A Homework Philosophy

I often reflect on how I implement homework (post here), and I am consistently disappointed. Although I do change it up now and then, my go-to tactic is to assign a set of practice problems based on that day’s instruction. We don’t have enough textbooks to send home with students (I’m not a fan of our textbooks anyway, so the limited number doesn’t really matter), so I either create or search for decent handouts to give for homework. Some of the practice handouts I’ve created are pretty good – asking students to reflect on what they learned, describe processes using math language, identify errors and write directions, etc. Unfortunately creating high quality homework assignments like these is extremely time consuming, and realistically, there is not enough time to do that for every assignment. And even when I’ve assigned the most creative and relevant handout, I can, without a doubt, count on hearing these three things the next day:

  • “I didn’t do it.” For some students, it’s a matter of time, motivation, circumstances, or a host of other reasons. I find this concerning, but that’s an issue for another day. What is within my power are the students that didn’t understand the lesson well enough to complete the problems. They went home, stared at the paper for a few minutes then shoved it back in their bag. Or even worse, when they left class they already knew there was no point even trying because they didn’t get it. This is definitely an indicator of a poor homework choice on my part.
  • “I did it…but I think it’s all wrong.” I find this particularly troubling because they are usually right; it’s all wrong. They’ve just spent a solid chunk of time practicing an incorrect method and now they’ve really got it down! AHH!!! So now, I need to try to “un-teach” that error and “re-teach” the correct method. Again, this indicates a poor homework choice on my part.
  • “I did it and it was SO boring.” I honestly don’t hear this very often, but I know some students are thinking it. They mastered the skill on the first couple problems, and diligently continued through the rest without being challenged or learning anything new.

What I would love to hear is, “I’m glad we practiced that more. Now I really get it!” Wishful thinking? Maybe. However, I believe that I can get closer to this ideal, and I definitely need to move further and further away from what I normally hear. With all of this in mind, I’ve been thinking a lot about my homework philosophy. I’ve never really given this particular “philosophy” much thought before and now that I have, I foresee a dramatic shift come September. Hold onto your hats…

Actively Think and Reflect about Math

Holy cow! Crazy, right? Stick with me…it seems so obvious but up until now my ideas about homework were very narrow. What I wanted was for my students to practice what we did that day or practice a host of things before a test. Practicing is part of it, for sure. However, to ACTIVELY think is what I really want. And, too often (see reasons above), the level of mental activity when completing practice problems is super low. And there are so many amazing ways to promote active and engaged thinking that could zest up the routine and connect with different learning styles! With this adjustment, I can implement some of the thinking routines (from Making Thinking Visible posts one, two, three, four) to help my students make sense of the content (bonus points for teaching great thinking tools for all content areas). In addition, homework assignments can become lessons in how to study on their own (make a set of flashcards, rewrite notes in a more concise way, other creative stuff that I haven’t thought of yet).

Reflection is also a key component to learning. If I can teach my students in class and through homework assignments to thoughtfully look back to that day’s lesson and make connections to previous concepts, this could be huge for their retention and engagement. Because we use Interactive Student Notebooks (ISN), I think the reflection piece can easily be woven into the routine. In class when we reach a question about a previous topic, I direct them to their notebooks; they search for the page, read and find an answer. In the past, I regularly told them to use their notebooks to study and help them on their homework, some did and some didn’t. So although this became part of our classroom routine, it didn’t translate into a homework routine. Homework assignments that require them to use their ISN to refer back to that day’s lesson will teach them to reflect on what they’ve learned and can extend this learning as well.

If asked before this summer, I would have ended the phrase differently – analyze and reflect about the day’s lesson. However, as I’ve read and thought more about homework, I think this is too narrow (again). Don’t get me wrong, I do want them to think about the day’s lesson, but I also want my students thinking about math in general. I want them to see math in the world around them, to problem solve, to notice patterns, to explore mathematical ideas that they find interesting, etc, etc, etc. So that’s why opened it up to actively think and reflect about math.

In tomorrow’s post, I will detail my budding plan


Thinking Routines – Introducing and Exploring Ideas (part 2)

Routines for Introducing and Exploring Ideas (chapter 4) continued…

3) Think-Puzzle-Explore (Activating prior knowledge, wondering, planning) Good at the beginning of a unit to direct personal or group inquiry and uncover current understandings as well as misconceptions


Similar to a KWL in structure, the key difference in Think-Puzzle-Explore is in how the questions are asked, which shifts the focus first to discovering students’ prior and partial knowledge (and misconceptions), then encouraging curiosity and planning. I’ve always found it hard to use a KWL in math class. Even when I was confident my students had prior knowledge about a topic, I found that they were reluctant to write things down in the ‘Know’ column, stating that they didn’t know if they were correct. The responses for what they ‘want’ to know lacked in depth and curiosity. Overwhelming the response was “I want to know how to solve it” or “how to get it right on a test.” I’m not great at going back to these types of activities at the end of a unit, so I never did follow through with the “Learned” column. I’m happy that the issues I have with a KWL chart are addressed with the Think-Puzzle-Explore routine. I think the shift to the phrase ‘Think’ will illuminate partial knowledge and misconceptions, which is really what I need to know when we start a new topic and is an essential tool in driving instruction. “… (‘Think’) gives permission to have a go, raise possible responses to the question, safe in the knowledge that you are not guaranteeing that you have the absolute facts but rather some thoughts about it.” I think the Puzzle section could be powerful as a whole class discussion providing a chance for students to build upon each other’s ideas. By recording a class list of ‘Puzzles’ on chart paper we could refer back to this list to check items off as they are discovered and add more ‘puzzles’ that arise as instruction continues throughout the unit.

4) Chalk Talk (Uncovering prior knowledge and ideas, questioning) – Open-ended discussion on paper; ensures all voices are heard, gives thinking time. A conversation conducted silently on paper. “It provides flexibility to move from one idea to another in a nonlinear way, to formulate questions as they arise, and to take the time needed to think through the collective information produced.”


With no names written on the posters, this routine gives students freedom to take risks and ask questions that they may not feel comfortable voicing in a verbal discussion. This routine gives every student equal contribution time and the chance for me to hear every ‘voice’, both of which are difficult to accomplish in other formats. The prompts can be single words and phrases, yet posing questions can take the conversation up a level. I used this activity once and didn’t love the result. I think the problem was that I stuck to phrases (e.g. Exponential Functions, Exponent Rules, etc), which seemed to stifle the conversation and they thought I was looking for a particular answer. I’m going to give this routine another try by posing questions instead. I find open-ended math questions hard to create, but I think it would result in a deeper conversation.

The authors suggest using Chalk Talk as a means to reflect on topics or learning moments – I love this idea! I envision using this activity before a cumulative test as a means to discover what the class remembers collectively about a variety of topics and to give them a chance to ask questions too. I anticipate misconceptions or gaps appearing in their work, that I could then use to structure the review activities that would follow. I also love the idea is to use this at the end of a term to reflect on what they learned. The authors provide sample questions to use for this purpose: “What have you been most surprised by in this unit of student? What is hard for you to master in this topic? Where would you most like to see improvement in yourself? What skills do you have around this topic that you could share with others? How do you know when you really understand something?” Nice!

I think this activity can be quite useful in a professional context as well. In a PD I attended last year, the instructor used this activity to pose questions about bullying and homophobic language. I found it to be very effective in giving every participant the opportunity to voice ideas in a safe environment. As a learner, I liked moving around the classroom, reading others responses and having the chance to respond or build off of these. I found it to be reflective and a chance to ‘hear’ many more voices than in a whole group discussion. An added benefit was that the follow-up discussion stayed on track, which I attribute to our collective focus on the chosen questions and realizing that a lot of people had meaningful ideas to share. Also, participants referred to ideas written the poster that struck them, which directed the conversation and fostered the idea of collective knowledge and experiences. I think this could be used in math focused PD, possibly to start the school year with questions focused on our department goals, the focus of the year, changes we are going to implement this year, etc.

**I would love to hear if you have used these routines OR if you have any ideas of what math topics for which they could work well.**

(Note: This is the second of three posts that detail a third of the ‘Thinking Routines’ outlined in Making Thinking Visible by Ron Ritchhart, Mark Church and Karin Morrison. After each number is the title of the Thinking Routine followed by the ‘Key Thinking Moves’, then ‘Quick Notes and Descriptions’. All of this information is directly quoted from the book Table 3.1 Thinking Routine Matrix. Then are the details of the routine and questions to accompany it. Finally, in italics, is a brief brainstorm of how I thought I might use this in a math classroom and/or in math department meetings.)

Keep, Change, Start, Stop – Student Feedback

I stumbled upon a great reflection form  to gather feedback from students (from Sarah Hagan’s blog Math = Love). I’ve tried many different methods over the years, which I have now scrapped because this one is awesome! I love this one because it’s short and sweet, while still being open-ended. Unfortunately the feedback won’t impact this year’s group of students, but I’m going to work on addressing these for next year’s crew. Also, I’m planning on giving this quarterly next year so that I can adjust things as we go. So here’s some of what they had to say!

KEEP (these fell into 3 main categories)

  • Helps me study; Easy to understand;  Super helpful; Color-coded notes; Graphs & Visuals; Layout of the notebook; Neat and Organized Notes
Reviewing/Practicing Content
  • Games (review strips, stations, jeopardy)
  • Review homework (throw-backs)
  • Review Packets with the correct answers so we could practice over and over
  • Step-by-step explanations that makes it easy to understand
  • Quiz Quiz
  • Doing quiz corrections
  • Staying after school to keep trying to help students
  • SAT practice
  • The homework and Do Now’s helped me to better understand
  • The agenda on the board
  • Interesting lesson plans
  • Do Now Packet


  • Do Now’s – make it a mix of SAT & what we are learning in class
  • More examples in the notes
  • Review games for every new topic
  • Go deeper into the lessons


*I asked them to consider things they do in other classes that helps them learn and include these ideas here
  • Weekend HW Review – for what was learned that week
  • Reviews throughout the entire year, instead of just the end
  • More projects, group work, teams and discussions
  • Having more time for questions after we have completed a topic
  • Give out SAT HW packet and we can do one or two problems a day to practice on our own *from Pre-Calculus class
  • Gather the questions students did wrong on tests and quizzes, then give an assignment in class to help improve learning
  • Time the Do Now
  • Math games & activities *this is from the class that needs to prep for the state test. There is a time-pressure that deters me from playing review games with the students, but maybe I should rethink this…
  • Binder *I did a poor job of helping them stay organized with all the other handouts, homework, etc. I think this comment is a plea for me to help them stay organized.


  • Giving quizzes a lot
  • Grading the problem sets so strictly – it’s too much sometimes
  • Harsh attendance policy *they have to be on time =)
  • You have the strongest rules in this school, so maybe you can make it a little easier.
  • Giving homework everyday

Here is a picture of the reflection form. You can download it from the original source – Thanks Sarah!

Keep Change Start Stop


July Blogging Challenge

I came across a blogging challenge, and I’m going to try this out. I’m a regular reader of math teacher blogs, and I’ve been trying to work up the nerve to jump into the ring.  The challenge suggested to start with a reflection on the past school year using the prompt, START/STOP/CONTINUE, and I think that’s a great way to begin.

3 things to START:

  • A couple years ago I used a lot of photos (art, architecture, etc) to launch lessons, but that fell off this past year. I want to start doing that again.
  • Planning lessons and activities with a focus on making thinking visible and the type of thinking in which I want my students engaged (inspired by a book I’m reading Making Thinking Visible by Ron Ritchart)
  • Regularly reviewing previous content and connect it to the new material.  I found that the students struggled to retain some of the content, especially vocabulary, after we moved on to a new unit. I occasionally would give ‘Throw Back’ homework assignments that would bring up some of these topics and the students appreciated it. I want to start this right away next year, and implement it weekly.

3 things to STOP:

  • Traditional homework problems…I’m finding that many of my students either don’t do homework, copy it from someone else, or end up solving the problems incorrectly and form bad habits. I’m still thinking about how (flipping, written reflections…), but I know it needs to change.
  • Over-booking each lesson. I tend to be overambitious in my lesson planning resulting in us working to the bell (which is good), but I then sacrifice the summary or exit ticket (which is bad). I need to either stop overbooking OR stop things early to get to the summary.
  • Feeling pressured to move on at the end of the unit. I got away from spending time with the students reviewing their tests at the end of the unit. I want to incorporate both test corrections and a written component at the end of each unit.

3 things to CONTINUE:

  • Interactive Student Notebooks! This was my first full year trying out this method of note-taking, and I’ll never go back! I used it in both Geometry and Pre-Calculus. The students loved it, I loved it, and it had a great impact on their learning experience!
  • Games and activities that increase student talk. I started incorporating more pair work at the end of the year focused on practicing content and verbalizing their thoughts. The students were engaged, talking about math, and happy. =)
  • A problem-solving strategy that I regularly implemented this year, Notice and Wonder. It really helped to develop my students’ confidence with open-ended and word problems. Notice & Wonder Record Sheet

Thanks for the challenge! Day 1 completed! =)