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Cogito Ergo Nerd


In the beginning of my teaching career, I was devoted to the idea that students needed to do nightly homework because math was a cumulative subject, and material kept building, and students needed to make sure they could do it on their own, and blah, blah, blah... But, I hated checking homework. I assigned only the odd problems, so students could check their own work and I could grade on completion. I still had students not even attempt the assignments, but more often than not, students just did the assignment for the grade. They never checked their answers. I had many students with high homework averages and extremely low quiz & test averages. The reverse was also true. I had students that mastered every test, but never completed a homework assignment. In the latter situation, I had students end up repeating the course because the grade was not high enough. Things needed to change!

My summer of 2017 was spent reading, researching, and stalking Twitter about other people's experiences. Processing my own personal "why homework?" question, I focused on that fact that homework, in my class, was purely extra practice. It was just a piece of the student's own personal math journey. I needed something that accurately reflected that learning. So, I completely revamped my grading policies. I decided to switch to Standards Based Grading AND eliminate the homework grade. Big steps!

I still believe that students need to practice, but more importantly, they need to learn when and how to practice. I no longer assign homework. I provide extra practice, daily. Additionally, I try to use sites like DeltaMath, where the students can have infinite amount of practice with immediate feedback. At the start of the school year, we have many class discussions on who the practice is for (their own personal use - not a teacher check), what should they be practicing (new AND previous material), when is good time to practice (daily when they can, definitely before quizzes and tests), why is there so much practice (so they can practice all the time, any time), and how they determine if they need the practice (low quiz grades or not solidifying understanding in class). Students should only practice enough to understand the material. It should not matter if they needed zero problems, 5 problems, or 20 problems to "get it." And they should not be rewarded nor penalized for needing or wanting that amount of practice.

In the years since I completely dropped the homework requirement, my overall class averages have not changed much. In fact, the class average has improved AND I have less repeaters each year.

I do have to constantly reiterate that just because I do not grade the practice does not mean they do not have to do it. It irks me when parents tell me that their child claims they have no homework, ever. At the beginning of the year, I make it clear to the students what happens when I hear this comment from parents. I proceed to show those parents exactly where to find the plethora of practice material AND explain how they can monitor the completion of the practice. Practice is not optional. The amount of practice needed, is optional.

UPDATE: At the end of the 3rd quarter of the 2019-2020, we moved to emergency remote learning due to the COVID-19 pandemic. My class average at the start of remote learning stayed the same as the end: 88.14%. I had no students repeat the course.

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The first real week of school is always devoted to learning routines. AND our first week is usually a four-day week! I cannot even begin to tell you the benefits of easing back into routines and the beauty of letting your body recover from the most exhausting week of the year.

To begin the year, I love using Sara VanDerWerf's Name Tents. It is a great way to get to know the students. I also provide a prompt each day, otherwise I get "I don't have a comment" on a lot of them. Since I sometimes teach the same students again, I change the prompts each year. This year, I used:

  • List 3 traits of your all-time favorite teacher

  • List 3 traits that define you

  • What is your favorite "sport" to watch or play?

  • Share a boring fact about yourself. (borrowed from @drrachelbrenner)

I do not need them to learn their names because I know who most of them are before they enter my room. I like to use them as a way to individually interact with the students. However, this week, I was horrible about remembering to return them. And reminding them to write in them. And collecting them. It was basically a disaster. None of the students seemed to notice.

Random Groups

Starting on Day 1, my students are seated randomly. Every one of the student chairs is numbered. Each student gets a number based on my roster. That is their number all year. I have a max of 16 students in each class and use 4 groups of 4. Every student is required to sit in their numbered seat every day. However, every morning I change where the seats are located based on a Random Grouping Sheets document. (All I have to do is highlight column A, click the down arrow, and choose randomize range. It then changes the group configurations.) They must get to class to find their seat before the bell rings. Best part of my day is watching them hunt for seats!

Day 1:

After having the discussion about Friday's activity, we worked through Sara VanDerWerf's 100 Number Activity. We play 2-3 rounds. After which, I always ask if they noticed me taking pictures (of either activity). It's a great discussion about how focused they are because they never know, even when I forget to silence the camera clicks.

In addition to discussing more group norms and routines, I use this time to explain my picture taking. Students (and/or their parents) sign a photo release for school. However, I still feel like I should ask and get their permission for using their picture. Everyday is different and there may be some days you just do NOT want a photo taken of you. I explain that I post everyday to Instagram through #teach180, but the pictures are of the math and not them. They will know I am taking them because I say things like "I need a picture of that," or "freeze your arms for an over the shoulder shot." If I ever take a picture of their face, I will ask them first, it will be staged, and it will be used only for the internal school slideshow or parent newsletters. I do not post their face to my Insta (even with permission). I just don't wanna deal with the mess.

Day 2:

Wrong answer! Cute boat though

About a third of my students had a field trip. Using Fawn Nguyen's Noah Ark problem (via Sara VanDerWerf's blog as the original links seem to not work anymore), I introduced the Stand-And-Talk routine that I also got from Sara. I love that the students usually see all of the important info before they ever see the problem. Many of my students even give ideas for what the question mark in the problem might mean before asked.

Day 3:

Now that everyone was back in class and I felt like I had been introducing so many routines, I decided to introduce another! Questions Stacks by Sarah Carter @mathequalslove

I love this routine. Self-paced and self-checking, the students begin to love them too.

Students are supposed to enter my class having already mastered solving equations, but ... things happen, new students arrive, assumptions are made (and we all know about those). So I spend two days having the students go through three different QS with three types of solving problems

The activity helps to remind students of their solving skills they already have, and allows me to work with those who need refreshers.

Pro Tip: If you print these on business cards, use a marker or highlighter to color the inside seam on both sides. This way you can still color-code your sets for when one ends up on the floor.

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My school always starts on a Friday with a half-day. I like it because teachers have been there all week, and it is a quick way to meet everyone. Unfortunately, it makes each class about 18 minutes long. Usually, teachers are handing out their syllabus and materials list, so students can get them completed over the weekend.

I do not have a syllabus (I have a digital interactive slide-deck posted on my webpage) and I do not require any materials more than a graph paper spiral notebook and writing instrument. We are a 1-to-1 iPad school, but they are issued those, so no extra materials to buy.

Instead, on the first day, I like to give my students a group challenge. It changes each year as I teach some of the same students each year. This year, I chose the Impossible Paper Puzzle to get them thinking. I taped them to the walls, so each group had their own to look at, without being able to manipulate it.

The Rules of the Activity:

Each person gets ONE piece of paper to re-create the puzzle.

Each group gets ONE pair of scissors.

Talk to your group and plan wisely.

You may get as close to the Paper Puzzle as possible, but NO TOUCHING.

You get 8 minutes to work.

I usually have about one or two students who figure it out during this period. I immediately make them crumple the answer into a paper ball and recycle it. They are not allowed to share the answer.

During the activity, I hear many things:

"This must be trick. It's impossible!" - Really? You are literally looking at a completed puzzle!

"Are you going to give us the answer?" - Ummm, no, never ... to any problem.

"I don't want to waste/mess up my paper." - Arg! Take a risk, try something!

But I also hear:

"As a group, we have 4 papers, so 4 chances. Let's try your idea and see what it looks like."

"I WILL figure this out!"

"We know it has to fold it the middle."

"Can I have more paper?"

Before they leave class, I make them hide all evidence of attempts. Crumple and recycle. Finally, I explain the main rule of class - No Spoilers!

This means not discussing the activity for the day before others have attempted it AND not ruining it by sharing answers. This rule works for every assignment, project, test, activity, or class discussions. Then they are dismissed to think about this puzzle all weekend long. And they will. Even though it was not an "assignment."

These bits that I overhear start my discussion on Monday. We talk about risk-taking, perseverance, group discussion, problem solving, and what we learn from mistakes. It is great start to class and setting the tone to how the class will run.

I also NEVER share the answer. Those who solved it are now free to show only those who ask. Some students will continue to work on it all week.

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