Author Archives: bstockus

Take It Away – CGI National Conference 2017

At the end of June, I attended (and presented at!) my first CGI National Conference. I also visited the Pacific Northwest for the first time in my life. Seattle was beautiful and the learning was great. I know there are folks out there who aren’t able to attend many conferences, so hearing from attendees is one way they learn from afar. So, in case you weren’t there, let me tell you what resonated with me from the conference.

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One thing I especially liked about the conference was the essential questions. Speakers weren’t required to connect with them directly. Rather they were designed for participants to personally consider and reconsider as they attended keynotes and sessions:

  1. In what ways are your students allowed to bring “their whole selves” to the learning of mathematics in your classroom and school?
  2. What do you know about the cultural and lived experiences of the students in your mathematics classroom? (How can you broaden your knowledge?)
  3. How does your mathematics classroom interrupt and/or reinforce narratives of who is and who is not capable mathematically? (How could your classroom become more interruptive vs. reinforcing of these narratives?)

Not what you’d normally expect at a math conference, right? The focus on culturally responsive pedagogy was a breath of fresh air.

I also appreciated the emphasis on making connections – both in person and virtually.  A special thanks to Tracy Zager for giving folks a nudge as well as support. There were quite a few #MTBoS members in the audience, and I hope by the end of the conference that number increased.

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The Opening Keynote was a panel discussion called “Talking Math With Kids.” The panel included Christopher Danielson who blogs at the aptly named talkingmathwithkids.com; Allison Hintz and Tony Smith from the University of Washington; and Megan Franke, Angela Turrou, and Nick Johnson from UCLA. They told stories of their experiences working with young children around mathematics. The (extremely important) theme of their talk is that young children have mathematical ideas. We should listen to, value, and encourage them.

Then we moved into our first of six sessions. I happened to present during the first session. It was a little stressful, especially since the projector was not cooperating at first, but I was happy to get it out of the way right up front. 🙂 My talk was called “Numberless Word Problems in the Elementary Grades.”

In the talk we solved a numberless word problem together to create a shared experience. Then I shared the story of Jessica Cheyney using numberless word problems in her classroom to help students connect the act of separating to the concept of subtraction. Next I shared the story of Casey Koester, an instructional coach who used intentional planning and numberless word problems to help 2nd grade students make better sense of word problems. I closed by sharing resources teachers can use to implement numberless word problems in their classrooms.

Since we started in the afternoon, the opening keynote and session #1 were all we did on day 1. Day 2 opened with another keynote called “Equal Math Partners: Families, Communities, and Schools.” The keynote included Erin Turner, Julie Aguirre, and Corey Drake from the TEACH Math Project; and Carolee Hurtado from the UCLA Parent Project.

I loved this keynote! We often talk about what teachers and students are doing in schools and gloss over or ignore the role parents can and should take in their children’s mathematical development. We also ignore the role that students’ family, community, and culture play in their learning of mathematics. The two projects shared in this keynote were inspiring to listen to and so important for us to hear.

The first story was about the UCLA Parent Project, a multi-year project that invites parents in to become partners in their children’s math learning. It also builds up the parents into leaders.

The second project was the TEACH Math Project. Pre-service teachers were required  to take a community walk to interview people and learn more about the community in which their students lived. We often ask teachers to create tasks and problems based around student interests, but this often leads to generic problems around what we assume the students’ interests are. In this project the pre-service teachers had to get to know their students, their lives, and their interests for real. Then they had to use what they learned to create relevant tasks and problems. I loved it.

After the keynote we attend session #2. I went to Megan Franke’s “No More Mastery: Leveraging Partial Understanding.” This resonated so much with me because it matches my current thinking about how we should be analyzing and interpreting student work.

According to Megan Franke, mastery learning “breaks subject matter and learning content into clearly specified objectives which are pursued until they are achieved. Learners work through each block of content in a series of sequential steps.” The trouble with mastery learning, however, is that actual learning isn’t that clean. Further, it sorts students into two groups – those who’ve got it and those who don’t – which contributes to inequality.

A partial understanding approach, on the other hand, looks at understanding as something we can have varying amounts of. What’s important is finding out what students’ current understanding and capabilities are and build from there. Megan shared an example of a preschool counting task where students had to count 31 pennies. According to the mastery approach – they either counted to 31 correctly or they didn’t – only 2.5% of the students demonstrated mastery of counting. However, when they scored the students on a range of numeracy criteria – knowledge of the counting sequence, 1-to-1 correspondence, cardinality, counting the whole collection, and organization – the picture changed completely. Only 12% of the students demonstrated little to no number knowledge while 64% of them demonstrated understanding of multiple criteria.

For session #3 I got to attend Christopher Danielson’s “The Power of Multiple Right Answers: Ambiguity in Math Class.”

I especially love the power of the phrase, “Well, it depends…” and hope to help teachers in my district see the power in crafting questions and tasks that lend themselves to some ambiguity. I also love this thought by Allison Hintz retweeted by Christine Newell:

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If you haven’t seen Christine Newell’s Ignite Talk from NCSM 2017, “Precision Over Perfection,” check it out because it touches on this very idea.

During session #4 I went to lunch, and I’m going to skip talking about session #5 because it didn’t really resonate or push my thinking very much.

Session #6 was fantastic though! I saw Jennifer Kolb and Jennifer Lawyer’s talk “The Importance of Counting in Grades 4 & 5 to Support Complex Ideas in Mathematics.” I noticed that counting in general and counting collections specifically appeared across the conference program. I have made the counting collections routine a mainstay in my primary grade curriculum materials. I was especially intrigued to hear stories of how intermediate grade teachers are using the routine. The two Jennifers did not disappoint!

In the example above, counting groups and then groups of groups helped nudge these 5th grade students into an understanding of the Associative Property of Multiplication.

This same idea of “groups of groups” led students to explore groups of 10 in a way that led to deeper understandings of place value and helped introduce exponents:

Counting is a skill we naively think students “master” in the early grades, but taking a partial understanding perspective, we can open up the concept to see that there’s so much more to learn from counting in later elementary grades and beyond!

On day 3 of the conference we opened with another enlightening keynote “Anticipatory Thinking: Supporting Students’ Understanding of How Subtraction Works.” This keynote was led by Linda Levi from the Teachers Development Group and Virginia Bastable from Mount Holyoke College.

Linda Levi’s portion of the talk reflected on the meaning of computational fluency. She reminded us that while many people think of fluent as being fast, the definition is much broader and more nuanced than that.

“Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently. The computational methods that a student uses should be based on mathematical ideas that the student understands.” (Principles and Standards for School Mathematics, 2000, p. 152)

We started with a video example of a student solving 5,000 – 4,998 using the standard algorithm. Is this an example of computational fluency? According to the above definition, no, it’s not. Producing an accurate answer like a calculator is not the same as demonstrating computational fluency. In this example the student did not demonstrate flexibility in the methods he chose, he didn’t understand and couldn’t explain his method, and his method is not based on mathematical ideas that the student understands.

We then watched videos of two other students who used subtraction strategies they invented. Were these students demonstrating computational fluency? The students clearly understood their strategies and they were based on mathematical ideas the students understood. However, we then watched these same students solve another problem and realized that these students were not flexible in their thinking. They used the same strategies for subtracting even though other strategies would have been more efficient for the new problem. It’s really important to remember how multi-faceted computational fluency is and attend to all facets as we work with students.

One of Linda Levi’s main messages was that understanding how operations work is the foundation for computational fluency. She shared with us how we can use equations that represent students’ strategies as objects of reflection for discussing why a strategy works and to help make explicit important mathematical ideas.

Virginia Bastable followed up with a talk about mathematical argument which was along the same theme of helping students understand how the operations work.

One thing that resonated with me from her talk was the important work of opening up mathematics learning beyond the narrow focus of answer getting. Rather, mathematics is a landscape that also involves sense making, exploring, wondering, and even arguing.

After the keynote I attended Kendra Lomax’s session “Learning from Children’s Thinking: A CGI Approach to Formative Assessment.” This session dovetailed nicely with Megan Franke’s session on partial understandings because the whole point of the CGI assessment is to get a sense of where the child is at in a variety of ways rather than a binary “yes, they have it” or “no, they don’t.”

If you’re interested in this assessment approach, then I have good news for you! A slew of assessment resources are available at Kendra’s website, Learning From Children. Look at the resources under “Listening to Children’s Thinking” in the menu at the top of the page.

For my final two sessions I went to hear more from Linda Levi and Virginia Bastable. Linda’s talk “Understanding is Essential in Developing Computational Fluency” gave us practice recording student strategies using equations as a way to make explicit the properties and big ideas embedded within the strategies.

Virginia’s talk “Support Math Reasoning by Linking Arithmetic to Algebra” dove more deeply into the role mathematical argument can play in helping students develop a deeper understanding of the operations. When I think back to the skill-based worksheets of my youth, I’m jealous of the deep thinking elementary students are given the opportunity to do in classrooms today.

We came back together for a closing session and that was the end of the conference. Spending three days with like-minded educators who care so deeply about mathematics education and nurturing children’s mathematical ideas helped recharge my batteries before coming back to work for the 2017-18 school year. It will be another two years before the next CGI conference – this time in Minneapolis – and I can’t wait to attend!

Inspiration – Summer Edition

As you may or may not know, I have a tendency to roam the seasonal aisle at Target, looking for mathematical inspiration. So far I’ve shared photos I’ve taken at Halloween, Valentine’s Day, and Easter. You can find them all here.

Today I was stopping by Target for some bug spray which just so happens to be next to the summer seasonal aisle. I couldn’t resist the urge to take a stroll and take some pictures. Here’s what I’ve got for you today.

How many large wooden dice are in the package?

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It’s totally obvious, right? For younger students, maybe not so much. But even after everyone is in agreement that it’s 6, what do you think they’re going to say once you reveal the answer?

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Not what you were expecting, is it? You probably thought I was wasting your time starting with such a simple image. So now you get to wonder, “Why/How are there only 5 dice in this package?” Perhaps this will help:

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That burlap bag has to fit somewhere!

Let’s move on to another large wooden product. How many dominoes are in this pack?

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It might be a little hard to tell from this perspective. Let’s look at it another way.

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Barring any more burlap sacks, you might just have the answer. Before we find out, stop and think, what answers are reasonable? What answers are not reasonable?

Ok, time to check if you’re right.

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No surprises here. Although after the first image, I probably had you second guessing yourself. There’s something to be said about the importance of how we sequence tasks.

Speaking of sequencing tasks, let’s move on to another one. How many light bulbs on this string of lights?

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I really like this box because you get this tiny 2 by 3 window, and yet it’s such a perfect amount to be able to figure out the rest. This would be one I’d love to give students a copy of the picture and let them try to show their thinking by pointing or drawing circles on it.

Again, this is a great time to ask, what answers are reasonable? What answers are not reasonable? Assuming the light bulbs do create a rectangular array, there are definitely some answers that are more reasonable than others.

After some fun discussion about arrays, it’s time to check the actual amount.

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So fun! Like I said, I love this image. Let’s look at another package that caught my eye.

How many pieces of sidewalk chalk in this box?

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I was pleasantly surprised to find that Crayola put arrays on top of all their summer art supplies. It’s like they were designed to inspire mathematical conversation! Granted, the box doesn’t give it away that the dots represent the pieces of chalk, I wouldn’t point it out to students. I’d let them wonder and make assumptions about it. It’ll turn out that their assumptions are completely right, and how satisfying that will be for them!

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Since we’re talking about arrays, which means we’re talking about multiplication, let’s shift gears a bit to look at some equal groups.

How many plastic chairs in this stack?

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And to throw a wrench into what looks to be a simple counting exercise, how much would it cost to buy the whole stack?

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Now students have got some interesting choices about how they calculate the cost. The fact that half the stack is blue and half the stack is red is just icing on the mathematical discussion cake.

My final image from the summer seasonal aisle has been a real head scratcher for me.

How many water balloons do you estimate are in this package?

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What is an estimate that is too low?

What is an estimate that is too high?

What is your estimate? How did you come up with that?

Take a look at the box from another angle, and see if you want to revise your estimate at all.

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We clearly have groups – eight of them to be precise – but the question I’m not entirely sure about is whether there are eight equal groups. Maybe? And if there are equal groups, then there are certain answers that are more reasonable than others.

So how do you wrap your head around this?

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I’ll give you a moment to think about why this is confusing me a bit.

Assuming there is an equal amount of each color, this doesn’t make any sense! But then I noticed the small white tag on the set of purple balloons.

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Oh! That explains it. There’re only 260 balloons in here so…no, that still doesn’t work if these are eight equal groups.

Oh, then maybe it’s 5 more than 265 so it’s actually 270 so…no, that doesn’t work either. So I’m left to conclude that either this is not a pack with eight equal groups or there is some funny math going on! Sadly, $25 is a bit steep to satisfy my curiosity. If any of you purchase this pack and want to count balloons, I’d love to get the full story.

And with that, my tour of the summer seasonal aisle comes to an end. If you’re just finishing the school year, bookmark this post to revisit when school gets back in session. What a fun way to start the year! If you’re still going strong, then I hope you’re able to use these to spark some fun, mathematical discussions in your classrooms.

 

 

The Slow Reveal

This year my colleague Regina Payne and I tried something new as we visited classrooms across our district – numberless graphs. Similar to a numberless word problem, you present a graph with no numbers and proceed to have a rich mathematical discussion as you slowly reveal more and more information on the graph. Early in the school year, I shared a Halloween-themed numberless graph, and I also wrote a blog post about it.

We briefly touched on this work in our session at the 2017 NCTM annual conference, and it’s been exciting to see my #MTBoS colleagues taking the idea and running with it in their schools! In case you don’t follow them – which will hopefully change after reading this post! – I want to share their work so you don’t miss out on all the great stuff they’re doing.

Kassia Wedekind

Kassia has written two wonderful blog posts about how she took our ideas and tinkered with them to create a data routine called Notice and Wonder Graphs. I like this name because it’s more inclusive than numberless graphs. When it comes to graphs, you might hide the numbers, but you could just as easily hide other parts of the graph first. It all depends on your goals and how you want the conversation to unfold. In Kassia’s first post, she shares this graph with students. Notice it has numbers, and little else.

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Curious what it’s about? Then check out Kassia’s post. I’m betting you’ll be quite surprised when you reach the final reveal.

I will share this snippet from her post:

I love this routine for many of the reasons that I love Brian’s numberless word problems–it slows the thinking down and focuses on sense-making rather than answer-getting.

But I also love it because it brings out the storytelling aspect of data. So often in school (especially elementary school!) we analyze fake data. Or, perhaps worse, we create the same “What is your favorite ice cream flavor?” graph year after year after year for no apparent purpose.

I’ve decided to make it a goal to think more about data as storytelling, data as a way to investigate the world, and data as a tool for action. In my next two posts (YES, people! I’m firing the ole blog back up again!) I’m going to delve into the idea that we can use data to discuss social justice ideas and critical literacy at the elementary level. I’m just dipping my toe into this waters, but I’m really excited about it!

And Kassia did just that! So far she’s followed up with one post where her students noticed and wondered about a graph showing the percent of drivers pulled over by police in 2011, by race. I love how the graph sparked a curiosity that got her students to dive more deeply into the data. How often does a graph about favorite desserts or our birthday months spark much of any curiosity?

Jenna Laib

Jenna shared a numberless graph that immediately got me curious! This is one she created to use with 6th grade students.

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I can’t help but notice a bunch of dots grouped up at the beginning with a just few outliers streeetttcchhiiing across almost to the very end.

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Once she included some numbers, my first instinct was that this graph is about ages. Apparently I wasn’t alone in that assumption!

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And then there’s the final reveal.

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So why did Jenna create and share this graph? What was her mathematical goal?

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I especially loved this observation about how her students treated the dot at 55 before they had the full context about what the graph is really about.

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Chase Orton

Chase wrote a detailed post about how he worked with 2nd grade teachers to do a lesson study about interpreting graphs.

…there’s so many rich opportunities for meaningful student discourse about data.  That is, if it’s done right.  Most textbooks suck all the life out of the content.  Students need to understand that data tells a story; it has contextual meaning that is both cohesive and incomplete.  Students need to learn how to ask questions about data and to learn to identify information gaps.  In other words, students need to learn to be active mathematical agents rather than passive mathematical consumers.

Chase walks you through the lesson he and the teachers created and tried out in three different classrooms. I love how he details all of the steps and even shares the slides they used in case you want to use them in your own classroom.

He closes the post with a great list of noticings and wonderings about continuing this work going forward. Here are a couple of them about numberless graphs specifically:

  • We need to give students more choice and voice about how they make meaning of problems and which problems they choose to solve.  Numberless Data problems like these can be be a tool for that.
  • The missing information in the graph created more engagement.

A huge thank you to Kassia, Jenna, and Chase for trying out numberless graphs and sharing their experiences so we can all be inspired and learn from them. I can’t wait to see how this work continues to grow and develop next school year!

If you’re interested in reading more first-hand accounts of teachers using numberless word problems and graphs, be sure to check out the ever-growing blog post collection on my Numberless Word Problems page. I recently added a post by Kristen Acosta that I really like. I’m especially intrigued by a graphic organizer she created to help students record their thinking at various points during the numberless problem. Check it out!

My First Ignite Talk

I’m a fan of Ignite talks. They’re short – which makes sharing them and using them in PD very easy – and they’re to the point – which means a focused message to get others thinking and talking.

Here’s the catch. To ensure each talk is short and to the point there’s a format each one follows:

  • Each talk is 5 minutes long.
  • You have exactly 20 slides.
  • The slides auto-advance every 15 seconds.

Sounds stressful, right? And up until a couple of months ago I was always happy someone else was in the hot seat. That is until I got an email from Suzanne Alejandre from The Math Forum inviting me to be one of 10 speakers at the NCSM 2017 Ignite event in San Antonio in April. My emotions upon reading her email were a mix of feeling honored and terrified.

The event has come and gone, so now I get to look back on it with relief and a sense of accomplishment that I took the challenge and saw it through. I’m proud of the final result. I chose to talk about doing less of 3 key things in our math classrooms, which sounds counter-intuitive, but it actually results in getting more of a few things we want. Check it out:

My Other Blog

As you may know, I’m the district curriculum coordinator for elementary mathematics in Round Rock ISD, a school district just north of Austin, Texas. I recently created an RRISD Elementary Mathematics Department blog to share posts on specific topics with teachers in my district. If you like what I write here, you might want to check out the posts over there as well. It’s only recently started, so you’ve only missed three posts so far:

You might notice a theme to all three posts. Maybe.

Here’s links to the three posts:

I’ve been on a bit of a geometry kick lately. In my work, I’ve focused a lot on computation generally and number talks specifically the past couple of years. Geometry is an area I haven’t explored much recently so I’ve been making a more focused effort to do so.

The blog also has a great resources page with lots of stuff for teachers and parents. Take a peek at that if you go by for a visit.

I’ll still be writing here. I just wanted to make sure people knew I was writing there, too.

Mathematically Correct

Last night I posted a short survey on Twitter. I asked participants to analyze the following question.

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Then I asked them to answer the question. I purposefully set up the survey so participants could select more than one answer, though I gave no encouragement to do this. All the question said was, “Your answer.” Finally, I left a section for comments.

When I tweeted out the survey, I didn’t provide any details about the problem or my intent. I was trying really hard to see if other people saw the same thing I did without leading them to it.

Turns out many people did. I feel validated.

So here’s the story. This is question #28 from the 2016 Grade 3 Texas state math test, called STAAR, that students took last spring. Back in February, one of our district interventionists emailed me to say that he thought both choice G and J are correct answers. I opened up the test, analyzed the question, and realized he was right. I immediately drafted an email to the Texas Education Agency to ask about it.

Good morning,

I have a question about item 28 on the grade 3 STAAR from spring 2016.
The correct answer is listed as J. This makes sense because the number line directly models a starting amount of 25 people and then taking some away to end at 13, the number of people still in the library.
However, the question isn’t asking for the model that most closely represents the story. Rather, it asks which model can be used to determine the number of people who left the library.
In that case, answer choice G is also correct. Our students understand that addition and subtraction are inverse operations. Rather than thinking about this as 25 – __ = 13, answer choice G represents it as 13 + __ = 25, which is a completely valid way of determining the number of people still in the library.
I look forward to hearing TEA’s thoughts about this question. You can reach me at this email address or by phone.
Have a great day!

About a month later I still hadn’t received a response so I emailed again and got a call the next day. It turns out I wasn’t the only person who had submitted feedback about this question. Unfortunately, according to the person on the phone, after internal review TEA has decided not to take any action. However, they do acknowledge that the wording of this question could be better so they will do their best to ensure this doesn’t happen again.

I told her I wasn’t happy with that answer and that I would like to protest that decision. She didn’t think that’s possible, but she offered to pass my email along to her supervisor or ask the supervisor to call me. I asked for her supervisor to call me.

Surprisingly, my phone rang about two minutes later.

The supervisor asked me to go over my concern with her so I explained pretty much what I said in my email. She said she understood, but if we looked at G that way then all of the answer choices could potentially be right answers. This was confusing to me because I don’t think F would help you determine the answer at all. If anything it shows 25 + 13, which will not give you an answer of 12.

I stressed that my concern is that answer choice G is mathematically correct with regards to answering the question asked. I get that J is a closer match to representing the situation, and if the question had asked, “Which number line best represents the situation?” then I probably wouldn’t be emailing and calling.

But it doesn’t.

The question asks, ‘Which number line represents one way to determine the number of people who left the library?” If you know how to use addition to solve a subtraction problem, then answer choice G is totally a way to find the number of people who left the library.

She said that is a strategy, not a way of representing the problem.

“That’s exactly what a way is. How you would do something, your strategy,” I replied.

She decided to redirect the conversation, “Let’s look at the data on this question. 68% of students chose J. 9% chose F, 12% chose G, and 10% chose H. The data shows students weren’t drawn to choice G. It’s not a distractor that drew them from choosing J.”

“I don’t care about that. The number of students who selected G doesn’t change the fact that it’s mathematically correct. If anything we should give those students the benefit of the doubt because we don’t know why they picked it.”

“Exactly,” she replied. “We don’t know why they picked it, so we can’t assume they were adding.”

“That’s not okay. Since we don’t know why they picked it, we’re potentially punishing students who chose to use a perfectly appropriate strategy of addition to solve this problem. There are a lot of 3rd graders in Texas, and 12% of them is a large number of kids. Who knows if this is the one question they missed that could have raised their score to passing?”

From this point she steered the conversation back to the question and how J is still the best choice because this is a subtraction problem.

“But you aren’t required to subtract to solve it! We work really hard in our district to ensure our students have the depth of understanding necessary of addition and subtraction to know that they can add to find the answer to a subtraction problem. We want them to be flexible in how they choose to solve problems. And again, the question isn’t asking students which number line best matches the situation. It just asks for one way to find the number of people who left, and both G and J do that.”

She went back to her original argument that if I’m correct then all of the answer choices could be used to find the answer to the question. She talked about how choice F shows both parts of the problem, 25 and 13, so you could technically find the answer. I disagreed because you end up with a total distance of 38. There’s nothing that makes me see or think of the number 12.

We went round and round a few more times. She wasn’t budging, and I was having a hard time listening to her justifications. She assured me they were going to be much more diligent about how number lines are used in future questions, but this question was going to remain as-is because she believes J is the best answer.

The whole exchange left me livid. In some small way, TEA is acknowledging that this question is flawed, but they aren’t willing to do the right thing by either throwing it out or making it so either G or J could be counted as correct.

They’re just going to do better next time.

But we’re talking about a high stakes test! Our students, teachers, principals, and schools don’t get to just “do better next time.” They are held accountable for their scores now. They can be punished for their scores. People can be moved out of their jobs because of students’ scores. So much is at stake that if a question is this flawed, TEA should show compassion to our students, not stubbornness. They should admit that both answers are mathematically correct and update each students’ score.

Because we’re not talking about a small handful of kids.

12% may not sound like much, but when 327,905 students took this test, that means nearly 40,000(!) of them chose answer choice G. That’s 40,000 students who are being punished because of a poorly worded item that has two answers.

That’s not correct.

A Dreambox Deferred

A year ago Tracy Zager wrote a must-read post called “My Criteria for Fact-Based Apps.” In it, she lays out her three non-negotiables for mathematics-related edtech programs:

  • No time pressure
  • Conceptual basis for the operations
  • Mistakes must be handled properly

Tracy goes on to share two apps she does recommend, one of which is DreamBox Learning. After Tracy’s enthusiastic review, I wanted to get my hands on it and try it out. I invited a sales rep to our district for a demo, but that was underwhelming as always. For whatever reason, edtech companies tend to reveal only the briefest of glimpses of the actual student experience of their products. This is so frustrating to me!

Back in the spring I was part of a request for proposal (RFP) process that looked at various computer-based math programs. One of my biggest questions when reviewing programs is always, “What is it like for a kid using this program?” The reps will show you a few screens, but generally not enough to get a sense of what kids are really experiencing. Rather, the bulk of the time is spent talking about things like adaptive pre-assessments, teacher dashboards, and the plethora of reports that can be generated and dissected. Since the companies aren’t marketing to children, they focus their time and energy on the features that the adults will use. However, students are the ones using these products the most to (hopefully!) learn more about math. Their user experience is the one I care most about understanding and evaluating.

I did get some sample DreamBox accounts to play with, but I really wanted to see how it works in the hands of a kid, especially considering the adaptive nature of the program.

Enter my daughter, @SplashSpeaks. We’ll call her Splash for short. Splash is going to be 5 years old in March. She’s on the young side to be using the program – it says it’s designed for grades K-8 – but we have been doing so much counting and talking about numbers in our day-to-day lives that I thought it would be worth giving it a shot. Since the program is adaptive, I figured it would ensure she was in appropriate content.

Over winter break, I decided to create a personal account and start a two-week free trial. This post is about how, at least for now, I’m not going to subscribe now that the trial is over.

When Splash and I sat down at my iPad Mini to play DreamBox for the first time, she was excited to try a new app. The first few activities were a piece of cake for her. All they asked her to do was determine either “Which has more?” or “Which has less?” from two images of dots. The only challenge was paying attention enough to know which was being asked for. Her default was to assume that it was going to ask her to find the one with more. All in all, she did well enough and new activities started opening up for her.

I will say I’m impressed with the variety of representations she encountered in DreamBox. These included ten frames, dot images, math racks, and number tracks. It was interesting to see which ones resonated more with her. The math rack is definitely her favorite!

Sometimes the interactivity to complete one screen was a bit cumbersome for her. In the above example, she had to count the beads in the static image, create a representation of the same number of beads in the interactive math rack, count the number of beads again to make sure she remembered the number, count along the number track until she found the number she was looking for, click it, and then click the green arrow to indicate she’s done.

Whew!

Thankfully not every screen was this involved, but when they were, she would often skip a step. For example, she would build the number on the math rack and then jump down to the green arrow, forgetting to also select the number on the number track.

The first red flag for me that this may not be a good choice for her was her reaction whenever her answers were checked by the system. If she got the answer right, she would turn to me and smile, but if she got it wrong, she had a physical reaction of frustration. Rather than knowing it for herself, she started putting her faith in the system to tell her whether she had counted correctly. I didn’t feel comfortable with that shift in authority. I want *her* to trust that she counted correctly or built the number correctly, not wait for a computer to tell her. And I didn’t like how that subtle shift so dramatically changed her reactions to being wrong.

I will recommend that if your children use DreamBox, young ones especially, you should sit with them. There are some activities that ask for things Splash didn’t understand at first. For example, after building some numbers with the math rack, it started asking her to do it in the fewest number of moves possible. She had no idea what that meant.

Perhaps I should have said nothing and let her fail at the task. Since the system is adaptive, it might have shifted her back to other activities. However, considering how quickly the system brought her to this point in the first place, my guess is that after another activity or two she would have been prompted with these same directions.

I opted to explain to her what the phrase meant and she was able to start doing it on her own with the math rack. It was definitely more confusing with the ten frame, but even then I started seeing her grab larger chunks of dots rather than just counting out one at a time.

Here’s where another red flag came up. If you make a mistake on a screen that asked for the fewest clicks possible and then correct your mistake, the system will chide you for not getting the answer in the fewest number of moves and make you do it again. For example, let’s say you were supposed to drag 7 beads on the math rack but you mis-click and drag 6.  If you drag all the beads back and then click 7, which is what my daughter did, your answer is still wrong because it counted all the clicks you made on that turn. It doesn’t matter that your last click was the efficient one.

This caused my daughter a lot of distress because she felt pressure to make sure she was completing the task perfectly, but the mix of her 5 year old hand-eye coordination and my small iPad Mini screen meant this happened somewhat frequently. She had a similar issue with the number track where she’d be counting and pointing at the numbers on the track to find the number she wanted and accidentally click one of the numbers she was counting. In certain activities there is no green check mark. If you click the number track that’s it; the system thinks that’s your answer. It was frustrating to watch her getting discouraged at being told her answer was wrong even though it was a user interface issue.

Her frustration reached a breaking point when DreamBox started introducing Quick Images activities. If you’re not familiar, an image is flashed for about 2 seconds and then covered. The user has to select the number of beads/dots that were in the image. This just blew Splash’s mind! She can identify 1, 2, and 3 on sight, but if it’s 4, 5, or greater, she relies on counting one by one. This activity made her so annoyed the first time she did it. That is, until she had an idea. She hopped up and said, “I’ll be right back!” She came back with her personal math rack:

Suddenly the activity became much more do-able for her. By building the images herself, she started to notice that some images only had red beads and others had red or white. If the image had red or white then she learned she only had to count the white beads. Clever girl! She still hasn’t had the “a-ha” moment that all of the red beads are 5, but it’ll happen at some point down the road. I’m not worried.

Bringing in a math tool was a lifesaver for her. She had a renewed interest in the program and felt empowered using her tool to support her thinking. That is until she started getting Quick Images with dot images. This is where I’m curious how DreamBox gauges student ability with regards to numbers to 10. I already know my daughter is super comfortable with 1, 2, and 3. She clearly needs more work on 4 and 5. Numbers 6-10 I’m less concerned about though I know she can count them accurately.

The Quick Images activity is all over the map. It would show an image of 3 dots. Cool, no problem there. But then it would follow up with an image like this:

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She took one look at this and was defeated. She had no idea how many dots there were. We haven’t played a lot of dice games yet, so she doesn’t know that arrangement of 5. And she doesn’t understand counting on yet so even though she can see two orange dots, that’s not useful for finding the total.

I let her take her best guess and get it wrong. I kept telling her it’s okay. If she gets it wrong the system knows she’s not ready for that problem and will give her a different one. This is where I ran into two big problems with DreamBox. First, the way it decides what numbers to give her seems random. After getting large quantities wrong, I figured it would adjust and only give her small quantities, but it kept ping ponging back and forth showing 3, then 9, then 2, then 8, then 10. In my head I was like, “Clearly she can’t figure out the big numbers, stop giving them to her!”

The other issue has to do with the length of the activities. Normally it seems like she answers 6-8 questions and the activity is over. There’s even a visual on the screen to help show progress. For example, a long dinosaur neck is inching along the bottom of the screen towards some leaves. In this same Quick Images activity, I saw that she was close to the point where the activity normally ends, so I encouraged her to do what felt like must be the last problem. And the one after that. And the one after that. And the one after that. It never ended! The dinosaur neck just kept inching and inching and inching toward that leaf. I felt like we were trapped in Zeno’s paradox. Each time, Splash got more and more upset and frustrated until she finally broke down in tears, and that’s when I ended it. If I had known the system was capable of extending an activity that long I would have backed out of it much, much sooner. As it is, I felt terrible! I love talking about and doing math with my daughter. The last thing I want is to bring her up to and well beyond the point of frustration.

We took a break from DreamBox for a day or two. When I asked her to try it again she said, “I don’t want to do it. I don’t like it.” That made me sad. I didn’t want to stop using DreamBox on the negative note of her last activity. I wanted to help remind her about all the amazing thinking she had been doing while using the program. I encouraged her to try again, but this time we would ignore those Quick Images activities. She was hesitant, but she agreed and we ended up having a good session. The next day we played again, but this time she chose an activity that I thought was something different but it turned out to be that dreaded Quick Images activity. Aargh!

Rather than give up, I took a quick look around the dining room and saw a tub of beads. Splash wanted to get right out of the activity, but I stopped her and said, “Why don’t you try using these to build the picture like you did with your math rack?” Building with beads sounded fun so she agreed. I also prompted her to look for small groups of dots in the pictures to help her. What a difference that made! She blew me away with her subitizing skills.

I was so proud of her! She managed to build every single image thrown at her. It wasn’t until the activity ended and said, “That’s okay, we’ll try Quick Images again another time,” that I realized the system was not as impressed with her performance. Apparently she was being timed. It took her a while to build and count each image. Even though she got every single answer correct, DreamBox considered it a failure and didn’t count the activity as complete.

A day or so later our 14-day trial ended and I was left with the decision about whether I should pay for a subscription. Splash clearly demonstrated some wonderful strategizing and thinking while using DreamBox, and I was tempted to see where it would take her, but I had a feeling in my gut that it wasn’t the right decision for her.

I couldn’t quite put it into words why until a week or so later when I read chapter 2 of Tracy Zager’s new book Becoming the Math Teacher You Wish You’d Had. The chapter is titled “What Do Mathematician’s Do?” In it, she shares the story of a primary classroom where students are asked what it means to do math. Initially their answers have to do with worksheets and giving answers. The teacher and Tracy work together to develop a mini-unit to open students’ eyes to what mathematicians really do. By the end of the unit, students are beginning to understand that math is about some wonderful verbs including noticing, wondering, asking, investigating, figuring, reasoning, connecting, and proving. They’re learning that math is all around them. Reading about the experiences of these students made me want to be in that classroom, experiencing that joy of discovery with them.

And then I thought of my daughter and all of the experiences we have daily with math. I realized that DreamBox might be better than nearly every other edtech program for practicing specific skills and working through a coherent progression of ideas, but it’s not the kind of math I want my 5 year old daughter to experience. I don’t want her worrying about whether a computer is telling her her answers are correct or whether she’s taking too long to come up with them or whether she’s finding them in the most efficient way possible.

In just two weeks I already saw that path leading to frustration and negative feelings toward mathematics. No thank you.

I want to continue down the joyful, meandering path we are already on where she investigates making shapes using her body and our tile floor:

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Where she wonders about the biggest shape we can possibly make with plastic strips called Exploragons:

Where we figure out important things in our daily life, such as, “How many more days until the weekend?” and where we notice and play with math:

Down the road I might revisit DreamBox for my daughter, but not anytime soon. Lest you think I’m just being a harsh critic, I will still happily recommend it for parents and teachers who have older kids. When a child has more math under their belt and you want a system to be able to flexibly move backward and forward to meet their needs, then this is a great choice. It’s not perfect, but it’s far better than other programs I’ve seen. Kent Haines said it best:

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But for a child just starting out and just beginning to develop her identity and relationship with mathematics, I’ll pass.