The Future of Math Education Highlights: Blended Learning and Promising Practices

Webinar Date: February 26,2014

Webinar Description

In the Blended Learning community’s latest webinar, Elliot Sanchez joined Dr. Tim Hudson, Senior Director of Curriculum Design for DreamBox Learning, Inc., and discussed the future of math education. Elliot, Founder & CEO of mSchool, and one of the 2014 Forbes 30 Under 30, is a leading education innovator with 14 state-funded classrooms that successfully leverage blended learning. Elliot and Tim discussed mSchool’s approach and successes, blended learning, formative assessment, meeting the diverse needs of all students, Common Core State Standards, and digital learning technologies. They provided a recap of insights from the January 22, 2014 The Future of Math Education: A Panel Discussion of Promising Practices webinar, with a focus on blended learning. That panel included NCSM President Valerie Mills, renowned math educator; author Dr. Cathy Fosnot, and past NCTM and AMTE President Dr. Francis (Skip) Fennell. Everyone interested in the success of all students in learning mathematics—educators, parents, and community members— can appreciate the valuable insights and approach to innovation from these education thought leaders.

Webinar Presenters

  • Elliot Sanchez - Founder at mSchool, Louisiana

View Transcription

Tim:So I’m excited to introduce our speaker for today’s webinar, Elliot Sanchez. Elliot is the CEO and founder of mSchool, which is an ed-tech startup that makes personalized learning incredibly simple for schools and community centers. Elliot started his career as a math teacher at Booker T. Washington Alternative Middle School. And later, he managed STEM initiatives for 700,000 students in Louisiana. He’s also served as a consultant for two State Superintendents of Education. Elliot has been featured in The Huffington Post, Education Week, and has been a guest author for Google’s official blog. mSchool has earned national recognition, including Teach for America’s 2013 Social Innovation Award, and Elliot was included in Forbes Magazine’s 2014 list of 30 under 30.

So we have a lot of things, excited to hear from him about the things they’re doing at mSchool. And without further ado, I will turn it over to Elliot. He’ll come on, and I will step off. Thanks, Elliot.

Elliot:Thank you, Tim. Appreciate it. I’m really excited to be here and tell you a little bit about what we’re working on at mSchool, what we’re doing and really just to share our perspective on how we’ve seen blended work in the classroom for students. It enabled us to do things with our program that I don’t think we would have been able to do if blended learning technology hadn’t gotten to where it is. And DreamBox has been a big part of that success, so I’m really excited to be here with Tim and Ingrid today.

Just a quick overview, what mSchool is. So we are a program that helps bring what we think is the best of blended learning to students in communities and schools. And I’m going to start by telling you a little bit about how we decided to make that our work, what I was doing before and how it kind of led me to this and then also, specifically, some of the things we think have seen get in the way in the implementation of blended learning and how we’re trying to tackle it and make it work for students.

As Tim said, I started off teaching in alternative school settings, but I later went on to manage STEM initiatives, and I’ll tell you a little bit about that, at the Louisiana Department of Education. We saw some real promise, but we also saw real barriers from the system level to making this work in all classrooms for all kids. And so I’ll talk a little bit about how we tackled this specifically and also how it impacted our work in the alternative and parenthetical education portfolio of our school district as well.

So let me start with a little story. About five years ago, I was standing in front of my classroom at Booker T. Washington. And towards the end of the class, we just taught a lesson on equations with exponents, and I put this problem on the board. And students had whiteboards and their markers, so everyone was working to solve this problem, making notes. And I noticed one of my students, Newman, stayed right in the center, had this really confident look on his face. So 30 seconds is up. On the count of three, everybody held up their whiteboards. About half the class had it right. About half the class had it wrong. And Newman, in big letters he said, “Forget math” in so many words. It wasn’t exactly that, but he was bought in and he was frustrated. He was frustrated because that day, I had failed in my role as a teacher, and a lot of teachers before him had struggled. He just had not been able to grasp the concepts we were working with. And that’s how I knew I wanted to dedicate my work to finding new and interesting ways to reach students who just hadn’t been able to connect with the material before.

One of the things that I always think about and surprised by every time is the fact that since the 1800s, around 1860, 1870, schools have looked functionally the same way. Now this may not be true for those of you trying to really innovative blended models, but for the majority of students, we work on 30 students to 1-lesson-a-day model. And it’s successful for some students, and for others, it’s not. Still, one out of four eighth graders in the United States today struggles with algebra writing skills, and they’re disproportionately students of color and students from low-income communities.

When we look at the U.S. overall performance, it looks, in terms of rankings internationally, like we’re almost there to Russia in the top ten, doing alright. Wouldn’t have medalled in the Olympics at ten, but it looks like we’re doing alright. But that’s not a complete story, because if we break it down by students who are working in schools with less students on free and reduced school lunches with schools with more, the schools who have at least half of their student population on free and reduced lunch scored almost as good as Slovakia on the TIMSS test. And I think that tells us something. I think it tells us that there’s a lot of things that we’re working to overcome working with students with disadvantaged backgrounds but also that whatever we’re trying, it pushes us I think to come up with new and innovative ways. And that’s really how, at mSchool, we’ve seen the promise of blended learning.

When I was working at the State Department of Education in Louisiana, we had put together this chart. And essentially, what it said was our goal was to get all students to perform at or above grade level in math by eighth grade. And that was the goal. We knew we couldn’t be there overnight, so our target by 2012 was to get 68 percent of students there. So you’ll notice on this graph as it moves up across 2009, 2010, 2011, 2010-2011 was the last year we had data for. So ’11, ’12 was our estimate of kind of the natural growth of where the students would be. And this is all the students in the state. The things on the right-hand side are all of the different interventions we had tried, and that runs a wide range. So you’ll see here the acronyms that look like gibberish. HPHP is high-performing, high-property schools, 21st century community learning centers and the one below that. We had principal-to-principal mentoring programs. We had different curricula and different professional development programs that we kind of placed.

And when we said if we take the effectiveness of those programs and we turn it into a percent and we calculate, based on the amount of money we have in the budget, how widely we can spread those things, how many students do we expect, by rolling these out, to go from failing at the end-of-year test to passing? And when we did that, we saw a modest improvement, but it wasn’t nearly enough even with all the money we had in the budget to solve it. And then we started to look into blended learning programs and kind of innovative learning models that were very different, and we saw something that was incredibly promising.

To give you some perspective—so this equation is not a real equation for the blended learning sticklers out there, but I’ll get to it in a second. We have student A and student B. And the real power of the adaptivity we’ve seen was that for student B, even if they failed lessons on their way to their goal, we could go back and remediate and bring in these dynamic elements. And it may take them more lessons overall, but we thought that by letting those students work at their own pace, we could get a lot more learning happening in one classroom over the course of the year.

And we also noticed that it made student classrooms look very different. In the pilots we’ve seen throughout the state—we had a couple of different districts who had done small pilots back in 2009, 2010. We saw students were working in groups collaboratively. They were spending a lot of time with technology, but also, you’ll notice the role of the teacher had shifted some. The teacher was facilitating, and managing the technological responsibility, but was also analyzing data a lot. And that made it difficult to put into the current professional development system we had, and we needed to get that message out to teachers.

The payoff for all these though, these changes in the way that students spend their time learning to work on different things, allowing them to take a technologically driven approach, was that on the few pilots we had for blended learning back in that time, the result was far and away about ten times more effective than the next most effective intervention we’ve seen. In fact, if we had just rolled out a modest increase in those pilots, we could have had all those students reach their targets by the end of the year.

The reason I think this is most effective—there’s a lot of great explanations about how that allows for greater time on task and zone of proximal development for these students, how it allows teachers to make more efficient use of their time and to spend the face-to-face time on behalf of the students who need it most. I like to think of it in terms of an analogy. What we saw really is that learning was equal to the quality of instruction that was going on and student readiness. And at first, I’ll be honest, I was focused on making my instruction really fantastic as a teacher. And I realized that even if I gave a fantastic lesson some days, there were students who were missing some fundamental skills that they would need to be able to really take it in and benefit from it. And so if my lesson was great but my students’ readiness was very low, I didn’t have much learning going on.

And the light went on in me in blended learning when I realized that even though some of the best blended lessons that we’ve seen or best technologically driven lessons, whether it’s video lessons or game-based lessons, aren’t nearly the same quality as what you’ll see an exceptional teacher able to do with that student. Even if they’re less effective or less engaging, comparing real person to a computer, if they’re closer to the student’s readiness, we saw that there’s still a major impact. In fact, I started thinking about it in terms of this kind of an equation, and we saw that this kind of mirrored our real-world results. If we put students who were just not ready for on-level material and let them work in an environment where they can work at their own pace in adaptive settings, making sure that they were staying in that zone of proximal development, we would see gains that were sometimes twice as fast compared to what they would have in a traditional classroom, being taught in a room where maybe all of the material wasn’t on their level or they weren’t ready for.

So that’s when I tried to take this pilot we’ve done with some of our districts back in 2009, 2010 and roll it out to more students. And because of the way that we had structured it, it was very difficult, and it turns out the only thing we really were able to do is find out that our baseline instruction was pretty good because we weren’t able to roll out any of those additional new programs. There were logistical hurdles, funding hurdles, and the results for those years ended up looking like this. So I was kind of frustrated by that experience and seeing some early pilots that were really promising and I knew it could help students who were struggling to succeed in school. And so I then went to go work with our districts. I approached our local school board here in New Orleans and a couple of other districts. And they were intrigued by those pilot results as well, but there were a lot of things that were competing for attention. There were a lot of constraints on what they were able to do, and none of the districts that we approached were able to roll out and expand these pilots on their own.

And so I had not been able to push blended or expand blended opportunities at the state level and the district level. And so I was almost going to give up, but a few weeks after that, I was working in one of our local community centers here in New Orleans. This is an Always Pursuing EXcellence or APEX community center here in New Orleans in the Broadmoor neighborhood. And the students who were there were many of the same students I’d been working with in my classroom, but they were there because they needed a place to go. It was a safe place for them to hang out or work on homework after school. And I realized that even though they didn’t have a lot of the resources as a traditional school environment, they also didn’t have a lot of the same constraints. And so I approached them and asked if we could take some of the technology we’d been working with and just bring it to their students. We had a small grant of a few hundred dollars to begin with. And so we went out and bought the cheapest tablets we could find, and we put them in the hands of those students. These are some of the initial pictures from that first year of pilots, and as you can see, we’ve got blended learning going on next to a pool table, in the middle of a larger table for homework help. This was really just anywhere we could get it in the hands of kids, making it available to them.

And they really loved it. We saw students who would show up consistently for 90 minutes after schoolwork was done not to work on their homework but to work on some of these blended learning programs, DreamBox being the first one we tried. We were excited, but we didn’t know if we would see the results. And it took us, actually, several months until then to see the results. In the meantime, we were working on the logistical challenges, and I think this is one of the places where our kind of struggles to make it work will hopefully be helpful to some of you if you’re thinking about making a similar shift. In your classrooms.

The big three problems we had getting this program rolled out, setup tended to be pretty complicated, and it tended to be pretty slow. It took quite a while for us to bring the community center in and train their volunteers and their directors what this was, how it worked, how to use it. We didn’t have any of the benefits of a grade-level grouping, so we didn’t know where to begin with most students. We just had a mixed-age classroom, everywhere from third grade to tenth grade. And we were stuck thinking in this one-size-fits-all framework. We didn’t know how we were going to find a solution that was going to work for all of these different students at all of these different levels and all these different ages.

And so we solved them one at a time. First, on the setup side, rather than try to get the best technology available and the best things we could in terms of tablets or laptops, Internet connection even, we went with the cheapest, quickest setup, home-level Internet connection. We just had one of our cable providers come out and hook up high-speed Internet at the lowest speed family tier. We then put everything that one of the centers would need in a box, and we sent it to them with the instructions taped to the front of each computer. We were using very cheap hardware. Like I said, just $100 tablets to start, and we eventually upgraded to $200 notebooks. By putting everything in one place, we realized we could kind of speed up this process of getting everyone situated. And with the instructions on each computer, it wasn’t perfect. There was still a lot to learn, but it was enough to get the students started, and that was the biggest barrier for us.

For grade level grouping, we eventually decided that we would just focus exclusively on getting informative assessment in the beginning and taking a comprehensive inventory of where the student’s skills were, and then we ignored their grade levels. We had students on third grade through tenth grade working on anything that was developmentally appropriate for them. And that was a scary prospect at first, but it was also very freeing. We ended up having third graders who were helping sixth graders on the same material. They could work together because we hadn’t separated them out by ages. We just said, “Help whoever you need to. Ask for help from your peers. But everybody here is here to help the others learn.” And with that kind of culture set, students were able to kind of feed off this one-room schoolhouse and really make a lot of progress really quickly.

The last for the one-size-fits-all. What we ended up doing was looking at a lot of data, and eventually, stitching together a combination or resources. So rather than try to find one perfect fit, we experimented. We tried out a lot of things, and we eventually settled on specific programs and specific resources for specific skill gaps. And then when each student comes to that skill gap, we know exactly what we can bring to them at that time. That approach can be logistically complicated. We wrote some software that can help us do that for a lot of students at once. But in a normal-sized classroom, if a teacher is comfortable using several different resources, then it’s really just that same process of stitching them together into a ladder or scaffolding that would make the most sense for that student’s progression.

So how did it work? What were the results like? Well, we ended up with classrooms that looked very different than most traditional classrooms. It was dynamic, maybe a little chaotic at times, but we also had a lot of volunteers who were able to come in and work with students in each of those different levels. Some of the students worked on their own. They didn’t want a lot of help. Some of them wanted more encouragement than anything. But by the end of the year, the one exciting part was that the program had really been incorporated into the community center. This is that first community center I showed you. We’re now at over 40 different schools and community centers within a couple of hundred mile radius of here. It became theirs where it was theirs and the school. They got to own it. Their students knew it just as their program. And the academic results were incredibly encouraging.

This was early on. We saw a student named Jazz entered the program as a sixth grader working on a third grade level. And after six weeks, she was able to make up two years of academic delay. She was a star, but all the students at that time gained at least half an academic year in shortly over a month. When we were able to get end-of-year assessment data, this is from the NCLB-mandated district-administered test, we had a control group of students who were in those same schools but did not attend the community programs and then a different group of students who did. We were able to see those students who had supplemental mSchool make 2.9 years of learning growth in one year. We added reference to the standard deviation so we could—that 2.9 years of learning is using naturally norm data, and the actual difference in the scale scores is based on Louisiana norm data. But that was far and above what we’d seen other places achieve in a game-based approach and also really exciting, because we didn’t have to fight through a lot of the barriers that schools and districts often do that compete for their time and energy. We were able to just bring it to the students and get them started right away. And so our hope is that if we were able to do it, teachers will be able to as well.

We’ve definitely gotten some accolades, but I think the most exciting part for us has been the communities across the world that have reached out to us asking for something similar. We’re only in this healthy starting stage right now, and it’s taking us some time to build up our technology so we could handle more students and manage this kind of process for more centers. But there’s really not a lot of barriers to a well-informed teacher who’s willing to do some tinkering doing this in their own classroom. All of the pieces were really simple, but it took us thinking through some of the real challenges on an implementation in order to make it work in the real world.

We’re hoping to expand as fast as we can over the coming year. But if there are ways that we can help share more about the challenges we faced and help encourage you take on some of the same ones in your classroom, in your district, then I think, hopefully, this idea and this potential of blended learning will expand much faster than we’re able to do.

So thanks, and I’m looking forward to being able to answer some of your questions later on.

Tim:Thanks, Elliot. Go ahead and stay on right now because I think there some …


Tim:Yeah, let’s go ahead and tackle a couple of questions. So first of all, you mentioned that it all started with APEX, right? That was Always Pursuing Excellence. And that was the first—it’s like a supplemental education, right?

Elliot:That’s correct.

Tim:And the kids are doing that before and after school both?

Elliot:After school mostly.

Tim:After school mostly. And then when you said you’ve now expanded into 40 different sites, one of your slides said they’re like Trinity Christian School or whatever, those are the sites where things are taking place?

Elliot:Exactly. And some of those are community centers that are separate from any school. Some of them are teachers who reach out to us and actually set up an after-school program on their school campus but just after school hours. And some of them are schools that actually set up a whole program on a different location but it’s only their students who go. It’s just that they didn’t have the time for building or the hours for their staff to be able to manage it.

Tim:And it’s very site-driven you said as well. You said it’s their mSchool.

Elliot:Yes. And I think that has actually been an important understanding for us, was that we had thought about it at first in terms of managing logistical challenges, but we realized it really took some ownership and investment on the part of the people who were going to be there every day. But every time we found somebody who was excited about it and excited about the prospect, they were able to make it succeed. And it wasn’t always people who have had a lot of formal experience or a lot of training. But with some supplemental help and really just some determination, they were able to get the programs to work for their students, and it’s made the difference, really, to have them there.

Tim:Great. If you talk a little bit about how there’s sort of student achievement progress information exchange between the mSchool and the student’s school. In attempting to personalize it at mSchool and have third graders helping sixth graders and things like that, is there—I mean do students show up at mSchool with, “Hey, this is what I’m doing at school. Can get some help?” Or is it when you walk in it’s we have a database at school and we’re going to pick up where we left off yesterday? How does that sort of blend work, I guess?

Elliot:Yeah. One of the limitations of what we’re doing is that it isn’t really well integrated into what the students are working on day to day. We definitely stepped outside of some of the constraints, but we also lost some of the advantages of kind of having a collaboration. The ways that we’ve been able to build that back over time have really been around making sure that we’re encouraging the students to celebrate their success, not just with us but also with their family at home, certificates, achievements, awards, and also bringing that back to the school. So every single school that we have a student that’s come to an mSchool but is attending from another school, we go back to their home school and we meet with the principal at least once a semester or whoever their data manager is. And we’ll go through a comprehensive report and show them what those students were able to achieve, what lessons were they able to pass, what standards are they still struggling on. And for them, for those administrators, it’s really helpful, hopefully, but there’s nothing they have to do with it, right? We’re hopefully a supplemental solution that is something that can support their work.

But because we’re driving it almost exclusively of our assessment of what standards are still weak, it may not have anything to do with the skills that they’re working on at school. Sometimes that can be a good combination, especially if the students need remedial work that they need to stay on pace at their traditional school, but I think it’s definitely not the perfect solution. It’s not the solution for everyone. It’s just the one that we have been able to find can get a lot of traction on the ground pretty quickly.

Tim:Yeah. Yeah, we have a similar thing with DreamBox where students might be working on different things in DreamBox than they are in their classroom, and it’s a matter of an additional data point that DreamBox provides as well as students need differentiation and schools aren’t always set up to accomplish that differentiation. There’s a question in the—a couple of things in the comments that came through, actually, somebody who’s in New Orleans who was interested in visiting one of your sites.

Elliot:Hi, Paula.

Tim:Yeah. If they wanted to come visit the site in New Orleans, what would be the best way to sort of take a tour or set something up?

Elliot: Yeah, absolutely. I’m going to go back to—can I go back to the slide where I have my email address on it for a second?


Elliot:Is that alright? Let me see if I can jump back there momentarily. I’ll say it as well, but it’s So send me an email, and I’d be happy to. We’ve got sites. If you’re familiar with the ones within your area, we have them on the Westbank, Mid-City, Algiers, Holly Grove. We have had programs that have been done in partnership with about a dozen schools, International High School, Algiers Charter School Association, Lafayette. I think we’ve got schools in Baton Rouge as well as McKinley. So yeah, there’s schools all over the place. We’d love to have you come see, and we’re really excited that we can have people from the community come in, have all of the educators come. We do about a tour or two a week just to share what we’re learning and hopefully learn from other people as well.

Tim:Alright, great. Well, I’m sure we’ll have a couple more questions towards the end. So thanks for sharing that.

Elliot:No problem. Thanks. I’ll be waiting in the background.

Tim:Alright, cool. We’ll see you in a bit. So for the next part of our conversation, just to share a couple of highlights from a great panel discussion that happened online last month. Between—I’ll go ahead and just put it up here. And so a couple of—three fantastic thinkers, respected leaders, and educators in mathematics, Skip Fennell, Cathy Fosnot, and Valerie Mills and I moderated the panel. And there were a lot of great things that came up out of that.

The topics that we discussed were: formative assessment, it’s always a big topic; how do you ensure success for all students in an era of Common Core and choosing the right resources to make that happen. I mean, you really heard from Elliot a way that they’re trying to figure that out, obviously, state wide, trying to get all eighth grade students to efficiency and understanding in mathematics. And it’s not just a—it’s interesting. It’s an eighth grade problem, it’s a third grade problem, certainly, students from disadvantaged backgrounds performing disproportionately low in mathematics.

But also, as a math major, one of the things that I always pay close attention to is the attrition rate among math majors, and I’m pretty sure it’s one of the highest. I don’t have the most recent statistics in front of me and just now, I was thinking to include that. You know, we have so many students who graduate high school and go in to choose to be a mathematics major, and we really need to explore the reason why they bail at a disproportionate rate as well. That’s another issue. Those are students who think they could succeed as a mathematics major.

Then lastly, the question of selecting and implementing digital learning resources which also is something that Elliot spoke to as they’re trying to just get the minimum bandwidth Internet connection, to get the cheapest hardware but really find a high-quality learning software to reach all students. How do you do that in your own context and with your own resources?

So formative assessment, these are the two guiding questions that panel discussed. How do we make sure that it’s not just another thing to do? How do we recognize that it’s an integral component of learning? That without formative feedback and assessment while you’re learning, you—it’s very difficult to learn? It’s not just another approach to assessment. It’s critical to making progress.

Cathy Fosnot started with this great quote. It’s not even about formative assessment, but it’s about mindsets about assessment and learning in schools from an anthropologist named Jennifer James. I remember I heard her speak back in—last 2007 or 2008 at the Learning Forward Conference, which is formerly NSTC. And she talked about culture as this tapestry, this body of assumptions and beliefs and practices that we accept as foundational and define who we are. And in a time of great change, as things look like they’re being torn apart, everything’s—you know, with fewer resources, higher standards, global competition, all of these different factors, things seem to be maybe falling apart. We kind of look backward, and we become pessimistic about the present because we’re not sure what the future looks like.

And that kind of describes how a lot of blended learning models are. It’s hard to envision how that will look in 5, 10, 15 years. And one of the things that’s kind of neat about mSchool is the approach to the—it’s a community kind of obligation and connection and relationship there, which is really neat. But in terms of formative assessment, what’s interesting is so often, we just think of I’m going to teach you a skill and I’m going to watch you do that skill. And I’m going to grade your paper, and there is the formative assessment. That’s the sum of it. And that’s kind of the old tapestry, and in reality, we need to envision new and better ways to think about formative assessment.

Fosnot went on to say formative assessment needs to foresee and even anticipate who is—that which is just coming into view in the distance. I like that. It’s not a matter of an a-ha moment. But understanding is developed over time, and they need time to make sense of things and really be able to transfer them independently. And so this idea of using—thinking of formative assessment not as an incremental skill-based monitoring but rather as a way to find out what kids are thinking, to figure out what are they just on the verge of understanding, what’s just coming into view.

And in her work—if you’re familiar with Fosnot’s work, this won’t be a surprise to you, she talks about you have to genuinely capture students mathematizing. You have to watch them do mathematics just like a great soccer coach needs to watch kids play soccer in order to know what they need to work on. Because you can pass in practice just fine, you can shoot free throws in basketball in practice just fine, but when the pressure’s on and it’s a game situation, how do you perform? So in mathematics, it’s the same thing. How do they model realistic problems? And how does that modeling give us evidence as educators of their understanding of key mathematical ideas?

Fosnot’s developed, with her colleagues, this idea of a landscape of learning, that it’s not an incremental, sequential—I mean you even saw on Elliot’s modules graphic. You saw the students failing and struggling, there’s this movement between different modules, trying new things. And in mathematics, you can be working on multiple mathematical ideas simultaneously. It just needs to be coherent, that students can be skip-counting, which is repeated addition in a way, as well as counting all strategies, grouping strategies, the counting of groups or early multiplication. So if you’re working on mathematics at the K–8 levels, her landscapes of learning are really helpful for formative assessment because they really give language to the ideas the understandings, the models that students are using and to be able to figure out where they fit on a coherent progression of learning.

Then Valerie Mills shared a couple of slides about three key elements of embedded formative assessment: needs to elicit evidence about their learning, close the gaps; gives educators information so they can adjust leaning experiences to close that gap; and then as an opportunity to involve students in the assessment learning process that in mathematics, too often, it seems as though all of the assessment is coming externally from the teacher or as opposed to a student having the opportunity to say, “This is really what I know well. I feel comfortable with this, not too confident about this,” but really using it as an opportunity to involve students in reflection, because that’s really what learning comes down to.

And so the productive goals and lessons need to focus on concepts and practices, not really specific mathematics problems but rather the concepts that are happening when students are solving the problems. Feedback has to be specific enough—I’m sorry. Assessment needs to be specific enough so you can gather that useful information about student thinking. And certainly, accuracy is one part of student thinking, but there’s also efficiency. There’s also the ability to deal with new problems. You know, every teacher has had it happen where you hand out the test, and a few minutes into the test, a student comes up to the desk and says, “Yeah, number four, can you give me some information about this. This isn’t a problem like we’ve seen before. It’s not familiar to me.” And as a teacher, you kind of have to say, “Well, tests need to measure your ability to transfer beyond what you have just seen and practiced already.” And it’s in those moments when it is an unfamiliar problem that you really do gather evidence of student thinking. Rather than students thinking, “How did my teacher show me how to solve this problem?” you have the student saying, “Here’s a problem. How should I attack it?” And that gives you great information as a teacher.

Goals and lessons need to be understood to sit within a trajectory of goals and lessons that span days, weeks, or years, that single lessons sort of sit in isolation in time but need to be connected between what happens before and happens afterward. And that’s a key planning thing.

This was an idea that Valerie suggested. This is a pretty typical textbook problem for simplifying expressions, and it’s just a matter of computation, solving them. And the suggestion that she made in terms of making this more formative is not focused on the answer, because quite frankly, Wolfram Alpha or a calculator can give you these answers and we need to give our students better reasons to understand math than something—sorry. We need to give them better problems worth solving that calculators can’t just instantly solve. So if we revise the directions to focus students on broader mathematical ideas, here was one suggestion that instead of saying, “Solve these problems,” say,“ Look at these problems, and identify which ones are going to be positive and which ones are going to be negative. Don’t fully simplify it, but describe the features of these expressions that helped clue you in to help you make the decision of whether it’s going to be positive or negative. And then you’ll have students circling things and saying, “Okay. These will be positive. These will be negative. Here’s how I know.” Maybe students don’t understand when you’ve got the negative symbols in front of the numbers that changes depending on the degree of the exponent and such. So that’s one way to maybe take something that’s pretty typical, skill-based computational thing that a computer can do and elevate it a little bit to have kids looking at more than just what’s the answer.

Cathy Fosnot gave this example, and it actually generated quite a bit of discussion. It’s called the two-pen assessment, and it’s a pretty simplistic idea for formative assessment where you give students, “Here’s a multiplication sheet.” And some of these are typical up to 12 by 12 times tables math facts, but there’s other ones as well that are related to the typical math facts. So what you do is you give students this assignment, and you give them two pens. One is—two different colors, whatever colors you prefer. And you say, “For the first two minutes, I want you to solve all the problems you can with the first color pen.” Then after two minutes, you say, “Put that color pen down, and pick up the other pen and solve the rest of them.” And give them as much time as they want. And what you get from that is a color analysis helps you recognize which ones they knew more quickly, which ones they were more confident in, that’s so confident that they said, “I only have two minutes. I’m going to do the ones that I know first.” And that elicits a great deal about problems that are related, because these problems all have relation to another problem on the sheet.

So for example if a student knows 4 times 25, four $0.25 is $1, and in the first two minutes, they, in their blue pen, write 100 but they don’t get the other problems, that tells you something about how they don’t understand multiplying by tens and don’t understand those relationships. Similarly here, if a student knows 2 times 13 and 10 times 13 but can’t use those facts to quickly figure out 12 times 13, then there’s a key misunderstanding there about the key distributive property, about partial products, which is pretty fun to figure out. Same thing here, if you know 3 times 9 but you don’t know 3 times 90 quickly, there’s an issue there. Maybe that student is just trying to remember all of their math facts rather than thinking about the numbers involved. And then, of course, these. These are fun ones in a sense that 12 times 9, if a student knows that but doesn’t know 6 times 18, that’s a doubling and halving thing. If you cut 12 in half, then you get 6. And then you double 9, to get 18. Those are very related, and students may or may not know the doubling and halving strategy. So that two-pen assessment is a pretty good idea. I like that quite a bit.

And then this is just one slide that Skip Fennell shared, a really high-level view of how—if you’re in a Common Core state, of course, you’re either part of the PARCC or the Smarter Balanced Consortia and thinking about the road to success on those assessments and really, mathematical proficiency on any assessment; thinking about student observations, kid-watching, interviews, have some kids to show you, exit tasks. And there was a bit of discussion about something called hinge questions that I don’t have more information on here, but you could run an Internet search on that. I wonder when we’re going to stop saying run an internet search and say, “Go search for that.” Adults say, “I’m going to do some research on the Internet,” and kids say, “I’m going to do research.”

So that’s kind of the high-level overview from Skip. Then we talked about success for all students in the Common Core era. How can we choose, wisely choose and create resources? There was a report, I think, that just came out last week that really looked at I think 45 textbooks that said aligned with the Common Core, which is a pretty rapid turnaround. And so there’s a bit of skepticism around things that are coming at the Common Core-aligned. And then what are the past initiatives about standards and resource implementation, is another thing we discussed.

And Skip Fennell started the conversation just by pointing out how often the word understanding shows up in the Common Core standards, that if we’re going to reach all students and help them be successful in deeply understanding mathematics, understanding is key. It’s in the standards. And also, the representation that you talk about, okay, students need to understand the fraction on the number line, but one piece of evidence that we need to have of that is students actually representing fractions on the number line diagram. And that’s in the standard, that multiplying whole numbers, that next one, illustrate and explain—well using what tools? And it’s right there on the standards. Kids need to be able to use equations, arrays and models, all three of them. And when you understand all three of those, it deepens your understanding of whole-number multiplication.

So you see there the last one, ratio and rate reasoning in sixth grade, reasoning about tables of equivalent ratios. Kids need to see tables of equivalent ratios, tape diagrams, double—yeah, I think it says double line diagrams. Sorry about that. So this representation, the focus on understanding are all heavily in the standards. And this was Skip’s big point. Conceptual understanding is no longer an option. It shouldn’t ever have never been an option, but it’s an expectation. And Skip feels it’s about time, so it’s right in there.

Valerie shared if you’re interested, you can go to this website. This is as President of NCSM, the National Council for Supervisors of Mathematics, they’ve developed some tools—it’s a toolkit for Common Core curriculum materials and analysis, and you see there And what you’ll find if you follow that link and are interested, of course, an overview and three different tools about content analysis, mathematical practices analysis, and some overarching considerations about equity, assessment, and technology as well as a facilitator’s guide and some PowerPoint slides, so a really helpful resource there from NCSM.

And then Cathy Fosnot suggested, you know, we need to take the Standards of Practice seriously, the Common Core Standards or Mathematical Practices, which are similar to mathematics process standards the different states have had over the years. And so we really need to think about that’s the way students are mathematizing their world, to say when the Common Core Standard says students need to look for and make use of structure, inherent in that is that students need to spend time in math class looking for structures, that they need to be doing that independently. Going back to the formative assessment point, that if students are actively looking for structures, teachers have a great opportunity to observe students in those investigations and gather evidence of the ways students are structuring and understanding structures of mathematics.

Professional development for teachers is so important. That’s what Valerie and Skip and Cathy, all very dedicated, spend tons of time in their careers emphasizing the importance of and actually doing the work of professional development for teachers of mathematics. And then lastly, thinking about how—thinking about mathematics learning and progression not just as a bunch of activities for kids to complete in order, a series of packets, for example, but really crafted sequences. And this is that landscape of learning from Cathy Fosnot I was sharing earlier, that the sequences need to be well crafted to support progressive development, to support strategic learning trajectories, the way that students naturally mathematize their world.

And the last topic we talked about was digital learning. How can we use technology to meet the needs of every child? It speaks back to what Elliot was talking about in blended learning and ways to optimize student learning and really reach the most number of students quickly with great learning. And how can we be—how can educators wisely select and implement these resources? I like these two questions as well. When does blended learning benefit from the inclusion of digital instruction? And when might it undermine learning? It’s a great question worth probably a whole webinar by itself.

And then what do teachers and administrators need to learn about effectively facilitating learning using digital resources? And what will it take for educators to develop this expertise? And Andy throws in a good question there. What do we want the technology to do? That’s exactly right, and that’s a whole backwards-planning idea. You first have to decide what you need students to accomplish in learning, and then choose the tool. Whether it be a classroom, whether it be a one-on-one, whether it be digital learning resources, the goal has to drive the strategies, without a doubt.

And I think that last bullet point too kind of speaks to the implementation and data conversation that Elliot and I were having. How do we—when students are doing more and more things perhaps in an mSchool or a community center or using a software like DreamBox, how does a school within a community respond to what students already know before they walk into the classroom? That’s a key thing as well.

When I think about digital technology, I love this tweet. It came through during the iNACOL Conference last year. And it’s not math related, but it could be, right? We’ve got teenagers asking, “Do I really have to be here at school to listen to a history lecture at 7:22 in the morning? Is this the only way I can earn this credit?” And I think that’s a very valid question that we as educators need to make the most and best strategic use of students’ time in the classroom. We really need to honor their time and make it worth their while. If it is just a lecture, then 7:22 in the morning is not when any of us in the webinar would like to attend it. So let’s be thoughtful about making the most and best use of class time.

And when I think about digital learning resources, as I’ve shared on this slide in other webinars I’ve done. Michael Fullan and Caitlyn Donnelly in their “Alive in the Swamp” report last July pointed out that too many technology tools are—they have a problem with pedagogy and outcomes. The innovations are using basic pedagogy. It’s video instruction. It’s a series of exercises. Or it’s just the same old tools that are just in the digital format. And we need to do better and expect better, and that’s one of the things we try to do at DreamBox. There was a great tweet too related to this from a physics teacher in New York, Frank Noschese, “The biggest shift in teaching will not happen by replacing textbooks with iPads but by replacing textbooks with experiences and questions.” And that is the best use of students’ time in the classroom and out of the classroom.

So Valerie Mills shared these ten design considerations when evaluating digital learning resources. You first want to make sure that there’s multiple representations involved. And I won’t read through all of that slide. I’ll just let that sit there for a second so you can have a chance to read through it. Mathematical discourse is valued. That’s a key one. So then the remaining ones, four through ten: tools should support the learning environment; variety of formats; mathematical experiences provided, number six, build conceptual understanding in conjunction with procedural fluency, and really take advantage of the technology. That kind of speaks to Fullen’s point as well. We have amazing digital technologies available, and we should be inventing and creating new learning experiences, which actually will be my last slide here coming up. Number nine, suggestions from the teacher, monitoring learning, and then the supplemental activities as well.

So last thing I’ll share, kind of along that point about let’s use digital technologies for the—let’s use them in new and innovative ways. If you’re not familiar with the SAMR Model, it’s pretty helpful. And you see the reference there at the bottom so you can go and learn more about it. But technology can be used just as a substitute. That’s like just a PDF of a worksheet on an iPad. There is no functional change. It’s just the same worksheet on an iPad. Then there’s augmentation, where maybe students can enter in answers into that iPad worksheet. So there’s a little bit of functional improvement in terms of data collection, but it’s still pretty much a substitute for a worksheet.

Whereas modification, where you’re actually creating new tasks. There’s significant ways to redesign learning tasks. That’s the modification and then redefinition. We create new tasks that were previously inconceivable without technology. And that’s the difference between enhancing what’s previously done or what’s done in the past as opposed to transformation, doing new things in new ways, all, of course, to the question earlier, in support of key learning goals. Now that’s one of the things we do try to do at DreamBox, invent new digital manipulatives that really empower kids to make sense of mathematical ideas. Yeah and TPack as well, Teacher’s Pedagogical Content Knowledge. Thanks, Andy, excellent point.

So now, we’re going to do a second round of Q&A. And if Elliot wants to hop on and—I don’t know, Elliot, maybe you have some questions for me. I don’t know. I wasn’t following the screen all that well, but Elliot, after I shared my piece, anything you want to build off of and talk about things I shared that maybe you’re doing at mSchool or questions you thought you have?

Elliot:Yeah. I mean I think the distinction between the SAMR model is really critical, because I think that there are a lot of people who are justifiably skeptical but they’ve seen technology we have to do in the classroom. And I think a lot of that is because they see people who are substituting it in. I was reading the other day, they talked about the fact that putting textbooks on iPads was not any more effective. It wasn’t any more effective than just using paper textbooks. And I think in the substitution level, we’ll see very limited results like that. But I think opening educators’ sense of possibility to what does it look like if we’re actually opening brand new tasks, if we’re using this as a tool to be able to create things that students wouldn’t have had the opportunity to create for years, until after graduation generally and bringing that into the classroom, I think that transformative space is really the one that, if we invest the effort into it, is going to really just open doors for students in ways we didn’t think was possible.

Tim: Here was one question. I’m going to go ahead and display it from Andy, “How can we get students to construct knowledge? Creators rather than consumers,” which is such a key thing. At DreamBox, we always want students to be actively involved in thinking, in reflection, in strategizing as opposed to sort of sitting passively and being a consumer. And I mean our design approach at DreamBox is we get students to construct the knowledge which they deeply understand by empowering them to make sense of it with the manipulatives that we create digitally.

And some of the manipulatives that we use have been around for decades, like counters and these things called math racks. They’ve been used for decades. And what we’ve done, to use the SAMR model, is we’ve actually been able to digitally modify the tasks so that whereas a teacher with 30 students couldn’t necessarily get around to every student to watch what they’re doing with the manipulative, with our software, we’re able to actually ask kids questions that are not only, “Build this number,” but also, “Build this number in an optimal number of moves,” which is something that’s not really possible either for teachers to monitor or to really capture as kids are working with their hands. But as we’ve gotten into more abstract mathematics concepts, we’ve actually—yeah, we’ve had to invent some new manipulatives that couldn’t exist with plastic or wood because it’s critically important for students to be constructing mathematical knowledge and making sense of it with those manipulatives. It’s a key design consideration.

Another questions—and this is—Elliot, I’ll pose this to you. This was one that came up. You mentioned you are using DreamBox at mSchool. What are the other programs that you are using for math or for other things?

Elliot:Yeah. We have kind of a multipronged approach. So for students who are in high school, we’ve used things from Think Through Learning. For middle school students, in addition to DreamBox, we had stuff from Curriculum Associates and MIND Research Institute. But we also have a lot of standalone resources, individual Khan Academy videos or lessons that teachers have put online that are not a complete resource but could potentially help at a very particular place in the student’s development. So we’ve got a resource library that students can go and pursue and find those things. So I think, for us, we’ve really seen it be find the best things that we can for certain needs and then expand the number needs we can meet by finding as many resources as we can.

Tim: One last question, Elliot, as you mentioned that sort of quality time’s readiness, that sort of formula, which definitely resonated with some people in the chat box. Can you talk a little bit about how you assess the readiness?

Elliot:Yeah, assessing the readiness. So we have—each student that came in complete a comprehensive adaptive assessment that hopefully, in about an hour, can give us a read not just on the student’s grade level but also their approximate grade level in each of the five major mathematic strands. And from there, we start to give more specific questions. So if the student is in DreamBox and we see that they are working on something that they’re consistently struggling on a specific skill, we can go through and kind of add that to the information we know about the student. Say, “Well, we thought you were at this grade level here and we see you struggling about here, so yeah, we want you to keep working on DreamBox and go do the lessons that DreamBox is going to put in front of you.”

So if we had a student that came in, looked like they were on seventh grade level in some strands and second grade on others, then we may have them split their time and use some programs to keep them going at that seventh grade level. We can get ready for high school readiness, but maybe an entirely different set or resources and tools for them to build from that second grade level in certain strands. So really, the assessment is kind of the backbone of how we would design a program around a student. And really, that’s the goal. We want to personalized learning to be an avenue to designing a program around each student not just the first day you walk in the door but every day they walk in the door after that. And the assessment is the way that we know where to begin, and it’s the way that we know if we’re succeeding over time.

Tim:Alright. Excellent. We’re coming up here on the end, so I really want to thank all the great questions that came through, thank everyone for participating. And certainly, Elliot, thank you so much for sharing what you’re doing at mSchool. It’s really exciting, and thanks for sharing the specifics of how you’re really making a difference for kids.

Elliot: Thanks, Tim. Glad I can be here. Thanks so much for having me.

Tim: Alright, great. So in conclusion, let me tell you a little bit about DreamBox in these closing minutes. At DreamBox, we combine three essential elements to accelerate student learning and understanding. As I mentioned earlier, DreamBox is a web-based adaptive math program for students in grades pre-K through 5 that differentiates uniquely for students. And we have some middle schools using DreamBox for intervention.

It’s rigorous mathematics. Kids have to think critically and conceptually. It’s not practice, but the practice is embedded and seamless in it. We don’t start our lessons by saying, “Here’s how to do it. Now go practice it.” Things like fraction division, invert and multiply, which everyone knows but nobody understands, but we hold ourselves to a high standard of understanding in DreamBox.

We have full-time experienced classroom teachers in our staff. We work with our talented programmers and creative team to build those manipulatives for sense-making I was taking about and really capture how students are thinking with like the array, the number line, those sorts of things, and focus on developing vocabulary. So when students are done using DreamBox and go back into their classroom, they can talk about mathematics in the language that needs to be conversed about. So we also have the adaptive engine, the intelligent adaptive engine which differentiates for students in real time. We have non-linear learning progressions. Students counting by ones, they need different lessons than if a student is counting by tens.

And then lastly, the motivating learning environment where we have engaging context, highly visual, concrete, and really highly-interactive virtual manipulatives. We really believe, as all teachers I think do, quality learning on a software is just as important as the quality of learning in the mathematics classroom. So we make sure that we adapt to students’ own intuitive strategies, like we talked about earlier in the webinar, the kinds of mistakes kids are making. Here you see fraction multiplication, double-digit multiplication, and adding double-digits on the number line, just three examples of our lessons.

We also have Robust Reporting. That’s a key thing that you heard Elliot speak about and really, as we get into more—as we get more information about what each student knows, DreamBox provides the kind of reporting at a very young age. You can put preschoolers and kindergartners showing what they know and how much time they’ve spent using DreamBox and how far the progress that they’ve made, making achievement the constant and time in DreamBox the variable, because we have to get all students to really deeply understanding.

And then providing teachers with tools for differentiating in their classroom. At the click of a button, teachers can pick a particular math concept or standard and see which student already know it, which students are working on it in DreamBox, and which students haven’t started it yet so that they can make that strategic use of class time, like I discussed. We also have a lot of our virtual manipulatives available for free online at, where any teacher today can go and check those out and use them with their class to help them make sense of some mathematical ideas.

Lastly, if you’re interested in a free school-wide trial, just go to our website,, and either click the orange bar up at the top that says get a free school-wide trial just go to /freetrial and you can find all sorts of great videos and information and our blog as well.

So I want to thank you very much for your time and remind you to join our edWeb Blended Learning community if you haven’t already.