Hearing Tests

In kindergarten I had a health screening that included a hearing test. I failed. The nurse notified my parents and I went to see a specialist. They confirmed I had hearing loss and ordered further tests to determine the cause. After putting my parents through days of worry, they crossed brain tumor off the list of possible causes, and we settled into a routine of yearly monitoring appointments with the specialist. The school, however, had its own routine. Health screenings continue after kindergarten. The nurse would call me down, and I would fail the hearing test. Of course I failed the hearing test, I have a diagnosis that I’m hard of hearing. I would try to tell the nurse before the test, or during the test, or after the test when she asked me why I didn’t follow instructions. I mentally rolled my eyes and headed back to class marveling at the waste of my time (and hers!).

The testing culture in schools isn’t limited to health screenings. How often are teachers asked to administer redundant tests? We haven’t taught the unit on dividing fractions yet, but let’s give this benchmark test that includes dividing fractions. We know the pandemic meant that students missed the section on histograms, but let’s give this pre-assessment including them. The results from the last three exit tickets all show students aren’t understanding, but the pacing guide says the test must be administered today regardless.

I actually enjoy taking hearing tests. I think it’s fascinating how a small change in frequency results in silence instead of beeping. That’s probably because my hearing loss is only in one ear so it’s not a major disruption, because I’m interested in science, and because I’ve never been shamed for having a physical disability. Teachers accommodated my need for preferential seating, people don’t attach a stigma to my hearing loss, and it’s relatively easy for others to understand what I need.

I can’t always say the same for math tests. Taking a math test on something I don’t know isn’t enjoyable, and that’s coming from someone who enjoys math. The testing culture had already gotten out of hand pre-pandemic and I’m worried it will only get worse from here. Here’s what I wish we would do instead:

  • Vertical alignment. That means students’ previous teachers communicating with their next instructor. Both on a course level (we didn’t reach unit x, they’re still mastering y) and on a student level (we were working on z with these three individuals)
  • Trust teachers. Teachers do formative assessments constantly. From thumbs up, to scanning and discussing during activities, to exit tickets, quizzes, and unit tests. Teachers are constantly gathering actionable data. They don’t need redundant benchmarks to determine what students need. They do need the flexibility and support to meet those needs.
  • Targeted diagnostics. Instead of a giant test at the beginning of the year, check in with students a few questions at a time. Only check if you truly don’t know what they know. If the previous teacher said it wasn’t taught, just teach it! But if the previous teacher said students were approaching mastery, or it’s a topic from over a year ago, give the task with a very clear statement to students that you’re interested in learning what they know. A diagnostic doesn’t have to be a test, it could be asking students to Notice and Wonder.

I hope that this year, your school will afford students the same grace that’s been afforded to me. I hope teachers will accommodate students’ needs for additional learning, not attach a stigma to someone not knowing, and acknowledge it’s relatively easy for others to understand what kids need. Because generally, all you have to do is communicate. The three bullets above can be summarized as: first ask prior teachers, then ask current teachers, finally ask students for any additional information you need. Trust the information from each of those stakeholders and use it to spend as much time as possible addressing grade level content. Because we all know time is a precious commodity.

Looking for professional support around mathematics instruction, curriculum alignment, developing and implementing intentional formative assessments, or more? Our Center for Mathematics Achievement at Lesley University offers targeted support for school districts, with evidence of improvement on student academic achievement. Check out our work and offerings here. Remember, we can always customize for your needs.

Who is a Mathematician?

Imagine a mathematician. What do they look like? What are they working on? 

Now imagine asking a room full of students to draw a mathematician at work. What do you imagine those drawings will look like?

Recently I got the chance to do exactly that with high school students in an after school program called Enroot at Somerville High School. Every member of this group immigrated to the United States and therefore have varying English Language proficiencies. So we started by defining mathematician:

mathematician, noun, 1. A person who does math. 2. An expert in mathematics. 3. A student of mathematics.

Immediately after I projected the definition and asked them to imagine who they could draw, I had students saying “Me!” and “My math teacher.” This was not the result I expected at all, which prompted me to think, “No need to have this seminar, they already see themselves as mathematicians!” I’m curious how much the first definition of “a person who does math” influenced this. If your students don’t need a definition of the term mathematician I would skip that step. The goal of this session is to counteract the stereotype of mathematicians as old white dudes, so it’s important to surface that idea early and often.

Here’s a selection of their drawings:

After students completed their drawings we asked them to work in groups to come up with words that describe mathematicians.

What are the characteristics of a mathematician? 

  • Describe the one you drew.
  • Describe a mathematician in general. 
  • What qualities does a mathematician have? 
  • What careers could a mathematician have?

During this section I pivoted back to thinking that this seminar was important. While kids’ initial reactions to the definition of mathematician was to include themselves, when asked to reflect on characteristics, they largely returned to stereotypes: talented, fast thinker, smart, intelligent, genius, some dude. But there were some other aspects that aligned better to what I hope students associate mathematicians with: curious, problem solver, hard working, creative, passionate. This session is designed to counteract the image of a mathematician as “some [white] dude.” The next session will build on the other aspects of mathematicians. (Stay tuned for a description of that one coming soon!)

To that end, we projected these six photos and asked students which ones they thought were mathematicians. Go ahead and make your own guesses before reading any further!

Students voted via the free site Poll Everywhere (bonus opportunity to analyze a bar graph and interpret percentages) and then we revealed the answers at the end. Surprise! Every photo is of a mathematician. A few students voted that all of them were mathematicians because they all know 2+2=4. This meant that students voted for someone that they wouldn’t associate with doing advanced math. If we had a do-over I would ask kids to vote on whether or not each person’s job is/was to be a mathematician.

  1. Carolina Araujo, Brazilian, born in 1976
  2. Moon Duchin, American, currently working at Tufts which is right nearby!
  3. Benjamin Banneker, African American, born in 1731
  4. John Urshchel, Canadian-American, getting his PhD at MIT so he’s also local!
  5. Mary Jackson, African American, born in 1921
  6. Artur Avila, Brazilian, born in 1979

After revealing that everyone in this diverse group of people was a mathematician we asked students to notice and wonder about the results of a Google image search for ‘mathematician.’

This set of activities culminated in a great discussion. Some ideas had come up in students’ individual drawings and the group discussions so they were ready to share their ideas at this point (about an hour after we’d started). This is just a small selection of the astute observations they made:

  • I notice they are all old white dudes from olden times, there is no one modern.
  • I wonder: Where are the Black people? 
  • I know that Blacks don’t get the credit despite ideas starting in Africa.
  • I wonder: Where are the women? 
  • I know they weren’t allowed to go to school back then.
  • I notice other people of color are also missing from this.
  • I know there’s a stereotype that Asians are good at math but I notice there aren’t any in the search.

We acknowledged how all of these things are true (with the exception of Ramanujan, who is Indian and in the bottom row), and then invited students to spend some time researching a mathematician who wasn’t an old white dude. They could choose among the 6 mathematicians in the photos or another one on our list. We’d curated a list of mathematicians that matched the countries of origin of the students in the group in order to build students’ identities as mathematicians.

To support students in their research we provided them with a graphic organizer. As a model of how we wanted students to complete the graphic organizer, we provided them with my math biography:

And in the last 10 minutes of the session, we invited students to complete their own math biography by filling out the graphic organizer about themselves. One of them asked if she could write down what she hoped to do in the future – absolutely! During the work time one student stopped me twice to tell me he likes math and is good at it. I wondered how often he’s in a space where he can tell someone he likes math and they’re enthusiastic about it. I hope frequently, but if not, I’m glad we could provide that space.

To close out the seminar we asked kids: What did you learn today? Multiple kids contributed ideas until we had collectively developed this sentence: 

Everyone can be a mathematician, 
from any race or ethnicity,
and you can continue to
change what you want to be. 

Note: all of these activities were inspired by the many sessions I’ve attended and blog posts I’ve read. Annie’s site has a comprehensive summary of her work on this.

The prompt “Draw a Mathematician at Work” comes from:
Berry, John, and Susan H. Picker. “Your Pupils’ Images of Mathematicians and Mathematics.” Mathematics in School, vol. 29, no. 2, 2000, pp. 24–26. JSTOR, http://www.jstor.org/stable/30212098.