Back when I was in the classroom, my colleagues would often commend me for being brave enough to teach math to eighth-graders. But I loved teaching eighth grade because it gave me an opportunity to prepare young minds for high school—and it gave students a chance to learn how to take more ownership of their learning.
My primary goal was to teach to grade-level standards and help students understand math concepts at a deeper level. My secondary goal was to send them off with soft skills they could use in high school, after high school, and in their future work. I wanted them to develop these soft skills so they could be successful wherever life took them after school. At the end of this trying year, I’d like to share some of these soft skills with you.
Soft skill #1: Let your curiosity lead you
I am a huge proponent of allowing students to be curious. Curiosity is what helped historic mathematician Pythagoras discover the Pythagorean theorem and led Muḥammad ibn Mūsā al-Khwārizmī to be revered as the “godfather of algebra.” To reward curiosity among my students, I encouraged them to rely on (and trust) their prior understanding of math concepts and make connections to new learning.
The lessons I planned that focused on curiosity took two or three days. Instead of teaching a skill first and having students replicate the examples I gave, I always had them take the first day of the lesson to explore and make their own conjectures, connecting the new skills with their prerequisite knowledge. I would put students in groups of three or four with assigned role cards and ask them to engage with one another in discussion using a guided exploration I created, designed to have them connect their prior learning to the new skill. These are practices I implemented from 5 practices for orchestrating productive mathematics discussions.
One of the hardest lessons I learned as a teacher was not to correct my students’ mistakes right away.
This first day allowed for their curiosity to drive their thinking and required making mistakes, which many students dislike because of the shame it can bring. One of the hardest lessons I learned as a teacher was not to correct my students’ mistakes right away. Allowing them to continue down the wrong path led to deeper reflection and the kind of learning that sticks. It also challenged their false beliefs about mistake making, like “Mistakes mean I am less than. Making mistakes means I am a mistake.” I realized that if I wanted my students to become mathematicians, then I needed to switch my role from solution-provider to supporter. I asked probing questions, carefully monitored small-group discussions, and directed students to other resources or group members if they needed help. Inquiry-based instruction requires students to take risks, and I created a safe space for them to do so.
The second day would consist of instruction with notes and examples. I would refer to and connect student inquiries from the day before with the new skill. I would highlight some student conjectures that accurately connected to the learning target as well as some conjectures that were inaccurate. Although this sounds like shaming, I helped the entire class make sense of the inaccuracy and showed how to redirect it to the correct path. This opportunity allowed for students to make sense of mistakes in a safe environment and ensured everyone was on the same page. For those whose conjectures were correct (or close), the instruction confirmed their thinking. For those whose conjectures were incorrect, the instruction redirected them to the right path.
Soft skill #2: Communicate clearly
Math is a language. Numbers can be combined to make words that create expressions that create sentences that can be used to build arguments to prove a claim, for example. Teaching math strategically can help students become better communicators.
To help me build a case for the importance of communication in the math classroom, I interviewed a former colleague, Gary Chu, about his unique approaches to implementing soft skills with his students. Gary teaches at Niles North High School, in Skokie, Illinois, the school most of my students eventually attended after graduating middle school. I often tapped into Gary’s experiences when I was teaching.
Gary’s number one goal for students is for them to be effective communicators. “You will be in situations where you don’t know people very well or maybe you don’t really like them,” he tells his students. “If you are tasked with something as a group, in school or at work, how can you effectively communicate with your team and complete the task?”
Communicating requires students to actively speak and listen, so for the first couple of weeks of each semester, Gary randomizes groups every day. He provides students with discussion-based math tasks where they share their ideas, voice their opinions or prior knowledge, and listen to one another. This was more difficult to accomplish during remote learning, but Gary stuck with it and students eventually engaged at the level he wanted. It’s all about building a safe environment.
Communicating requires students to actively speak and listen.
In my classroom, I had students do a “Which one doesn’t belong?” activity at the start of class two or three times per week. This opener is very nonthreatening and helps students transition from their previous class to math class. My main purpose was to have students become more comfortable justifying their reasoning verbally. I would not let them come up to the board and write out their proof because I wanted to focus more on verbalization of an argument rather than a written form. This could cause some anxiety, but the safer our classroom became, the less anxiety they felt. I would also ask other students to repeat what the first student claimed. This allowed them to practice listening carefully and asking questions.
This activity created a safe space because there were no right or wrong answers, as long as students could back up their arguments. Our focus was on understanding the mathematics deeply enough to build a case to convince others. With problems like these, there are usually multiple cases to be made. Students can respond to others’ choices by asking questions or even making an argument as to why their choice may not be unique, thus building their skills at reasoning and problem solving.
Another strategy I used was for their homework assignments. I would repeatedly tell students to show their work not so that I, their teacher, could understand but so that a friend unfamiliar with the concept could. Students often claim they understand a concept but can’t put that understanding into words. This process can help them find the words to explain their thinking clearly. It is similar to the “Convince yourself. Convince a friend. Convince a skeptic” strategy described in Thinking mathematically (see page 87).
Soft skill #3: Practice self-assessment
To prepare my eighth-grade students for high school, I often reminded them that they would sometimes have teachers with teaching styles that just wouldn’t match their preferences. I encouraged them to rely on themselves and trust their own minds and abilities by assuring them that they could be self-directed learners. One way I did this was by asking students to reflect on their learning.
Throughout a unit, I would give students an exit slip as a way to formatively assess their understanding and prompt them to reflect on each learning target with a quick self-check for understanding (“I got it. I sort of got it. I don’t get it.”). I would then evaluate their work, check for their understanding with the same scale, provide feedback, and give them time to read through feedback and make any adjustments.
After each unit’s summative assessment, I also had my students fill in a self-reflection sheet. The purpose of this was for them to be honest with themselves and build self-awareness. They reflected on homework, feedback, effort, and participation. Here’s an example.
Upon reflecting on their evidence of learning, if students wanted to take a test again to prove their understanding of learning targets, I gave them that opportunity. It was contingent on some extra work, however. I would ask them to reflect on their homework practice. Did they skip the practice to the respective learning target, for example? If so, they needed to complete it before retaking a test. If they didn’t, then they had to complete extra practice for that learning target, which I provided for them. They also had to reflect on their effort and role in receiving feedback. What did they do with the feedback? Did they put forth their best effort? If not, what could they have done differently? How was their participation in discussions? Finally, they had to set up a time to meet with me for additional support.
Many of my students showed up with their evidence and put in the work. Although they had to adjust to these expectations at the beginning of the year, they slowly became better at reflecting. They even discovered that it took more time and effort to reassess than to just try their best the first time around. I am confident that my students left my classroom believing more in their ability to be self-aware and take ownership of their learning.
In Gary’s classroom, his students are allowed to choose their own grades. He puts criteria in place for them to be accountable for their learning in this way. His philosophy, he explains, is that the grading process should “allow for a student’s voice to be part of it, for them to take ownership and empower their voice.” Instead of giving points or standard letter grades on assessments, he uses a proficiency scale, where 1 = Does not meet and 4 = Advanced. “This changes their perspective of grades from receiving to reflecting,” he explains. “Traditional grading practices are similar to an exchange: students give something to teachers in exchange for a percentage or points.”
Recognizing that his grading model is a huge shift for students (and families), he uses the beginning of the school year to explain and model this process frequently. For example, Gary creates fake samples of student work and the class goes over them together using the proficiency scale. Students provide feedback to the fake student to support them in correcting errors and understanding concepts. This process has helped his students understand that “choosing my own grade” isn’t as easy as they thought.
Since the high school where he teaches requires standard letter grades, Gary has one-on-one conferences with his students to discuss what letter grade they believe reflects their learning (not what grade they deserve). They are required to bring evidence of their learning to justify their reasoning for choosing the letter grade while Gary also brings his evidence of their learning. He talks more about his grading practices in Ungrading: Why rating students undermines learning (and what to do instead).
Finish the year with a focus on soft skills
During the last couple months of quite possibly the hardest school year you have ever taught, my hope is that you will see how soft skills are important and intrinsic to learning and seek ways to promote them in all learning formats.
Allowing students to express their curiosity goes beyond a math classroom. When students feel free to be curious, they give themselves permission to explore and express their thoughts, feelings, and beliefs. Nonjudgmental inquiry gives them an opportunity to trust themselves and their peers, not just adults. This is a skill that can help them tremendously for the rest of their lives.
Communication, too, is a valuable lifelong skill. It helps students not just understand what they know, but also share that understanding with others. Finally, self-reflection is a key process for students to become self-directed learners. If they can have a more honest view of their learning, then they can set more accurate goals for themselves and learn to be held accountable. Both my students and Gary’s have shown it is possible for young people to take ownership of their learning.
Helping students develop soft skills can lead them to success in the math classroom and well beyond. Let’s prepare our students for the next grade level and for their next stage in life by teaching them the skills that empower them as self-directed learners.