The adventures of a fourth grade teacher in East Central Illinois.

Posts tagged “Mathematics

Step by Step Instructions

Far too often in education, we make sweeping assumptions about what our students know and are able to do, often based on our own past experiences or our nostalgic beliefs about past experiences. As a result, we sometimes assume that students already know how to do something when, in reality, they have never been taught.

This is true for social behaviour just as much as it is for academic skills. (I have blogged recently about social behaviors several times, including here, here, and here.) I have been reflecting on the need for step by step explanations that are free of assumptions as I have begun teaching my students the fourth grade math standard of identifying and measuring angles.

It is far too easy to assume that, given a protractor, a ruler, and a worksheet with with practice problems, students will be able to quickly figure out how to use the tools they are given to accurately determine the size of an angle in degrees. What I have learned is that this is far from the truth. In past years, when I have given students protractors and a pre-assessment, I have had students construct arcs instead of angles, measure the length of one ray instead of the distance in degrees between angles, or just left the page blank with a giant question mark over it.

So this year I tried something new. I made no assumptions at all. I began the very beginning and walked my students through each step, slowly and methodically. We had a lesson on plane figures, so they knew what points and rays were, but we reviewed anyway. We constructed the angle one piece at a time: first a point. They a ray pointing in one direction. Then we examined different kinds of protractors. Then we placed the protractor on the paper with the ray pointing at 0. Then we noted the 90° mark and drew a dot on the page at the right spot. Then we used the straight-edge to construct another ray. We labeled the parts and then used a different protractor to see if we got the same measurement.

Repeat with 30°, 45°, and 180° angles. These are our benchmark angles. We know what they look like, so we know that a 135° is much larger than a right angle, so when we look at the protractor, we are looking at the bigger number, number the smaller one.

In taking students through the steps one at a time, there were still some who were confused. There were still some who didn’t quite get what we were doing. But there were many more who did get it, who understood the process, and who realised that they could use any size protractor to identify, measure, and construct angles.

And sure, there were some students who already knew how to do it. But even they were patient and took their time to make sure they didn’t make any mistakes. They also helped others, because we are a classroom community and, as a colleague is so fond of saying, a community is a group of people who work together to help each other. Step by step.

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Competitions in the Classroom

I love watching movies, and I really love watching movies about inspiring teachers. Lean On Me, Mr. Holland’s Opus, Music of the Heart, Freedom Writers, Stand and DeliverSister Act 2, Akeelah and the Bee… the list goes on! I think what I love most about them is that they are movies that remind me that I am not the only teacher who has struggles in the classroom, but also that it can and does get better. These movies are also reminders to me that student engagement is such a huge component in contributing to a safe, positive learning environment. In fact, of the movies I listed above, each of them has a turning point in which the teacher finds a way to connect with their students’ interests and discover the joy of teaching students where they are at.

The reality of day-to-day teaching, however, is that I am not the final voice of what I do in my classroom. I have building, district, and state rules, policies, procedures, curricula, and standards that guide my instruction and inform what I teach. That being said, I am fortunate to be in a district that has leaders who encourage teachers to do what works best with their students.

So, even though I have spent this entire year teaching math with a curriculum that is much more rigid than I am used to, I have found ways to change things up to meet their needs, most often by utilising small groups and taking advantage of the abundance of student teachers and tutors and volunteers I had at my disposal throughout the year.

With just six school days remaining to the year, we are definitely in wind-down mode in many ways. My students are also working on culminating projects for writing, they are finishing books, and they are reviewing all of the concepts and skills they have learned during mathing workshop.

Yesterday and today I took a new approach to reviewing math skills. I have had a set of math and English/language arts “task cards” that I picked up from a school supply shop years ago but hadn’t really used much this year. In fact, they have mostly sat on a shelf collecting dust. I decided to brush off the dust, take out the cards, and set up a challenge:

Students self-selected teams of three or four and spread out in the room. Each team was given a random task card (face-down) that connected to a specific Common Core State Standard for Mathematics. I set a time for 30 minutes and set up a tally sheet on my Promethean Board. As soon as the timer started, students flipped the cards over and began solving the problems or completing the tasks given to them. As soon as a card was correctly completed, the team would earn one point and then receive a new card. The process repeated until the timer ran out.

Over the course of the two days that we did this, my students completed about 45 different math tasks. They were engaged, working together, encouraging their group members, checking work, explaining answers, and shouting with excitement when they completed a card and earned a point.

I don’t think I have ever seen a group so focused or engaged in mathematics as I did this afternoon. For the first time, my students were actually excited to do math. Was it because it was a competition? Because the winning team members got to select prizes from my prize box? Because they were able to work together? Most likely, it was a combination of all of the reasons and others that I haven’t even though about yet.

The entire process made me wonder: why haven’t I been doing this more often? Why have I been so reluctant to break out of the rut I found myself in, to give my students a lot more freedom than I had been giving them, the kind of freedom they have during reading, writing, and inquiry workshop times? I think a big part was that I was using a new math curriculum this year (along with everyone else in the district) and no matter how confident I was in the content and my delivery, I needed to see how the curriculum works “as written” before I start changing it up, in much the same way that I do when baking. I always follow the recipe exactly the first time to know what to expect, then I start tinkering with the ingredients to see what I can do to make it better or just different.

So I imagine that my mathematics instruction next year will be much more flexible and group-oriented than it was this year. I’m not saying that my math instruction this year was lacking, mind you. I am just saying that next year it will be better.

And it will certainly include more competitions.


Switching It Up

My class schedule has been fairly consistent through the year. Students knew what we were going to do throughout the day each day because I made a point to make sure we kept it that way. But as we approached the end of the semester, I knew it was time to switch it up a bit.

At the same time, my fourth grade partner and I wanted to try a new approach to guided reading / reading workshop. We put all of our students’ literacy data into a spreadsheet, organised them by different criteria and created new groups that combined students from both classrooms. We ended up wth nine groups. She takes four of them and I take the remaining five. We decided to place our literacy block in the morning after our specials (fine arts, library, and/or physical education), moving mathematics to the afternoon.

Today was the second day with this new schedule. Not only did I switch my mathing and reading workshops, I also switched students. The transition has been remarkably smooth so far! The students have readily accepted this new format and are excited to be with some of their friends from the other classroom for part of the day each day. We will be periodically reviewing the data we are collecting to see what changes should be made to groups and changing groups to allow us both to work with all of the students throughout the semester.

Having mathing workshop in the afternoon has also been an interesting change. I feel like we are not quite as pressed for time, even though we are using the same amount of time as we have before. The students seem to appreciate having a different pacing for the day. We will still be doing our inquiry workshop in the morning, too, of course, but mathing in the afternoon allows more flexibility and it means the entire afternoon is not just literacy.

All in all, I am liking how we have switched things up. Of course, this was just day two, but I am nothing if not eternally optimistic about the future!


Return of the Chromebooks

It has been a long three weeks or so without Chromebooks in our classroom. There was an issue with the district’s cache servers shortly after school started that resulted in all devices having to be shut off and put away until they could resolve the issue. Today was the first day we were able to access the devices and wow, what a difference it made!

When I first got my cart of Chromebooks, I signed an agreement that I would infuse technology into my classroom practices and instruction. I spent the past two years or so researching websites and online learning tools, trying them out with my students, studying best practices of technology integration, and generally designing my classroom around the use of Chromebooks throughout the day.

Some people have expressed shock that my students access their devices first thing in the morning and keep them out until the end of the day. They are not on them all day, of course, but they are nearby and used much more than they are not.

During our mathing workshop, students use their Chromebooks to access sites such as Zearn, Front Row, Prodigy, and XtraMath to support and supplement their learning and help them improve on skills. The devices are accessed for fluency practice and for independent work while I am with small groups.

During our inquiry workshop, the Chromebooks become the principle tool for researching a variety of topics, keeping notes, and demonstrating learning through multimedia presentations. The students also use their devices to communicate with one another using shared documents in Google Drive.

During our writing workshop, students take their early drafts and type them into Google Docs, then use the available tools to edit, revise, and format as they prepare for publication. They also use the Chromebooks to research ideas and find better ways to express ideas.

During our reading workshop, the Chromebooks are used as students access eBooks through Storia, read articles on Wonderopolis and Newsela, continue writing that they started during writing workshop, and engage in creative writing through Storybird. They also record reading through sites like Whooo’s Reading.

On top of all that, we use our devices for online quizzes through Google Forms, Google Classroom, and Kahoot! Students take brain and body breaks with sites like GoNoodle and find ways to focus with music accessed through Google Play. (We have access to the full suite of Google Apps for Education.) They review and discuss digital citizenship through the Common Sense Media Digital Passport and share projects with one another, with students in other classes, and with their families.

Like I said, I have a technology-infused classroom. So we were all very excited when we were given the green light to start using our devices again! I can hardly wait to see what my students do with their devices tomorrow!


Learning with Zearn

I spent several weeks over the summer learning all about Eureka Math and preparing myself as much as possible to implement it in my classroom this year. My goal was to hit the ground running and take my students with me on the wild ride of learning math in a way that is not only aligned to our standards and our curriculum but is also more rigourous and focused that what students have seen before.

One of the supplemental resources I learned about was a free website (as an instructional technology specialist, two of my favourite words!) called Zearn. I played around with Zearn a bit over the summer and set up a student account for myself to see what it would look like. I was excited to be able to partner my students with this, especially since this site was designed to mirror what students are working on in Eureka Math. (I will not be dropping any of my other online learning sites, though; I love being able to give my students wide access to multiple ways to engage with and think about math!)

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We did a test drive of Zearn as a class today. We had to use the computer lab due to our student network still being down (something our tech team has been working on for over a week now), but this did not seem to be a hindrance. The students were able to easily access their accounts and quickly figured out how to navigate the site. The best part was that the work they were doing online really supported exactly what we have been doing in class for the past several weeks!

One of the features I was most impressed by was the “Math Chat.” This features a video recording of a teacher explaining the concepts. Students then work through problems and, depending on how they do, are directly to subsequent videos that help further explain concepts. I firmly support the idea that students learn best from hearing similar messages from different voices.

I am really excited about this new resource and hope that students and families will add it to their math learning toolkits. Zearn will be a great way to supplement what I am teaching and giving students an opportunity to learn at their own rate while I am working with small groups.

[NOTE: The creators of Zearn were not contacted previous to the writing of this post, nor was I asked by them to write it. The content of this post is entirely of my own opinion and should not be considered to represent the official views or positions of my building or school district.]


Vertical Number Lines

My school district has adopted a new math series, called Eureka Math, to support our elementary curriculum. I have mentioned this in passing a few times, but I thought now would be as good a time as any to write more specifically about what this is (and what it is not).

Eureka Math started out a few years ago as EngageNY. It was started with a grant and was a cooperative process intended to align math materials taught in the classroom with the Common Core State Standards. (Illinois has adopted these standards but is also adopting new social studies and science standards, which is why you will sometimes see them referred to as the New Illinois Learning Standards, instead.) A not-for-profit organisation, Great Minds, was formed to take over EngageNY and develop it further, which they did under the name of Eureka Math. It has been built from the ground up by teachers and for teachers.

What Eureka Math is not is a prescriptive curriculum intended to force teachers to read a script with the vain hope that students will respond exactly as expected. There are sample dialogues included in each lesson to give an idea of how a class discussion might go, but anyone who has spent 30 seconds in an elementary classroom knows that students rarely follow the script, especially when they don’t even know it exists!

Even though I have only been teaching with Eureka Math for a couple of weeks, and even though we just finished Lesson 8 today, I am already very impressed with what I have seen. The first few lessons were very challenging, as students were asked to do more with and think more deeply about numbers than they were used to. One of the most common words to describe the “new” math standards is rigour, and boy howdy is this rigourous math! (I put “new” in quotation marks because, honestly, the math hasn’t changed; what has changed is how we think about it and how we expect students to think about it.) Coming off of a textbook series that had third grade, fourth grade, fifth grade, and sometimes even sixth grade work all wrapped into one, it is relieving to have a set of materials that is focused on just fourth grade standards!

One challenge is that Eureka Math is designed to be cumulative. Students build on their knowledge from year to year. Of course, this is the first year for any of us in our building (except for those students’ whose teachers field tested parts of Eureka Math last year), so my fourth graders are coming into it with no prior experience. That just means that I have to pre-teach some concepts and spend more time explaining ideas, words, phrases, and tools that, in four or five years, will be completely familiar to them.

Which finally brings me to the actual topic of this post. (Hey, only four hundred words or so to get to it!) One of the tools we have been using for rounding multi-digit whole numbers is called a vertical number line. It is exactly what it sounds like: a number line that is oriented top to bottom instead of left to right. In case you are a person like me who does not visualise things, here is an actual picture:

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Because we are using the vertical number line to round, the students first identify the endpoints, then they find the midpoint. For example, if you were to round 4,105 to the nearest thousand, this is what your vertical number line would look like:

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The bottom endpoint is 4,000, the top endpoint is 5,000, and the midpoint is 4,500. The students then write the original number (4,105) on the number line. A quick glance shows that, because 4,105 is less than the midpoint (4,500), it is closer to 4,000 than 5,000, therefore 4,105 rounded to the nearest thousand is 4,000.

Simple. Clear. Brilliant.

I am sure that other people have used vertical number lines before, but I had honestly never seen nor heard of them before this. It makes so much sense, though! We talk about rounding up and rounding down. Now students can actually see how to do it.

The challenge for tomorrow is to try to round without using the vertical number line. But, honestly, if my students need to quickly jot down a vertical line with arrows, mark the endpoints and midpoints, and then label the original number in order to determine how to round, I am 100% okay with that! The one thing I have always emphasised in my classroom when it comes to math is this: if the tool you are using allows you to quickly and accurately find the answer, then it is an efficient tool for you to use!


Learning Workshops

As part of my goal to have my students’ days full of inquiry and student-centered learning instead of traditional teacher-led lessons and independent work, I have organised my daily schedule around four major workshops. With one excepting, each of these workshops is titled by a verb ending in -ing. The four workshops are as follows:

“Mathing Workshop”

I decided to use the word “mathing” instead of just “math” because I want my students to think of math as something they actively do. We are using Eureka Math in my district this year, a curriculum series designed around the Common Core State Standards by teachers, for teachers. A committee of teachers in my district selected Eureka Math among many options as our new math series (replacing the old textbooks published by Houghton-Mifflin.) As the students become more familiar with the language and format of Eureka Math, I will give the students the opportunity to do math independently, with partners, and in skills-based small groups each day. We will also be using technology through websites such as Front Row, Zearn, and XtraMath.

“Writing Workshop”

I am continuing to use the Lucy Calkins framework for Writing Workshop to help the students improve their skills as writers. Students will have short 15-minute lessons each day on a specific writing task related to narratives, essays, opinion pieces, or other writing formats. Then they will have 30 minutes to work on their own writing as I meet with students individually or in small groups. We started this today with an overview of the format and then with students doing a quick write on the topic of pie. (I learned that some of my students, like me, love pie while others absolutely hate it. All of their beginning drafts were quite passionate on the subject!)

“Reading Workshop”

Our third daily workshop is designed around the Daily 5 and the idea that students benefit from being able to read independently, read with someone, meet with the teacher in a guided reading group, and work on developing vocabulary every day. We will also have daily read alouds and will read together as a class so that they can experience the fifth daily activity, listening to reading. Right now we are working on building up stamina to read independently so that we can start implementing the other activities later over the next couple of weeks.

“Inquiry Workshop”

My last workshop focuses on general inquiry, during which the students will be learning a variety social studies and science topics. I have been able to arrange my schedule so that this can happen every single day. Our social studies topics will focus on asking (and answering) one big question: how and why are we here? The science topics will be aligned to the Next Generation Science Standards and will focus on deepening students’ understanding of the scientific inquiry and engineering design processes.

I am really excited to use this workshop model for the year! I hope that my students are just as excited!