Showing posts with label Eureka. Show all posts
Showing posts with label Eureka. Show all posts

December 28, 2017

Learning Long Division

Math was definitely not my favorite subject growing up... I had trouble remembering multiple steps to solve problems and never had a good idea if an answer was "reasonable." Nevertheless, one of my favorite memories of doing math in elementary school was creating and solving extended long division problems during indoor recess in 5th grade.  We would write up 25 or more random digits and then try to divide by 2 or 3 or 5, working our way across the entire chalkboard! It was so satisfying to simply "divide, multiply, subtract, drop down" and get a huge answer that I could feel confident was correct! I now realize that I had no understanding of why those steps worked or what that answer meant, but it felt "smart."

Now as a math teacher, I don't want my students to
blindly accept that a set of steps "just works" -- I want them to be able to explain how, why, and when any algorithm is useful and efficient. Last year our math curriculum intentionally avoided teaching long division in 4th grade to encourage students to use place value understanding and other strategies to divide.  I enjoyed teaching this way... I could explain why each method worked and observed students making logical connections between multiplication and division to solve complex problems.

This year, however, we are using Eureka math which does teach the long division algorithm (alongside other place value strategies) in fourth grade. As much as I loved using this method myself, I was anxious to make it meaningful for my kiddos. We began with mental math division (25 ÷ 5 or 18 ÷ 3), which required students to use multiplication facts to solve quickly.  I wrote the equations out using the long division symbol, but resisted reciting the "divide, multiply, subtract, drop down" mantra. Instead I asked the kiddos questions like "why do I write this here?" and "what should I do next?" and "what does this number represent?"


Then we added in using "place value disks" to represent the division (see above).  I demonstrated using the long division algorithm alongside the place value disks to help students see the connection. The kiddos totally got it!  My Teaching Fellow even commented how clearly she could recognize the steps of the algorithm within the place value model when it was taught this way!  

After two days of using the place value disks and word problems to provide context, it was time to go all in on using the long division algorithm!  Rather than keep everyone on the carpet for a traditional lesson, I allowed the kiddos to decide when they had mastered this new skill. When they felt confident with the algorithm (without drawing out the place value disks),  they could leave the carpet to start the Problem Set. Those who still felt stuck or unsure, stayed with me to keep practicing. I could practically see the gears turning in their heads and they pictured each step. When the lightbulb finally went off, they were so proud of themselves! 

Naturally, there were a few kiddos who were still struggling at the end of class. Rather than move on or wait another day to review, I offered to host a "Long Division Lunch Bunch." I ended up with 24 fourth graders eating lunch and doing long division in my room that day (I teach three classes so I offered the Lunch Bunch to all of them.) As the kiddos ate and worked together, I could see them gaining confidence!  By the end of lunch, most of them had the same satisfied, smart feeling I remembered from 5th grade. But this time, as they followed a set of steps to solve multi-digit long division problems, I knew they really understood what it means to divide one number into another and how those set of steps make their problem solving more efficient! 😄

January 3, 2017

Eureka Math Myths

Student work from an Investigations lesson
For the past five years, I've been using the Investigations Math curriculum, both in first grade and in fourth.  So when my school district announced this year that we would be switching to Eureka math, I was a little apprehensive. Fortunately, our team was allowed to take this year to get to get familiar with new curriculum and make a gradual changeover.  As the math planner for fourth grade, it was my job to figure out to make this transition smooth.

My initial plan was to teach Investigations for the first part of the year, going at slightly accelerated pace and skipping one or two units, but mostly teaching each Investigation with fidelity. However, as I got to know Eureka more, I realized that pulling in pieces from this new curriculum early on would benefit our mathematicians. We quickly incorporated some of the fluency pieces, including "Sprints" and "Application Problems."  As we have moved further in to the year, I've included a few whole Eureka lessons, and even entire Module (unit) in between our Investigations lessons. The results have been impressive: my kiddos are doing better, faster math than they were before and they are able to explain their thinking more clearly -- both verbally and visually!

Student work from a Eureka Math Problem Set
I've heard a lot of criticism about Eureka, especially about the level of rigor it demands, but from the training I've received and my own experiences, I think a lot of it is unsubstantiated.  Eureka is definitely an accelerated program compared to Investigations (and most math other curricula I'm familiar with), but this is a result of the curriculum's tight alignment to the Common Core standards (read more about this here: http://www.edreports.org/math/reports/series/eureka-math.html).  While I have had had to go back to second- and third-grade lessons to fill in gaps and meet the current understanding of my fourth graders, I've still found that the majority of my kiddos have been thriving with the structure of the Eureka lessons and the methods of instruction. Of course, it's hard to know whether they would have been prepared for the level of math was have undertaken this year without the strong background that I believe they acquired from Investigations in Kindergarten-3rd grade, but nevertheless, I think that Eureka has some really smart ways of teaching number concepts that will benefit all young mathematicians.

So, what are the myths about this new curricula?  How does it really play out in my classroom?
Here we go:

 (Disclaimer: This is just my understanding from the instructors I've spoken to and my own interpretations of what I've read.)

Myth #1: It's a script.

As the professional developer who led my first training about Eureka put it: "If you try to follow the Eureka Teacher's Guide like a script, you'll find that your students have not been studying their lines."  Just like other curricula, the Eureka Teacher's Guide provides a sample conversation between a teacher and students -- the text is not intended to be the exact or only words that teachers use when explaining concepts to students. The dialogue can be a guide for how to explain new concepts and the types of questions to ask, but may include more language than needed or may not be sufficient for any given lesson.


Myth #2: You have to do every part of every lesson / assessment.

The Eureka Math lessons are packed -- most include multiple fluency exercises, sample problems, and discussion questions. There are also times associated with each component of the lesson. Just like with the "script," most of these components are suggested to support the skills and strategies that are being taught in the lesson/module. According to the professional developers and planners I've talked with, the times are guidelines to prevent students from spending too long on any one component, rather than a mandate to fit as much as possible into one lesson.  I've also been advised that the bulk of the lesson should be in the Concept Development, with enough independent practice for students to try out new skills but not so long that they get frustrated or bored.

Even the assessments are designed to give teachers choices. Our district has been told that the Mid-Module and End-of-Module Assessments were actually designed to be used a test bank for word problems and multi-step computation problems. Teachers are encouraged to select only the problems they think will best assess their students' skill and understanding, and also to add additional basic computation or simple identification problems as needed.


Myth #3: You can't differentiate.

Yes, there is a reason that the Eureka designers laid out certain lessons the way they did and that they chose to develop concepts across grades and modules, but that doesn't mean that each class and every student will master those lessons and concepts in the same way and in the same amount of time. Of course, some differentiation will always be needed.  In fact, one of the great things about using a well-aligned curriculum is that teachers can go back to previous grades or Modules to see how skills were initially taught or practiced.  Especially in our first year of using Eureka in fourth grade, I've gone back to second- and third-grade lessons to see how concepts like fractions, standard algorithms, and place value develop. I've taught some of these earlier lessons to my whole class and others to a sub-set of students who needed more background.


Myth #4: You can't use hands-on, interactive or investigative approaches.

It's true that Eureka relies more on direct instruction than more constructivist math programs, but I've still found plenty of opportunities for my kiddos to use manipulatives and investigate concepts.  Again, sometimes these experiences are built into lessons from previous grades that can easily be brought up or revisited with older students; other times I've incorporated the manipulatives and games that I used with Investigations. If kids need to build, bundle, balance, or bisect... then by all means, they should!  Eureka does provide tools for students to visualize concepts, including individual white board templates, cut outs, place value cards, etc.. In addition, I've found that the Application Problems work really well for partners or small groups, while many of the Concept Development problems lend themselves to being "investigated" using a constructivist approach. Plus, online resources like Zearn.org can give students additional blended-learning practice with skills directly from Eureka.

So there is it ... my assessment of Eureka Math. All in all, I'm enjoying getting to know this new curriculum and seeing how it supports my kiddos' math learning.