As the K-12 Mathematics Specialist in a school district in Wisconsin, I often wonder how we can guide our students to develop the qualities of strong mathematicians. Our district is a large district with about 17,000 students who attend one of 30 schools across the city and its six surrounding towns and villages. Unfortunately, according to our state metrics, we “Meet Few Expectations” despite the many powerful programs we have in place to support our urban student population that is 62% economically disadvantaged and 12% English Language Learners.
Our students finish elementary school not ready for middle school math, with many skill deficits and an already-formed poor relationship with mathematics as a whole. This is particularly true when it comes to perseverance when they are presented with a grade-level math task that requires them to analyze the problem and form a plan to a possible solution pathway: in essence Math Practice Standard 1 – Make sense of problems and persevere in solving them.
I recently began using the Math Milestones™ tasks with some of our 7th-grade students. Over a two-month period, I visited nine different classrooms to teach lessons using one of the 14 Math Milestones™ tasks designed for grade 7. As a guest teacher in their classrooms, I was surprised that the students were easily interested in attempting the challenging tasks I was presenting to them. One student stated that “it was more fun because it was a change in the normal routine of school,” while another student said that she “could see [herself] in the tasks and that made [her] more interested in trying to solve them.”
One of my first lessons was based on Math Milestones™ task 7:1 Phone Cost. I thought this would be a way to assess standard 7.RP.A.3 – Use proportional relationships to solve multistep ratio and percent problems and standard 7.EE.A – Use properties of operations to generate equivalent expressions, while being a real-life situation that our students could easily relate to.
The students were excited to work in collaborative small groups at a vertical non-permanent white space (VNPS in Liljedalh’s Building Thinking Classrooms). They immediately saw connections between the task and their recent classroom instruction, even though there had not been much instruction around expressions and/or equations at this point in the school year. Students jumped at the opportunity to use what they already knew to find an entry point to solving this task. I enjoyed hearing their discussions about the task and possible solution pathways. The students engaged in discourse and even tried another solution method if they got stuck.
Later in the school year, I taught a lesson based on Math Milestones™ task 7:11 Ticket Offers. This task also addressed standard 7.RP.A.3 – Use proportional relationships to solve multistep ratio and percent problems. Students used a variety of different representations to model this solution. Some used a table of values; some wrote equations and then graphed them as a system of equations; some used tape diagrams to represent a percentage; some simply used a guess and check method—but all groups were able to come up with a possible solution to both parts of this task.
This group actually started with a $30 ticket price because they were able to reason that 25% would have to equal the $7.50 discount for the two websites to be of equal value. So, this student multiplied $7.50 by 4 and found that the $30 original ticket price would offer the same discounted price after either of the discounts were applied. The group was able to reason abstractly and quantitatively, and they had a platform to justify their reasoning to their classmates.
The final lesson that I taught with students was based on Math Milestones™ task 7:4 Foul Play. This task addressed standard 7.SP.C – Investigate chance processes and develop, use, and evaluate probability models. I incorrectly assumed that this task was going to stump our students because we all know that the Statistics and Probability units are always the ones that get skipped when we are running out of time at the end of a school year. I was impressed when the students greeted this task with an asset or strength-based approach by; utilizing what they already knew about basketball and the odds of making a shot.
Throughout this two-month journey, I have found that these tasks offered a great opportunity for our students to interact with mathematics in a different manner. The tasks were engaging and relatable, and our students wanted to complete them rather than the traditional drill and practice that they were used to. I found that the Math Milestones™ tasks are quality supplements to the grade-level instruction of any adopted curriculum resource. It was easy to see common mistakes and to address them in real time as students were working on the tasks. I also loved how the tasks offered small ways to incorporate writing into a class that commonly does not include as much writing as it should.
Not only did I see development in our 7th-grade students’ ability to explain connections between equations, verbal descriptions, tables, graphs, and/or diagrams, but I also saw an improvement in their mathematics growth mindset and overall ability to persevere when the task was challenging. Utilizing the Math Milestones™ tasks has truly changed the relationship of our middle school students with Math Practice Standard 1 for the better!
