that?
Tisha: When we're talking about horizontal enrichment, we are looking at how do we enrich the curriculum, but on grade level? So, not trying to accelerate into the next grade level. But how do we help them go deeper with the content that is at their developmental level currently?
Mike: That's really interesting because when I was teaching, I would've said enrichment and acceleration are exactly the same thing, which, I think, leads me to the next question, which is: What are the features of a task that might be designed with horizontal enrichment in mind?
Tisha: So, I like to think about horizontal enrichment as an opportunity to engage the practice standards. So, how do we help kids do more of the things that we think being a [mathematician] actually is? So, how can we get them more invested in problem solving? How can we get them using tools? How can we get them thinking creatively in math and not just procedurally? And, of course, we try to do that on a daily basis in math, but when we're enriching, we want to give them tasks that raise the ceiling of their thinking, where they can approach things in lots of different ways and push their thinking in ways that maybe they haven't, where they can apply the concepts that they're using to solve interesting and novel problems.
Mike: I think that's really helpful because you're really clarifying for me, one way that we could “enrich” kids would be to teach them procedures that they might learn in a grade or several grades that are beyond where they're at right now. But what you're suggesting is that enrichment really looks like problem solving and novelty and creativity. And we can do that with grade-level ideas. Am I making sense of that correctly?
Tisha: Absolutely. And I get excited because I also think that it's fun working a problem where the path is not clear-cut to get to the answer and try some things out and see what happens and look at how can I learn from what I did to make new decisions to try to get to where I'm going? To me, that's bringing in the joy of doing math.
Mike: So, this is interesting. I think that maybe the best way to unpack these ideas might be to look at a specific task. So, I'm wondering: Is there a specific task that you could help us take a look at more closely?
Tisha: Absolutely. So, we're going to take a look at a task from third grade, and it comes out of Concept Quests, which is a supplemental resource that's published by [The] Math Learning Center. And this task is called “The Lasagna Task.” So, I'm just going to read it and then we can talk about what is it asking kids to do.
So, it says, “You need to assume that you like lasagna and would like as much lasagna as possible. For each of the ‘Would you rather…?’ scenarios below, justify your reasoning with equations, pictures, or both.” So, that's the setup for the kids. And then there's three “Would you rather…?” scenarios. So, the first is, “a) Would you rather: share three lasagnas between two families or share four lasagnas between three families?” “b.) Would you rather share four lasagnas between six families or share three lasagnas between four families?” And the last one is, “c.) Would you rather share five lasagnas between three families or share six lasagnas between four families?”
Mike: Ahh, this is so great. There's so much to unpack here. To step back and try to analyze this, what are some things that you would want us to notice about the way this task is set up for kids?
Tisha: So, there's a few things. The first thing is, I love that there's this progression of questions, of scenarios. I think what's also really important is, when you're looking at this on the page, there's no front-loading here. There’s no, “Well, let me tell you about how to do this.” This is just, “I'm going to give you this problem, and I'm going to ask you to just take a stab at it. Give it a shot.”
So, what we want kids to do is start to learn, how do you approach a problem? What is your first step? What things do you do to make sense of what it's asking? Do you draw a picture? Do you start with numbers? Do you try to find important information? How do you even get started on a problem? And that's so important, right? That's a huge part of the process of problem solving. And when we front-load for kids, we take away their opportunities to work on those skills.
Mike: So, there's a couple things that jump out for me when I've been reading the text of what you were reading aloud to the group. One bit is this language at the end where it says, “For each of the ‘Would you rather…?’ scenarios below, justify your reasoning with equations, pictures, or both.” And that language just pops out for me. I'm wondering if you could talk a little bit about the choice of that language in the way that this is set up for kids.
Tisha: Ahh, I love that language. So, I think this is amazing for kids because as a teacher, we've all had kids that come up to us and they hand us their paper and they say, “Is this right?” And when we ask them to justify their response, I think we're putting the responsibility back on them to be able to come up to me and say, “I think this is right because of this.” So now, who is owning what they did? The kids are owning what they did, right? And they're owning it because they've gone through this process of trying to prove it not just to somebody else but to themselves. If you're justifying it, you should be able to go back through and say, “Well, because I did this and this is this and because I did this next step and this is how this worked out, this is why I know my answer is correct.” And I love that kids can own their own answers and their own work to be able to determine whether it makes sense or not.
Mike: I'm going to read a part of this again because I just think it's worth lingering on and spending a little bit of time thinking about how this question structure impacts kids or has the potential to impact kids. So, I'm going to read it again for the audience: “Would you rather: a.) share three lasagnas between two families or share four lasagnas between three families?” So, listeners, just pause for a second and think about the mathematics in that question and then also think about what mathematics might come out of it. What is it about the structure of that question that creates space for kids to solve problems, encounter novelty, and make decisions?
Well, Tisha, since we can't hear their answer, I would love it if you could share a little bit of your thinking. What is it about the design that you think creates those conditions for kids?
Tisha: So, while there is an implied operation, it's not necessarily an obvious operation, right? I think that it is something that easily lends itself to drawing a picture, which, I think, when students start modeling the scenario, they now have—that opens up all kinds of creativity, right? They're going to model in the way that they're seeing it in their head. They're not focused on trying to divide this number by that number. They may not even, at first, realize that they're working with fractions. But by the end of it, because it's something that they can model, there's still a lot of room for them to be able to find success on this task, which I think is really important.
Mike: It seems like there's also opportunities for teachers to engage with kids because there's a fair number of assumptions that live inside of this question structure, right? Like three lasagnas for two families, four lasagnas for three families, but we haven't talked about how large those families are, how many people are in each family.
Tisha: How much lasagna there is. (chuckles)
Mike: Yeah! Right?
Tisha: Absolutely. So, I think it's also fair to say that maybe a kid would decide that the four lasagnas between three families—those are going to need to be bigger pans of lasagna. So, how are they bringing in their world experience with feeding people and having to make these decisions? There's nothing in here that says that the lasagnas have to be the same size or that the families have to be the same size. So, as they're justifying the way that they would go, as a teacher, I'm looking for: Is their justification a sound justification?
Mike: Well, the thing that I started to think about, too, is, if you did introduce the variable that, “Oh, this family has three members and this family has, say, 12. Well, how many lasagnas would you need in order to give an equal share to the family with 12 versus the family with three?” There's a lot of ways as a teacher that I can continue to adapt and play with the ideas and really press kids to examine their own assumptions and their own logic.
Tisha: Absolutely, yeah. So, I think that's a really great point, too, is that, there's a lot of room to even extend these problems further. Would your answer change if you knew that one family was a family of six people? So you can even push their thinking even further than what's just on the paper.
Mike: I keep going back to this notion of justification. And we've talked about the structure of the problems as a way to differentiate for kids, to really press them on justification. But the other side of the coin is, as an educator, it really gives me a chance to understand my students' thinking and then continue to make moves or offer tasks that either shine a light on the blind spots that they have or extend some of the ideas in interesting and productive ways.
Tisha: Yes, I would agree with that.
Mike: So, I want to play with a couple more questions, Tisha. One of the ones that we touched on right at the beginning was this idea that a task can be characterized as enriching and challenging, and yet it can still be at a student's grade level. And I think that really stands out for me, and I suspect it probably might be a challenging idea for educators to get their heads around—especially if you've been a teacher, and for the majority of your career, “acceleration” and “enrichment” have meant the same thing. Can you unpack this just a little bit for the audience, this idea of enrichment?
Tisha: So, I like to think about enrichment as, how do we help our students think more deeply? There's so much room within a school year for a particular concept, for example. Like, let's say with fractions. There's a lot of room for students to think about things in ways they haven't thought about or ways that maybe we don't ask them to think about things in the curriculum that, if we don't give them the opportunity, they're not going to, right? With enrichment, it's like we're giving them more opportunities to apply what they're learning about concepts.
The other thing that I think is really important about enrichment is that it isn't just for the kids that maybe characterize as being your high-level students. Because enrichment is still important. Problem solving is still important for all kids. No matter where they are computationally, we want to make sure that all kids are getting opportunities to be problem-solvers, to apply their thinking in ways that work for them and not just the ways that we're asking them to through our curriculum. Acceleration, I think, often applies when kids are just well beyond grade level—but enrichment is really for every single kid.
Mike: Yeah, I think you answered, at least partly, the question that I was going to pose next, which was a question about access. Because at least with Concepts Quests, which is the MLC supplemental resource, we would describe this as a tool that should be made available to all students, not a particularly small subset of students. And I'm wondering if you can talk a little bit more about the case for that.
Tisha: So, if we go back to our lasagna problem, once our kids have had opportunities to read it and make sense out of it, at that point, I truly believe that there is an entry point in these problems for any kid. These are not dependent on computation. So, a student can draw pictures. I believe that all of my students that I've had throughout my years of teaching were capable of drawing a picture to model a problem. Then I really believe that a good problem can have an entry point for every student.
Mike: The other thing that you're really making me think about is, how much we've equated the idea of enrichment, acceleration. We've fused those ideas, and we've really associated it with procedure and calculation versus problem solving and thinking creatively.
Tisha: I think that happens a lot. I think that's a lot of how people think about math. You know, it's who can do it fast, who can get there? But what I think our goal is, is to create students who are not just able to be calculators, but who are able to apply their understandings of multiplication, addition, subtraction, division. They can apply them to novel problems.
Mike: Yeah, and the real world isn't designed with a set of “Free set, here's what you should do, repeat directions.”
Tisha: (laughs) I would love some of those. Where can I find them?
Mike and Tisha: (laugh)
Mike: This has been fascinating, and I think we could and probably should do more work on Rounding Up talking about these versions of enrichment that are available for all kids. And I have a suspicion that this conversation is going to cause a lot of folks to reassess, reevaluate, and reflect on how they've understood the idea of enrichment. I'm wondering if we can help those folks out. If I'm an educator who's really interested in exploring the idea of horizontal enrichment in more detail, where might I get started? Or, perhaps, where are there some resources out there that might contain the types of problems that you introduced us to today?
Tisha: Well, of course, I have to say Concept Quests. We've put a lot of work into creating some really great tasks. But some other places where you can find tasks that are engaging and help kids to think more deeply are Open Middle and NRICH and YouCubed are just a few resources that I can think of off the top of my head.
Mike: Ahh, those are great ones. Tisha, thank you so much for joining us. It's really been a pleasure to have this conversation.
Tisha: This has been so fun.
Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling individuals to discover and develop their mathematical confidence and ability.