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.

Mathematics Coaching During COVID-19

As a former K-5 Math Coach and co-instructor for Lesley University and Metamorphosis Teaching Learning Communities’ annual Mathematics Content Coaching Institute, I have been thinking much about the uneasiness all my fellow math coaches (and instructional coaches) must be feeling during this social distancing time. You are a teacher leader and your role is vital to the success of mathematics instruction at your school. Yet you don’t have your own classroom, so are likely feeling that your talents can’t be put to good use until core classroom teachers have a chance to adjust to the new normal. I feel you. I started brainstorming ways you can support your school and teachers during this time, where your work feels like support and value added, not extra or a burden to teachers. I hope you find some of the ideas helpful.

Ways You Can Support Your School and Teachers:

  • Community Building
    • Host daily or weekly “office” hours where you commit to being available on Zoom, Google Meet, Google Hangout, whatever the video platform, so teachers, administrators, or parents can sign on for support.
    • Create a school staff Facebook page or Slack channel for you all to connect online. Post math or tech supports that your teachers would find helpful.
  • Synchronous Learning
    • Co-plan, co-teach, and debrief
      • If you follow the three part coaching cycle of co-planning, co-teaching, and debriefing, you could continue your model if you are teaching synchronously.
    • Model a routine
      • Offer your teacher a model session where you model a small routine, such as a number talk, a ‘Which One Doesn’t Belong,’ or any other engaging launch. Doing this will allow you to micro-model online teacher moves, such as how to annotate on a tech tool, or how to ensure equity of voice.
  • Asynchronous Learning
    • Co-plan with teachers
      • Your teachers are still preparing materials for students even though they aren’t “live” teaching. This could be a great place for you to offer support, while modeling important planning moves, such as anticipating student responses. You can support them by doing a video call with them or even simply through a shared Google doc.
    • Create a landing page via the district or school’s website for parents that your teachers could share.
      • Many parents are feeling overwhelmed by the number of resources out there, the idea of having to teach their child, and “undoing” what the teachers have done by showing their ways.  Help your school and/or district by creating a one-stop-shop resource page where resources are housed (my recommendation: for all subjects) so parents and caregivers only have to look in one place.
        • We at the Center for Mathematics Achievement created our own resource document. We highly recommend districts make their own parent landing page that might house this resource, so parents have one place to look.
    • Create one resource for teachers of all grade levels you service where they can look for remote learning activities to use.
      • I have found Fawn Nguyen’s work a great model for this. She is a 5-8 TOSA (Teacher on Special Assignment) for the Rio School District in California.
    • Work with administrators to determine a re-entry plan if schools resume and/or plan for addressing the regression upon the start of the school year.
      • No one is prepared for the clean up that will need to happen either at the end of this year or the beginning of next year in order to keep students on grade-level. Now is a great time to help relieve your administrators of one more thing to think about and for you to start thinking about how you, as a school, will address the missed standards.  
        • How will you re-enter school if your school does resume some time this school year?
        • Will you adjust your scope and sequence next year to extend the length of each unit to include 4-5 days of pre-teaching of previous year’s content standards to ensure students have access to current grade-level work? What will need to be dropped in order to make this work?
        • Will you adjust your scope and sequence next year so the first month is teaching content missed from the previous grade level? Again, what will need to be dropped in order to make this work?
        • Be as prepared as possible and start thinking about this now.

This is not an easy time for anyone. Coaches, know you play a vital role in the success of your school.  Use this time to determine how your talents can best shine. If all of the ideas above sounds overwhelming, then my next suggestion would be to read the book Agents of Change by Lucy West and Antonia Cameron and focus on developing you during this time.

This is not an easy time for anyone. Coaches, know you play a vital role in the success of your school.  Use this time to determine how your talents can best shine. If all of the ideas above sounds overwhelming, then my next suggestion would be to read the book Agents of Change by Lucy West and Antonia Cameron and focus on developing you during this time.

Our Mathematics Content Coaching Institute mentioned earlier uses Agents of Change as the main text and provides educators and their administrators time and a network to navigate the challenging waters of coaching.

The event, originally scheduled for July 6 – 8, 2020 (8:30 am – 4:30 pm ET daily), has been postponed to August 4 – 6, 2020. If the event is canceled due to COVID-19, no processing fees will be charged. We will notify all by June 5, 2020 of our intentions to host or not host the event, all dependent on the COVID-19 situation. If the event goes on as planned, registrations will be fully refundable until July 24, 2020 (with a $50 processing fee).

Any coaches out there — let us know how you’re faring via Twitter and if any of these suggestions have been helpful for you.

Source:

West, L. & Cameron, A. (2013). Agents of Change: How Content Coaching Transforms Teaching and Learning. Heinemann, Portsmouth: NH.

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.

Routines and Their Importance

It wasn’t ever apparent to me how routinized my life is until this week.

I have a morning routine that I never blatantly established, but naturally just grew to own.  I wake up around the same time each day, usually to the licks and head butts from my adorable cat.  Before I get him situated, I always take care of myself first, in a selfish effort to help me “wake up” – brushing my teeth, showering, getting dressed, putting make-up on – and then I look at the clock and realize I’ve spent far too much time dilly dallying and now I’m running late.  My husband saves the day by feeding our cat and making my breakfast so I can run out the door and head to the school where I am working that day.

This has become my routine. During this COVID-19 isolation, it became clear to me how vital routines are to function.  The past two days have been so different. The alarm went off, but there was nowhere I really needed to be.  Knowing that I can’t go anywhere, I lounged around in bed, checking the swarm of social media notifications and news. Without a routine, staring at my phone has consumed the first hour of my past two days and hasn’t helped my mental state.  I didn’t need to get up and get dressed because I had nowhere to go; didn’t need to spend 20 minutes over-powdering my face with make-up. Suddenly, my sense of normalcy and regularity was gone. Time was a meaningless construct.  

Routines help us function. They give us structure in our lives so that we can focus our energy on other important things.  I never realized that the way my days are structured puts my mind at ease.  Today, I tried something different.  I woke up and pretended I had to be in a classroom on time.  I did my normal routine and immediately a sense of normalcy and calmness struck me.  As I reflected on my mental and physical response to my simple daily routines, I realized how vital instructional routines are for our children.

I certainly am not the first to think of this, but my experience during this pandemic has only further justified why routines are critical.  Specifically in teaching mathematics, using predictable and repeatable routines provides students structure. What routines do you implement in your classroom? How does class start? How do students interact with each other? How do you analyze a task as a class? How do you engage students to think and reason mathematically?

Many of us are away from our classrooms, and those “typical” routines now.  If you’re transitioning to online learning, we suggest you keep in place as many of the routines you had as possible.  Anything that still applies to an online space will support your students in a continued sense of normalcy. If your school is on an extended break – and you have the mental capacity to reflect – consider what routines you’ve used this year that you love, and which ones you might want to change when you get back to teaching.

If you really have time on your hands, a great next step would be to read Routines for Reasoning. This summer we’re hosting (dependent on current COVID-19 situation) the first ever Routines for Reasoning Institute: Redesigning Classroom Interactions to Foster Math Thinking with Amy Lucenta and Grace Kelemanik, authors of the book Routines for Reasoning.

Amy and Grace have developed specific instructional routines for mathematics that have transformed how students show their thinking.  Their “instructional routines are specific and repeatable designs for learning that support both the teacher and students in the classroom… enabling all students to engage more fully in learning opportunities while building crucial mathematical thinking habits (Kelemanik, Lucenta, & Creighton, 2016).”  

Reading the book during your social distancing time is one thing, but as we all know, developing quality teaching requires much more than reading about theory.  This Institute will provide educators the much needed time, space, and guidance to bring these routines into the classroom routinely, with follow-up opportunities to ensure implementation is successful.

The event, originally scheduled for June 30 – July 2, 2020 (8:30 am – 3:30 pm ET daily), has been postponed to August 10 – 12, 2020. Registrations are fully refundable until June 19, 2020 (with a $50 processing fee). If the event is canceled due to COVID-19, no processing fees will be charged. We will let everyone know our intentions to host, or not host, by June 12, 2020, dependent on the COVID-19 situation.

Let us know (in the comments or on Twitter) what new routines you’re building as we are engaging in distance learning. We’re interested in routines you’ve established for yourself or for your students in this ever changing world. We look forward to growing as a community and supporting each other.

Resource: 

Kelemanik, Grace, Amy Lucenta, and Susan Janssen Creighton. Routines for reasoning: Fostering the mathematical practices in all students. Heinemann, 2016.