The weather has finally cooled, fall break has come and gone and now with just a few days into December the talk around my classroom has turned to Christmas. In our class we build our calendar together each day and I was pointing out important days coming up in December; when our book order is due, Hanukkah, Christmas, Kwanzaa, students’ birthdays and our Winter Program performance. Of course I was immediately hit with, “How many days ‘till Christmas?” I explained to my students that we will not be in school during Christmas and that we will be on our winter break during that time. We counted the days until Christmas together. After counting I realized that the number of days at this point does not mean much to my students. The students need to SEE the amount of days. They need something tangible. We currently count the days we have been in school, and use straws to represent those days. With this in mind I decided to create a “Countdown to Winter Break” for my students (i.e our last day together before the vacation). I created a simple paper chain out of construction paper to represent the days left until winter break. As part of our morning routine I have a student remove a link from our chain each day as we count down the days until our break. Then we count the remaining links and I write the number up on the board. This way the students have a visual and tangible representation (the chain links) in addition to the number that represents the amount of days. This further reinforces the concept that numbers represent quantity. I really like using the chain links but there are many different ways you could represent the days; marbles, craft sticks, or any type of manipulative. Further, you can use this strategy for any time you want to count down to an important day, such as the 100th day of school, classroom celebrations, spring break and even the last day of school! This concrete representation allows the students to physically interact with an otherwise abstract concept like time. The students love taking away the days, which is a foundation for subtraction and seeing the chain get shorter each day!
After three great years of teaching Kindergarten I have made the move to upper grades. This year I am teaching sixth grade at a K-6 elementary school and I couldn’t be happier. We will be following Robin through this school year as she makes the transition from Kindergarten to sixth grade.
We’re on our third month of school and I finally find myself identifying as a sixth grade teacher. If I had met you two months ago and you asked me what I did I would have replied, “well I’m teaching sixth graders this year, but I used to be a Kindergarten teacher.” As if I were standing there with one foot in the water, wondering when I would be ready to jump in. But we all know the thing with teaching is, you just have to jump in. The kids need you to be 100% and there is no time to waste.
The best part of this move to sixth grade (besides my commute being a tenth of what it used to be) is that I am teaching just math and art. While I enjoyed teaching other subjects, my heart has always sided with math and I love getting to pour all of my energy into it. I am also really excited about the sixth grade curriculum. It is so applicable to daily life and the real world links don’t seem like a stretch. Sixth graders, in the midst of some major emotional and physical changes, can be very self-involved. Being able to relate math to their worlds is key for engagement.
While I have absolutely loved the switch to teaching sixth grade math, there are definitely some new and unique challenges. When I was teaching Kindergarten, I could feel the gap between beginning and advanced students, but sixth grade is a whole new beast. The gap between low and high achieving students can be incredibly daunting, seeming to grow and widen with year. How to push my advanced students into deeper thinking while helping the many who don’t know their basic facts is a daily question. And honestly, what I find to be the more alarming problem is the gap between levels of student interest. Kindergarten was full of bouncy five year olds ready to take on the world. I felt like I always had so much joy and energy in the room during math time. The little ones loved problem solving and what they believed was just “playing” when we pulled out the manipulatives. I remember everyday when we would review the daily schedule the students would cheer when we got to math. By the time these kids reach sixth grade they have pretty much divided themselves into two groups, those who like math and those who abhor it. As we all know, this gap in interest and will only widen the gap in achievement. A goal that I have set for myself this year is to bring back the love of math. What are some ways that help create a classroom that is excited about math again?
We all know that fluency is more important than ever since new math standards have arrived. Each Eureka/Engage lesson in K – 5 provides 3 fluency activities for each lesson. I’ve been in classrooms where teachers are devoting 30 – 45 minutes to fluency because their students don’t have mental math skills and don’t know their multiplication/division facts. This is definitely not recommended! Fluency is important, but so are concept development and problem solving. How are you handling the issue with your students?
Many teachers utilize something called an exit ticket as part of their daily instruction. An exit ticket-basically a student’s “ticket” to exit the class-is a strategy that can provide feedback to a teacher about a lesson, require students to do some synthesis of the content being covered and challenge students with a question requiring some application of what was learned in the lesson. Exit tickets are used frequently and with great success in the older grades and in secondary. The teacher generally writes a question or poses a problem that pertains to the lesson and the students must answer or provide a solution in writing in order to exit the class. This is a great way to get instant feedback on your lesson and serves as an informal assessment for the students.
I have always loved the idea of the exit ticket but I needed to make it work for my kindergartners! Posing a question on the board and requiring a written response would clearly not be developmentally appropriate for my kids. I decided that a verbal exit ticket would work very well in our classroom. Recently after conducting a standard district math assessment I noticed that while many of my students were able to count all the way up to 100 (or close to it) many were struggling with number recognition, particularly the TEENS. They were either switching the numbers, for example changing 18 to 81 or saying “seventy” in instead of “seventeen.” While many children enter kindergarten with strong number recognition skills, many do not come will this prior knowledge and therefore review and repetition are crucial. This version of the exit ticket may be used for any content area but for the purpose of this article I am focusing on mathematics, specifically; number recognition. The beauty of the exit ticket is that it takes minimal prep, it is quick and it is a great way to interact with each student. I have my students line up and when they are exiting the classroom for recess, lunch, a library visit, physical education, etc. I will use this strategy. I put a number and dots to represent that number on a post-it. The dots allow the lower level students to be able to count the quantity and say the number. I place the post-it on the frame of our door at eye-level for the students. I stand in the doorway and point to the post-it and ask them “What is the number?” if they aren’t sure I tell them “Try counting the dots.” Many children take the initiative to count the dots on their own, others will need the guidance. The children get excited to show their knowledge and the children that need extra help with this are exposed to the content repeatedly while waiting for their turn. Not only is it a low-stakes activity for children who may be a bit shy, as opposed to coming up to the front of the room, but the repeated exposure is beneficial to all students. If a student is struggling I will have the students behind them in line help them out. The goal of this strategy is a quick check-in and for the students to feel successful. It is not meant to cause anxiety; so make it fun, show lots of enthusiasm and provide assistance if needed. When I want to challenge the students I might put two different numbers up on the door frame to identify and/or ask them which number is greater or less than? I have numbers 1-30 on cardstock, laminated with a magnet so I can easily take them on and off our magnetic door frame and reuse them. Post-its of course will always work too! As the year progresses and their math knowledge increases simple addition and subtraction problems will become exit tickets.
The possibilities are endless and your own exit tickets should be aligned with the content you want to assess, review and that is applicable to your students and their needs. You can also switch it up and make this strategy an entrance ticket that can be used when entering in the morning, or after recess/lunch, or whenever. When the children get more familiar with this strategy it would be possible to transition to written responses but I strongly suggest beginning with a verbal exit ticket and working up from there.
Good luck and Happy Teaching!!
Barkelonging down the trejinga, the skeppy flappit floppered the flippit.
You may be asking yourself, “What is that even supposed to mean?” Regardless of what it means – if it indeed means anything – almost 100% of people could answer the following question correctly:
What did the flappit do?
If you said that the flappit floppered the flippit, then you got the right answer. Is it meaningful or has it improved your understanding of the sentence? Not at all. This is exactly what our students experience when we focus solely on the procedure. While many are able to perform the process and arrive at the right answer, the path they have taken has not been meaningful. They are just blindly following the steps outlined for them. Conceptual understanding of the problem is essential for students to develop deeper levels of understanding and be successful with mathematics. Without understanding the WHY behind the HOW, they will traipse along until they stumble over something new. Once that happens, it is very difficult to undo.
Tips for developing conceptual understanding:
- Always provide a familiar context when introducing a new concept.
- Follow the CPA approach – start with a concrete item and build into the pictorial stage before introducing the algorithm. One such example of this can be seen while using the Place Value Disks to introduce the four operations.
- Give students a chance to explore a concept independently or in small groups before providing formal instruction.
Earlier this month I set out on a six hour drive from Los Angeles, CA to Scottsdale, AZ. I was heading to the Singapore Math Summit. This coming school year I will be making the switch from a multiple subject Kindergarten teacher to a sixth grade math teacher. My hope was to gain some base knowledge of the sixth grade curriculum and some key strategies for instruction. Hands down I can say that I got so much more out of the Singapore Math Summit than I ever expected to. Every session I sat in was incredibly relevant and engaging. I met so many great educators with varying experience teaching a Singapore Math curriculum, and I loved that each session met all of our needs. Not only did I walk away with very realistic instruction strategies from the presenters, but I also received a lot of valuable advice from the veteran math teachers sitting around me. In addition the all of the collaboration that happened at the summit, I was incredibly impressed by how interactive each session was. The presenters had us all engaged in solving common core math problems the way we would ask our students to. We dove in to the problems, struggled at times, and ultimately worked together to learn multiple ways of solving each problem. I can’t wait to get this school year started, I feel so prepared and excited to teach sixth grade math thanks to the Math Summit. I have already planned out anchor tasks, like the ones we got to experience with Dr. Yeap Ban Har. I have read and heard about using anchor tasks to start a lesson many times before, but watching Dr. Yeap Ban Har lead us in them truly modeled their power. Anyone looking to grow in their math instruction and have fun while learning should check out the Singapore Math Summit.
As we pack up this school year and start planning for the next I want to talk about one way to improve your math time in the classroom. Math Journals! If you are not already using math journals for your Kindergarteners I highly recommend putting together a class set as you prepare for next school year. Math journals are a place for students to take the Common Core standards and your daily objectives and apply them to relatable situations, which is exactly what Common Core wants us to be doing. Not to mention the pride a Kindergarten receives just by having his or her very own journal. I always love seeing my students get excited about their journals.
Math journals should start out with relatable with prompts like:
How many eyes do you have? Draw a picture of yourself and write the number.
How many people live in your house? Draw a picture of your house and write the number of people who live there. Don’t forget yourself!
These sorts of prompts are ones that any student can relate to. There is no stretch for them to apply the math and make sense of it. As the year moves on it is important to include more “real world” prompts that may not be as directly relatable. Maybe a story or situation that your students have to stretch a bit to understand, something that isn’t a shared experience. In my classroom I have included prompts such as “Your mom wants to make an apple pie. She needs 6 apples to make the pie, but she only has 2 at home. How many apples does she need to buy at the store?” Maybe your Kindergarten student hasn’t baked an apple pie or doesn’t go shopping with their mom or dad. It is important to include these problems because it is exactly what they are going to see on Common Core tests in the upper grades. Our students need to be able to dissect and understand a word problem for what it is, not whether or not they have experienced the problem.
I wish that I had been using Math Journals this whole year. I didn’t start using them until March when we were getting deeper into concepts of addition and subtraction. I have already started creating my journals for next year. I have stocked up on cheap Composition Notebooks and have begun creating a prompt a day. The prompts are small, just a sentence or two typed and printed. I then cut and paste a prompt to the top of each page. This is the perfect project for parent volunteers! You can always start with just a week or month of prompts in each journal, or you can do the whole thing from the beginning. It all depends on how your pacing goes.
Thinking of prompts can get a little tedious as the days go on so I have found a ton of great resources online. You can find links to these resources at http://www.pinterest.com/mathsingapore/ With all the great pre-written prompts out there your math journals will practically make themselves!
As teachers, we are constantly striving to improve our instructional approach. We want every lesson to be direct, efficient and informative while improving a student’s understanding of the concept being presented. We are left to interpret and develop our own approach to a lesson and hope that it connects with students. We then grade our successfulness based on the grades that our students receive and, more often than not, realize we were not as successful as we had hoped. Lesson study helps to address these issues by making lesson planning and evaluation a teacher-directed and teacher-researched event. After completing one iteration of a research lesson, “[o]ne teacher commented that lesson study puts a professional component back in teaching… and treats teaching as a science” that can be analyzed and improved (Lewis, Perry, and Hurd 21). To fully understand how this conclusion was reached, we must first examine the lesson study process (shown below).
“Improving something as complex and culturally embedded as teaching requires the efforts of all the players, including students, parents, and politicians. But teachers must be the primary driving force behind change. They are best positioned to understand the problems that students face and to generate possible solutions” (qtd. in Lewis and Hurd 1). Lesson study provides us with a means of examining the problems and determining the efficacy of our suggested solutions through our own proven research. It begins with a team of teachers examining the concept to be taught and determining what skills students will need and already have in order to complete the lesson. Once planned, one member of the team actually teaches the lesson while the other members collect detailed narratives – how students reacted to the material, what questions were asked, the answers provided, the materials used, the obstacles encountered, and what specifically encouraged student understanding (Lewis, Perry, and Hurd 20). During the final stage, the team members share the collected data and reevaluate how the students learned during instruction. Then the process is repeated in a different classroom.
The important thing to remember is that the intended product of this process is not the lesson itself. The results of this process are a better connection to long-term goals, bringing the standards to life in actual lessons, developing stronger collegial networks, and an overall improved approach to lesson planning. By completing a research lesson, you are providing your own in-house professional development that can be continuously revisited any time a teacher is struggling. “If lesson study is to avoid the graveyard in which so many other once-promising innovations are currently buried, then U.S. educators must understand that lesson study means far more than just walking through a set of specific activities. It means building a set of pathways that enable continual growth of the knowledge, interpersonal resources, and motivation required to improve instruction in the classroom and beyond” (Lewis, Perry, and Hurd 22).
Lewis, Catherine C., and Jacqueline Hurd. “Introduction: What Is Lesson Study?” Introduction. Lesson Study Step by Step: How Teacher Learning Communities Improve Instruction. Portsmouth, NH: Heinemann, 2011. 1-5. Print.
Lewis, Catherine, Rebecca Perry, and Jacqueline Hurd. “A Deeper Look at Lesson Study.” Educational Leadership (2004): 18-22. Web. 12 Mar. 2015. <lessonresearch.net/DeeperLookAtLS.pdf>.
Let’s be honest. Americans want to be entertained. American children, especially, want to be entertained. If we want to get their attention during math class, we have to “hook” them at the beginning.
A recent 8th grade teacher I observed had created a fabulous word problem to introduce a lesson on constant rate. The lesson was during the week before the Superbowl. Her problem involved the running speed of the fastest runner on the Seahawks and the fastest runner on the Patriots. Those students were engaged and excited. From there, all she had to do was reel them in.
We started the New Year out in El Paso, Texas. We brought of team of 5 trainers. This was our 8th visit to schools in the Socorro District. These visits have been during summer PD sessions, on Saturdays, on-site visits and workshops. The common thread is the enthusiasm these teachers have for meeting the Texas Essential Knowledge Skills (TEKS). As a state, Texas standards are definitely one of the more rigorous sets of standards in the country. The willingness of these educators to come in on their days off; the support of “Specials” staff coming in on those days to show solidarity says a lot about the dedication they have to their students.
One of the unique standards Texas has set is Financial Literacy which tends to get folded into math. We applaud Texas for adding these standards but in doing so we need to add time to the day to teach them. One of the reoccurring issues we hear from teachers across the country is that the new standards require discussion and thinking time. Many are trying to implement in a 60 minute math class and are finding it difficult. We need to try to expand math across the day and incorporate it into other subjects or have activities handy that do not require prep or set up time to do on the fly. Keep up the great work Socorro teachers!