Author: Wayne SmithWe have an inter-school collaboration group, sponsored by Math for America. This has given five of us the opportunity to meet together, discuss teaching strategies and more importantly find better ways to use our textbook. We all use the Glencoe Math course 2 math book for our 7th grade math classes. Our group includes: Geoff Busby- Timberline Middle Nita Wood- Timberline Middle Erin Barlow- Lehi Jr. Melissa Cossey- American Fork Jr. Wayne Smith- American Fork Jr As a group we want to use our textbook and not feel like we need to recreate every lesson in order for it to be of high quality. We assessed the strengths and weaknesses of our textbook and picked a few areas where we saw a need for improvement. The first area we picked was in chapter 2, the percent chapter—specifically we picked percent change problems. We built the entire unit around an introduction using bar models and a visual concept of 10%. Much of our discussion has been around the proper uses of bar models in helping students understand integers, percent’s, equations and ratios. Bar models are not a one and done concept. We are trying to find ways to use them throughout the year to aid in a visual understanding of many of the 7th grade concepts, such as understanding positive and negative value, including absolute value. Also, the bar models are excellent for helping to understand ratios and proportions. There is real power in learning using the Bar Models. We first heard about their use from the Singapore Math concepts found in the Singapore elementary books. Now we are using those ideas on a middle school level. Our unit was built around this first lesson that starts with this question: Visually, this problem creates bar models to show 10% units. Everything we taught in the unit was linked back to the idea of visual, mental and 10% Next we used the ideas to start doing routine percent problems like: This was followed up with problems that required more thought, for example: This was all in preparation for teaching our original purpose: With the bar model approach, students could now logically, pictorially and algebraically do many kinds of percent change problems.Percent Change. In chapter one, students learned about ratios and used cross products to solve them, relating it to equal fractions. In chapter two students used the visual model to relate the visual to the proportion. It is hard to convey the power of the bar models until you see it in action and see how students can visualize and do problems that were inaccessible before. Even simple things like, “Why do you do 9 lines in a box when you want 10 spaces?” That simple concept alone helps students understand parts of a fraction, ratios and proportions.
About the author: Wayne Smith teaches math at American Fork Junior High School in the Alpine School District. He is the team leader for the 7th grade math teachers, wsmith@alpinedistrict.org
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Author: Jennifer Boyer-Thurgood Reblogged from: Utah State Elementary Mathematics Teachers AcademyDo your students know you LOVE math? Do they think you even LIKE math? All too often negative attitudes about mathematics start with the negative feelings teachers (and other influential adults) pass on to their young students. As a mathematics methods teacher at a university I am well aware of how pervasive and even debilitating these attitudes can be. Students who enter my classroom as college seniors are not afraid to express their fear of a course syllabus that includes division of fractions and alternative algorithms. In fact, my own fear of mathematics as a college student and an elementary classroom teacher is what eventually led me to my field of study. I was determined that my students would have a more positive experience with math than I did. Learning to love math as a teacher, and in turn teaching your students to love math, often means rethinking math instruction as you’ve always seen it. Students pick-up on and often imitate your attitude. Make sure they are learning that you LOVE (or are at least learning to LOVE) math by eliminating these clues from your curriculum. 5 CLUES THAT LET YOUR STUDENTS KNOW YOU DON’T LIKE MATH:“I’m Not a Math Person”: I always get a mixed response when I tell strangers what I do. The phrase, “I teach math,” is usually met with the same facial expression as if I’d explained, “I taste test dog food.” In fact, being the math teacher and researcher I am, I have kept track of these responses. Out of the strangers I’ve talked to in my community, on airplane flights, and even educational settings within the past 18 months, only 1 out of dozens has responded positively to my profession. Why? My belief is that we as a society have accepted a dislike towards mathematics. “I’m just not a math person,” is something I frequently hear from others. Consider what would happen if you, as a teacher, said this about reading. “I’m just not really a reading person,” sounds absurd and would likely be met with fierce criticism. Even if you don’t enjoy a good math problem like you do a good book, don’t devalue mathematics, especially in front of your students. Make sure that your students know you are a math person by pointing out the many times we use math during the day. Your class might read a thermometer, count how many days until Friday, or even calculate how many minutes until recess. These are all important mathematical tasks.Spending Less Time on Math: Spending less time on mathematics than on other subjects is a sure way to let your students know that you don’t value mathematics. If math is something you have to “get through” each day students get the message loud and clear that math isn’t important. Be sure to carve an appropriate amount of time out of your day for mathematics study. Once you’ve worked on making this time interesting and valuable it may even start to take up more of your day than you’ve planned for.Sudden Change in Teaching Methods: This is one I have to say I’m guilty of. As a teacher during my first few years in the classroom I knew my math teaching wasn’t up to par, but I didn’t know how to improve it. My reading instruction was woven in throughout all the other subjects I taught. I often brought in outside resources to supplement stories we were reading as a class and my students knew from the way I talked about reading and the books I was reading that I really loved and valued them as readers. Math in turn was usually a series of timed tests and worksheets completed during the set math time each day. The dual teaching personalities I exhibited to my students and my great discomfort with this dichotomy was what drove my search for better methods. In order to strengthen your ability to teach elementary math search out reputable resources and trainings such as the Elementary Mathematics Teachers Academy. Also, search out mathematics experts in your school district and find out what support and resources are available to you.Different expectations: Without realizing it teachers, even teachers who are conscious about equity issues, treat students differently. Some have expectations that boys are better at math than girls. Others value students who complete math quickly over students who take more time. Others prefer students who follow prescribed algorithms and show their work to students who arrive at correct answers through mental processes. Think about how you respond to students during math, what expectations you have for them, and why you have these expectations. Considering and valuing the mathematical processes of your students will make you a much more insightful math teacher. I often plan my math lessons based on the questions I predict students will ask and the different ways they will each think about the problem. “Our family just isn’t good at math,” was something I heard from more than one parent at parent-teacher-conference as an elementary teacher. I can’t help but cringe every time I hear a student or parent of a struggling math student use this phrase. Please know and let others know that your genetic makeup may limit you from ever having naturally blonde hair, but it does not determine your mathematics abilities. Often helping students learn to LOVE math also means working to dispel their own negative beliefs about their abilities and helping them learn to LOVE themselves and believe in their own potential. Struggling math students are often those students who don’t “see” math in the clean linear way teachers teach them to. Take time to get to know and complement the unique mathematical thinking of each of your students.Belief in the Math Gene: All students (and teachers) are capable of doing well in mathematics. Make sure this is the message you are sending your students. - See more at: http://online.usu.edu/teachmath/blog/post/do-your-students-know-your-love-math#sthash.q3qgx90v.dpuf About the author: Jennifer Boyer-Thurgood is the director of the Elementary Mathematics Teachers Academy at Utah State. She is also serves on the UCTM Board. Desmos.com is my number one use of technology in my classroom. My students and I use it to create lines, analyze data, and solve problems. The interface is simple and user-friendly. Here's how Desmos describes their product, "At Desmos, we imagine a world of universal math literacy, where no student thinks that math is too hard or too dull to pursue. We believe the key is learning by doing. When learning becomes a journey of exploration and discovery, anyone can understand – and enjoy! – math.To achieve this vision, we’ve started by building the next generation of the graphing calculator. Using our powerful and blazingly-fast math engine, the calculator can instantly plot any equation, from lines and parabolas up through derivatives and Fourier series. Data tables open up a world of curve-fitting and modeling. Sliders make it a breeze to demonstrate function transformations. As browser-based html5 technology, the graphing calculator works on any computer or tablet without requiring any downloads. It's intuitive, beautiful math. And best of all: it's completely free."The best way to start learning about Desmos is to launch the calculator and just start playing with it. Make sure that you check out the Just Add Sliders, Tables of Data, and Regressions tutorials on the main page. These are some of the coolest features of Desmos.Desmos sliders have transformed my teaching of linear functions. Sliders have helped my students understand how manipulating the slope and y-intercept of an equation changes the graph of the line. What are sliders? Check it out: Once you have graphed a line in Desmos, you can click on the line to find ordered pairs that lie on the line. If you have two lines graphed, you can click on their point of intersection to find the solution. Adjusting the window is as easy as zooming in or zooming out like you would do in Google Maps. I also love the artwork on Desmos. Last year, almost half of my 8th grade honors students had used Desmos to figure out how to graph circles so that they could make their graphing art more interesting. One student was even graphing sine waves and animating them with sliders. He figured out how to do this in his spare time at home. In class, I never taught any graphing beyond linear functions. On their own, my students used the art examples on Desmos to learn so much more than that! Students can create an account so that they can log in and save their graphs. If your students are going to be creating art in Desmos, they will want to know how to 'end their lines' by creating domain and range restrictions. (Did you catch my use of the phrase ' want to know' in that last sentence? I'm not kidding. Your students will be begging you to teach them more math once the magic of Desmos gets under their skin.) Here's a quick tutorial on how to do create domain and range restrictions in Desmos: I'd love to hear your thoughts after you spend some time playing with Desmos.com. Have you used it before? Do you use Desmos or a similar graphing technology in your classroom? How do you incorporate graphing technology into your classroom? About the author: MaryAnn Moore (@missnarymm) teaches 8th grade math in Davis School District. She coordinates the UCTM teacher blog and is also a regular contributor to the UCTM teacher blog. Please email her at mmoore@dsdmail.net if you are a Utah teacher interested in contributing to this blog.
When I first learned about math teacher blogs, Dan Meyer's blog was one of the first that I stumbled onto. I spent about half the day reading his posts, watching videos on his blog, and browsing through his 3-Act Tasks. I was hooked. In one afternoon, I'd gotten more good quality professional development from Dan Meyer than I'd gotten from years of state and district sponsored classes. And it was completely free! I'm still learning from him and still working on implementing some of the great ideas I've gleaned from him. Recently, Dan Meyer posted a video of a presentation he gave at the 2014 NCTM annual conference. It's about an hour long but entertaining, thought-provoking, and well worth the time.
Here's what Dan Meyer has to say about this presentation:
"Students generally prefer video games to our math classes and I wanted to know why. So I played a lot of video games and read a bit about video games and drew some conclusions. I also asked my in-laws to play two video games in front of a camera so we could watch their learning process and draw comparisons to our students. These are the six lessons I learned: - Video games get to the point.
- The real world is overrated.
- Video games have an open middle.
- The middle grows more challenging and more interesting at the same time.
- Instruction is visual, embedded in practice, and only as needed.
- Video games lower the cost of failure."
About the author: MaryAnn Moore (@missnarymm) teaches 8th grade math in Davis School District. She coordinates the UCTM teacher blog and is also a regular contributor to the UCTM teacher blog. Please email MaryAnn at mmoore@dsdmail.net if you are interested in contributing to the UCTM blog. |