Day 2 of the NCTM Salt Lake Regional Conference offered “Low floor High Ceiling” by Susan Loveless an instructional coach in Tennessee. We explored three different activities that increase problem solving in the classroom while allowing multiple entry points for students. The first we worked through was Three Reads. While I have heard of three reads before, I have never used it or seen it used in the way it was suggested to. The first read is meant for students to just listen, without any numbers, and without the question that is ultimately asked. This forces the students to describe the situation of the problem without being able to plug and chug. The second read the students can view the problem on the board, but still without a question. They are allowed to discuss the numbers and what they think will be asked from this situation. On the third read they are given the question for the situation. This is when they are allowed to begin solving the problem. I love that this forces students to slow down and think about the scenario before they even know what will be asked. This also allows students who are slower to process to be at the same speed as their classmates.
The second activity was three act tasks. Three act tasks are just that, given in three parts, where part one is a hook video that has no questions, no numbers, and Is typically less than a minute. The students create a list of question that can be asked from that video. Act 2 has the students seek information from the problem, but only what is necessary or that they ask for. I have done a spin on this where my students had to determine what info they needed and come ask me in their group. If it was information I had I would give it to them, if not I would say I can not answer that. Act 3 is the reveal. Before showing act 3 students should have solved the problem. Act 3 is so exciting to watch in a classroom. Students gets so passionate about their answers and if they were right or wrong. It fosters a great discussion in the classroom naturally. Three act tasks can be found by Dan Meyer, Graham Fletcher, and others.
The third activity in Susans session was numberless word problems. These problems are presented to students as situations without any numbers in them. The students need to describe the situation and how they would reason through it without using numbers. You then present the same word problem with numbers in it and ask students to explain their method by justifying. You can them give them the question and ask them to solve it. Numberless word problems force students to discuss situations and describe mathematically without actually being able to do it just yet. There is a theme in this session of three parts for these activities. They all increase student engagement and discourse and allow the teacher to become a facilitator in the classroom.
Since I thoroughly enjoyed Fred Dillon’s session from day 1, I attended his session day 2 titled “All About that Base” on Log Functions. While I am no longer a high school teacher, since I am focused on middle school in my specialty role, this session provided me a lot of ideas to incorporate into lessons. Students began by activating prior knowledge of exponential functions and laws of exponents. This was compared to function notation (which I did not do as often as I should have) and students were reasoning through and writing their predictions. The teacher was facilitating the lesson, and including purposeful “think pair share” times, but not doing this exploration with the class. He then had students fill in a table of log function values using their calculator. This is the moment when he introduced the vocabulary of a logarithm and stated “ only introduce the vocabulary when it is necessary for the student learning at that point in the lesson.” This part really resonated with me since I found myself very quickly introducing new vocabulary in a lesson so students were not “frightened” when they saw it. The exploration students were doing led them to predict laws of logs without knowing they were doing so. They were able to use their table to find other values that led to multiplication of logs, division of logs etc. This lesson immediately had me thinking of ways to include this level of student reasoning into middle school lessons as well. If we as teachers can lead students to build concepts and understand concepts, we can spend less time practicing skills. Even though this specific lesson was on log functions, the design of this lesson applies k-12.
Additionally I was able to attend a Texas Instrument session where we matched the graph using the rovers. This was an amazing opportunity to explore the rovers, program in them, discuss math with other math teachers, and speak with representatives from Texas Instrument. All of these lessons are available on the Stem Projects portion of the Texas Instruments website. The district I work in uses Ti-Nspires in the classroom so the rovers are an easy addition to the classroom. The interdisciplinary connections are what intrigued me and the fact that students are writing the program for the robot, then matching their graph. You can reach different depths of knowledge by having students examine the two graphs and explain the similarities and differences between the two. These rovers can be used individually or in groups and can be used in lessons anywhere from middle school math through calculus. Your district can apply to have these TI products lent to you for a certain period of time. You can borrow them for training with teachers, a specific lesson you want to use in class, or to explore yourself. You can apply for them on the website or speak to your local TI representative. I can not wait to partner with a teacher and watch students using them in class.
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