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!
Teachers are superheroes! Not only do we have one of the most difficult jobs, but also one of the most rewarding. Seeing a student’s eyes light up when they finally understand a concept they have been struggling with is exhilarating. But what happens when the light seems as if it will never illuminate? SUPER TEACHER to the rescue! Like many who have gone before, we swoop in to save the day and try our best to make our students feel successful. Now, don’t get me wrong, we definitely need to be there for our students, but are they actually benefiting from our efforts? A recent study published in the Journal of the Learning Sciences by Manu Kapur, a researcher at the Learning Sciences Lab at the National Institute of Education of Singapore, and co-author, Katerine Bielaczyc, sheds some light on the subject.
Providing lots of structure early on, until students demonstrate they are able to complete tasks on their own, is a very intuitive teaching model. However, Kapur’s research on “productive failure” shows that allowing students to struggle helps them to learn better than the aforementioned intuitive model. One group of students was taught utilizing intensive scaffolding and instructional support, and they were able to arrive at answers for their assignment. The second group was given the same set of problems and instructed to collaborate without any prompts from the teacher. While they were not able to correctly complete the problems, they did develop their personal understanding of the problems and what solutions might look like. When tested on that concept, the second group “significantly outperformed” the first.
Real world problems are hardly ever neatly packaged and will take some considerable thought to solve. Being able to find the deeper structure of a problem, as the second group was able to do, will allow students to easily apply their knowledge to similar problems. According to Kapur, it is important to “design for productive failure” by intentionally managing the way students fail.
* To see the original article, click here.
The Bermuda Union of Teachers recently held a conference to provide professional development to the teachers of Bermuda. Experts from around the world were brought in to share their knowledge and experiences with the teachers in a wide range of subject bands. SMARTTraining’s presence was also requested. After flying all night on a 9 hour flight with 2 plane changes, Phoenix-based SMARTTrainer, Jennifer McElvania, arrived at the Bermuda International Airport.
“Spending two whole days on the sunny island of Bermuda working on developing teacher insight and math content knowledge was a great experience. On Monday, we discussed Singapore Strategies to be implemented in grades Pre-K through 5. With the largest group of any of the sessions, these teachers showed their dedication by sharing manipulatives, seats and desks as there was nearly standing room only. Tuesday was focused on learning hands-on techniques for Algebra, Geometry and Problem Solving in grades 6-9. With a much more intimate group on this second day, we were really able to dive deep into the content and generate some good discussion. Many teachers said that they walked away with a better appreciation for math and ideas on how to conceptually introduce new topics.”
We’re excited to say that they have already asked us back for additional training days this spring!
The sun is shining, apple décor is flooding the shelves of every craft store, and snotty noses are walking through my classroom door. Yup! It must be the beginning of a new school year. As I sit at my desk after a long first week I find myself looking more often than usual at a quote posted on my desk. The quote from Ruth Beechick reads, “A teacher who loves learning earns the right and the ability to help others learn.”
This quote is going to be my motto for the 2014-2015 school year. It just has to be. In everything I do this year I want to convey to my students an absolute love and excitement for learning. As the years go by our students are getting more and more interested in their iPads and Netflix and less and less interested in practicing basic skills. And as the saying goes “If you can’t beat ‘em, join ‘em.”
To keep the learning fresh and new I have decided to create superhero type characters this year that focus on different basic math skills. For example, during the first couple of weeks of Kindergarten we focus on color and shape recognition. My student’s current favorite superhero is “Mr. Vertice”. Mr Vertice is a boy in a green cape who is an expert at counting the number of vertices on each shape. The students are so engaged in the lesson and being able to use “Mr. Vertice” that during independent practice they don’t even realize they are completing a basic skill practice sheet. Not to mention to rich vocabulary they are learning as they chant “Go Mr. Vertice, go!” I also have “Rainbow Girl” who identifies colors around the room. I just put a little picture of “Rainbow Girl” on each color worksheet and it’s like they can’t get to work fast enough.
With Common Core in full swing it is more important than ever that we are teaching these basic foundational skills in Kindergarten. If a child is expected to complete a conceptual math problem that incorporates multiple skill sets then they need to have a firm foundation. While we can choose to be discouraged by how little our Kinders know at the beginning of the year, we can also choose into projecting a love for learning. Once the excitement is there, the kiddos are motivated. And once the kiddos are motivated, they cannot be stopped!
Superheroes may not be your “thing”, but I encourage you to find a theme that does work in your classroom. Even the consistency of using one theme throughout all your math lessons help students build a stronger foundation. Animals, popular TV shows, sports, and music are all ways to engage your students. I would love to hear what you use at your school to make learning fun from Day 1!
From the title of this article, you are probably thinking, “That’s not possible.” According to David Ginsburg*, it’s the only way for students to truly succeed. What is meant by success in this context is that students should be prepared for the independent and resourceful thinking required in high school and beyond.
We as teachers are very caring and giving when it comes to our students’ success. This means that, more often than not, when our students come to us for help, we jump right in and try to save them. Yes, WE. I am also guilty of this at times. But consider this: in college or the workplace, will the professor or employer jump in every time they struggle? Did yours? The answer is most definitely, no. We need our students to be able to help themselves.
How can we accomplish this? Teach less! Now this doesn’t mean step back and never help. What this means is, make students work for your help. Give them resources in the classroom that they can turn to before they come to you. This could include notes, textbooks, technology, or even each other. To summarize Lev Vygotsky, a pioneer in the field of social learning, what children can do in collaboration today, they can do independently tomorrow. Isn’t this one of our ultimate goals?
This is going to be a change for your students as well as yourself, and isn’t something that will happen overnight. You will be met with resistance, by both students and their parents. However, according to Ginsburg, the risks are well worth the reward. Ginsburg’s “conviction around cultivating resourcefulness in students is stronger than ever because of the effect [he has] seen… Higher test scores? Absolutely. But more important, better preparation for future academic and employment challenges.”
Challenge yourself this school year to teach less. Use your lesson planning time to develop questions and activities that will foster student understanding through exploration. Try to limit how often you “answer” questions posed to the class and script out questions that you can use in response to student inquiries. “To do otherwise is to hurt students rather than help them” (Ginsberg).
* To read David Ginsburg’s original article, click here.
Many, if not all, of us are familiar with the hundreds chart. This free tool is primarily used in Kindergarten through second grade to emphasize pattern recognition, place value, addition, subtraction, and more. However, how many of my fellow middle school teachers have continued to use this resource in their classrooms? If you are not currently using it, my guess is that it’s due to a lack of inspiration on how it can be used. You’re not alone!
How many of you realized that the patterns we had our students recognizing in first and second grades can be expanded upon in higher grades? Rather than simply using language to describe the relationships, use equations. The value in the box below a given number is no longer just 10 more, it is n + 10, where n represents the number with which you started. Have students explore and discuss this concept to see if the pattern always holds true. Change the values in the hundreds chart from one through one hundred to -49 through 50. Now students can experiment with integers too. See what patterns you can discover for yourself. The more time you spend discovering these patterns, the better you will be able to facilitate the discussion in your classroom. I would recommend starting out with sums & differences and building to averages & beyond. The possibilities are infinite!
Do you understand the meaning of *#^ ? If a student does not have a complete understanding of place value, that is what a three-digit number means to him. Place value is an abstract concept to a second grader. It is a second grade teacher’s responsibility to provide many opportunities for students to build meaning of the number symbols according to their place in a three-digit number. A student must have a solid understanding of place value to be successful in every math concept. Therefore, teachers need to take their time when teaching place value to ensure that the students’ foundation is strong. Teachers might spend more time on place value than they planned, but this will help the students master every other math skill more easily, especially renaming when adding and subtracting.
Students usually have no trouble answering the questions, “In the number 328, what place is the 2 in?” or “What number is in the hundreds place?” However, place value is so much more! When a second grader sees the number 328, he should have an understanding that the number can be represented in an endless amount of ways. He should know that 328 is not only 3 hundreds, 2 tens, and 8 ones, but it can also be 2 hundreds and 128 ones. Also, 328 can be 3 hundreds, 1 ten, and 18 ones. Do you see how this understanding would make renaming when subtracting and adding much easier to grasp?
In order to build a strong understanding of place value, students need to first work with representing numbers with many different types of concrete objects. Different types of manipulatives that teachers can have their students use are base ten blocks, coffee stirrers, Legos, and paper clips, to name a few. When using coffee stirrers, I would have students bind groups of ten with rubber bands. Then they would place ten tens in a large plastic cup labeled “100.” When using paper clips, students would connect ten to make groups of ten and place ten groups of ten in a “100 cup” also. Legos worked better than both the paper clips and coffee stirrers because they are easier to connect. However, students must work with several different types of concrete objects to be able to transfer their knowledge of place value to real life situations.
The place value chart builds the bridge from the concrete objects to the abstract concept of place value. When working with three-digit numbers, the chart has three columns labeled “ones,” “tens,” and “hundreds.” By placing objects in labeled columns, students see that each number symbol represents a different value according to its place in the number. To begin, teachers should explain to students that nine objects is the most that they can have in any column. I would make place value charts by laminating two different colored, long sheets of construction paper. The top half of the chart was one color, and the bottom was a different color. Leave a small gap between the two to be able to fold it in half for easy storage in a pocket chart or desk pouches. The two different colors made it possible to represent two different numbers on the chart. This way, students can use the chart to compare numbers or to add and subtract.
Once the students demonstrate an understanding of three-digit numbers with concrete objects, they are ready to move to the pictorial stage. I would use play money first in this stage. The one dollar bills would represent ones, the ten dollar bills-tens, and the hundred dollar bills-hundreds. This builds on the students’ prior knowledge that all of the dollar bills are the same shape and size, but each one represents a different value. This also prepares students to work with the number discs. Using the money works great with comparing numbers. Any second grader will tell you that he would rather have 200 dollars that 68 dollars. The students can then transfer that knowledge when comparing numbers.
After representing given numbers with dollar bills, I would introduce the number discs. Number discs are color- coded circles which are all the same size but represent different values, like the dollar bills. They have 1, 10, or 100 written on them to indicate their values. The number discs are easier to work with than other manipulatives, and they connect the concrete to the abstract number symbols.
Once the students have reached the abstract stage of number symbols, there are many activities and games to reinforce their understanding of place value. My students’ favorite game was the dice game. Students can play this game in pairs or small groups. Each group needs 3 dice and sticky notes. Each player needs 6 large index cards each labeled with a number range: 100-199, 200-299, 300-399, 400-499, 500-600, and Greater than 600. Players take turns rolling the 3 dice and making a three-digit number with the numbers rolled. They write the number on the sticky note, then place it on the appropriate index card. The first player to have three sticky notes on every index card wins.
The Empty Hundreds Chart game is a good mental math activity. Display a hundreds pocket chart with only 5 numbers in it. Every student is given a number. Students take turns placing their numbers in the hundreds chart and explaining how they figured out where their numbers belonged on the chart.
In the math practice center, I would place Missing Number Grids. I downloaded these grids from the website www.k-5mathteachingresources.com. The grids are made of 5 columns of squares in 4 rows. Only five 3-digit numbers are dispersed on the grid. Students fill in the missing numbers.
Students cannot get too much place value practice. A place value and a math fact center should remain in centers throughout the year, simply change the activities. When students obtain a solid understanding of place value, they will have the strong foundation for all other math concepts to build upon.