Full disclosure before I begin describing, in my middle school classes, I teach grades six through eight, in four different sections, all multi-grade. The sections are also single gender. I have two sections of girls and two sections of boys.
So, I am trying something new this year with my middle school math units. I am offering a choice of three. After I assess a unit, I am setting up the next unit, for three different levels of math, and then allowing students to decide what they want to learn next. On the surface, it sounds like a lot of voice, and a lot of choice… new educational buzzwords. I’d like to defend my reasoning. I will do so by way of example as I think that is easier for us linear math-ies.
I start the first day of the new unit with a preview day. First up, ratios. The unit is a “typical” sixth grade level unit on ratios, understanding and application. I do three problems that the students would see in the beginning of the unit so that the students can ascertain for themselves if they have every seen ratio notation and can manipulate a fairly simple ratio table. I also set up a proportion, solving for a variable. The second level unit is proportional relationships, and is crucial, in my opinion for foundational learning of math. I always over-estimate to students that if they can master learning of proportions and how they work, they can solve 80% of all math problems going beyond the 7th grade. To preview the proportional relationship unit I give students three problems to try- scale factor, percentage decrease, and estimation of sales tax and tip (using number sense, not a calculator). Again, these preview questions were ones that would be found in the beginning of the unit, giving the students a sense for themselves if those are types of problems they could solve with ease, with or without a simple reminder. The last unit offered was an abstract unit on understanding numbers. On the surface it seems simple because it starts with sorting numbers such as fractions, negatives, and decimals into categories; however, at the heart of the unit it is about exploring sets of whole numbers compared to natural numbers, about closed versus open sets, about what makes a rational versus irrational number and how to describe them, etc. Most middle school students, even the most advanced ones, are able to calculate and manipulate the numbers, but are not able to describe and apply the vocabulary to numbers enough to truly understand them.
The preview lessons were interactive as students use their individual whiteboards to try their best to answer all of the questions presented. In the mixed ability, mixed grade classes, there were students who could answer most or all of them, and some students who had not even been introduced to ratios at their old schools. The challenge of using the class time wisely is not to get too bogged down in teaching the concepts, but also to allow for some validation of the dedication of work of the students. For example, after the first problem I put on the board: Write the ratio of stars to all shapes as a ratio in 3 ways: △ ★ ★ ⮹ ⮹ ★ ⮹ ★ . I gave the students only about a minute to answer because they either knew it or they didn’t. Then when providing the answer, I used language such as “remember there are 3 ways” and “colon is the most common” and “the word ‘to’ is the one most people forget” so that all students would begin to feel comfortable, even those who have never seen ratios before. After demonstrating the answer as 4/8, I ask all students to reduce to simplest form, as just about all do not. This task is something that even students who have never seen a ratio can do, and then they feel some success. All of this teaching takes 2 minutes, at most, which allows me to see who knows ratio, gives the students an idea of their understanding of ratios, and also provides a nice review or learning experience for the day before we move to the next question where more learning occurs. In this way, pre-assessment is also a learning activity.
After the preview of all three units, which took approximately 3/4 of our class period, or about 40 minutes, I encouraged students to decide where along the continuum they felt they would best be served, even if they would not be following the path of their previous unit. For example, students who just took a post-assessment on decimals and volume would next be studying ratios, if only following a sixth grade curriculum was the norm; however, if they have previously learned it, or feel confident doing that unit on their own without direct teaching, they can move “up” to proportional relationships. Similarly, if students previously studied and tested on square roots (a pre-algebra level class), but really missed studying proportional relationships and need the foundation, they can choose to do one or two units with direct teaching.
The practical- I had the students write their names next to the unit(s) of their choice on a public dry erase board in the classroom. From there I assigned their first lesson on our LMS so that the students could independently answer the questions and complete the learning activities. I knew that a few students would select units that were a little too difficult for them, and from this first unit they could adjust before starting the direct teaching and the more difficult, lesson two. I also knew that some students would choose units that were too easy, and some students did self-select to move on to other units, and others needed help to select other learning. A third by-product of allowing students to self-select unit was that some students chose to challenge themselves and also reinforce their own learning by doing multiple units- one that is self-taught that is reinforcing their gaps from previous years and one that is guided by the teacher and moving them forward in their curriculum. Utilizing the LMS helps me personalize the learning.
This isn’t the first time this year I have had the students self-select their learning or their units, but it is the first time I have been as pragmatic and, honestly, as thorough and personalized once chosen. I am challenged by the shift and I am excited to see where it goes.
As always, I encourage discussion, on this forum, or on the social media from which you found this post. I’d love to hear your feedback.
Talking Math 