Taking Care of Teachers, Teaching and Learning
Keeping math fresh and alive for your students during the holidays goes a long way in keeping both rigor and motivation high throughout the holiday season. In last week’s blog post, the mathematical motivation ideas I shared centered on ways to make holiday learning fun for your math students. However, keeping things fresh and alive for yourself also needs to be a priority during this busy and sometimes overwhelming time.
Whether you’re working in a classroom with students or as an administrator with teachers, this season brings with it all kinds of hectic activity. I’ve received much advice about this over my thirty years in the teaching world. In addition to injecting a little holiday cheer into student assignments, I frequently take the advice of my colleagues to ensure I don’t burn the candle on both ends during this month. Here are a few of my favorites:
- Seek Out Positive Friends and Mentors: Hang out with people who love teaching and express positivity. Negativity brings everyone down, and sometimes it’s those who are closest to you who may not be good influences at the moment. Gravitate towards positive people when you’re feeling close to the “edge.”
- Plan Ahead: Take some uninterrupted time to get your lessons planned and prepped for the first week back after break – your time off will be so much more relaxing.
- Create Self-Deadlines: Set a timer to get tasks done – tasks such as grading papers, writing lesson plans, or reading a book. Far too often, we allow ourselves too much time for tasks and end up getting distracted. When I must tackle a task I’m not eager to do, I’ll set a timer for 60 minutes (or whatever seems appropriate) and commit to not letting myself get distracted till the time is up. You’d be amazed at how productive you can be with this kind of goal.
- Don’t be a Perfectionist: “Don’t let perfect be the enemy of good.” Sometimes good enough truly is good enough. Let yourself off the hook.
- Simplify: Break large tasks into smaller, manageable tasks. You don’t have to complete the entire project to make headway.
- Say no: It’s easy to over-commit during the pre-holidays. Remind yourself that you’re teaching and self-caring at the same time. It’s okay to say no to extra things that others can do. And it’s okay if you don’t bake every plate of cookies from scratch or attend every holiday celebration to which you’re invited.
- Take Time to Think: Give yourself some uninterrupted alone time. This is a great time to meditate or to try out free writing. Pick up a pen and a piece of paper (or a journal) and just let your thoughts freely flow through your hand onto the page. You just may discover some new ideas you didn’t even know you had.
- Breathe: Schedule time just for yourself – put it on your calendar, turn off your cell phone, get away from the hustle and bustle, and do something you enjoy. Creating time for yourself may be just the thing that helps you stay centered.
If you’re needing more ideas for stress management for educators, check out this article on beating holiday stress or this infographic on self-care. Taking care of yourself this season will make a difference for your personal motivation, making you the best you can be on behalf of students.
Here’s to a fantastic month!
Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.
Please share your thoughts on stress management for educators in the comments box below. Our collective wisdom will go a long way in supporting students.
Game Play, Math, Problem Solving, Teaching and Learning
As the holidays approach, and with them an extended break between semesters, motivation wanes, not only among students but also within the teaching ranks. Classroom teaching can be a challenge – trying to keep students on-target with their learning goals while acknowledging the distracting festivities all around.
As a classroom teacher, I sometimes found myself frustrated by the ways in which my students got caught up in the holiday cheer. After a few years, I realized that it wasn’t only the students who were pulled away from the learning at hand; I suddenly realized that I was contributing to the tension between learning and celebrating. I was eager to get out the door to get more shopping done, to get ready for yet another party, to be released from the pressures of work so I could engage in more holiday play. I was contributing to the frenzied atmosphere in my classroom because I was distracted by my own desire to be on vacation. I was tired, overwhelmed, and a bit burned out — and my students knew it.
At that moment, I realized I needed to do two things: have fun with teaching during the holiday season and attend to some self-care.
Having Fun with Teaching and Learning
First, I made a list of the standards to be covered during the weeks between Thanksgiving Break and Winter Break. I looked at the tasks and problems included in my district-adopted textbook. And then I contemplated ways I could redesign the tasks to include holiday flair while meeting the objective.
- Shopping Task: Given that shopping is a big activity this time of year, I like to set students up with a math activity that involves buying gifts for others. I give them a budget, a list of people, and a time limit for purchasing gifts for each person. This activity may be as open-ended as letting them shop online or as limited as giving them a specific scenario such as this one from NCTM. You might even take your students on a field trip to the mall. When I did this, I made arrangements ahead of time with 5 stores, all of whom agreed to ring up the purchases and give my students mock receipts (no money changed hands). The students worked in groups to buy gifts for a family of 5. They had to plan ahead as there was a minimum for each family member in order to qualify (they couldn’t just buy a deck of cards for the last person because they had cut it too close). The team that came closest to $100 without going over “won.” Afterwards, each team received $25 (earned from a math-related fund raiser we did before Thanksgiving) to shop for a child on the Angel Tree at the mall.
- Coordinate Geometry: My 5th-graders are usually working on coordinate geometry around December, so I like to replace some of the textbook tasks with graphing tasks that result in creating holiday pictures on the coordinate grid. The students love this so much that they ended up creating their own coordinate grid puzzles for one another.
- Game Play: Designating a set period of time for game play provides a fun way to review concepts already covered during the year. I like to set out some marshmallows and chocolate chips for the kids to munch on as they play games that have become favorites throughout the semester such as One, Two, Switcheroo or Go Fish.
There are so many ways to connect holiday fun to the math standards you’re currently teaching. Give it a try…and let us know how it goes!
Attending to Self-Care
I’m saving this one for next week. In the meantime, take some time for yourself!!!
We wish you the best as you navigate these weeks between Thanksgiving and Christmas. Focus on making things fun for your students – and you’ll have more fun, too! And be sure to take care of yourself in the process.
We would love to hear from you. What are you going to do to make math fun for your students during the holidays?
Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.
Problem Solving, Professional Learning, Teaching and Learning
Last week, I shared ways to shift homework practices to maximize student learning and understanding. This week, I turn my attention to grading practices. Just as with homework, when students receive their projects or tests back with grades written at the top, they simply look at the grade, make a judgement about whether or not they are good at math or if their teachers like them, and pretty much disregard any other comments on the paper.
We, as teachers, know that reflecting on work and learning from mistakes is where real learning takes place. However, even when we ask students to reflect on how they did, that score at the top of the page supersedes anything else on the page that could lead to a learning experience.
So…what can we do to push students to focus on the learning rather than on the grades? Here are a few ideas you might try…
- Grading Practices 1: Give students the opportunity to share everything they know. As teachers, we hold the power to choose which facts and details we deem most important to include in an assignment or test. However, our students have so much more knowledge to share than we have anticipated with our questions. Why not include a blank page at the end that asks students to tell us everything they know about the topic at hand that wasn’t asked? The example below is from a science class, and is easily transferrable to math class!
- Grading Practices 2: Highlight mistakes, but don’t give a grade. When grading an assignment or test, simply highlight the mistakes each student made. Do not assign point values, and do not put a score at the top of the page. At first, your students will ask, “What did I get?” or “How much is this one worth?” Resist, resist, resist! Do not go there.
- Grading Practices 3: Give students time to reflect upon and discuss mistakes. Rather than going over the assignment or test as a class, ask students to reflect on their on their own work. They may discuss and compare answers with their friends, but in the end, everyone must learn from his/her own mistakes if learning is to take place. As teacher Leah Alcala says, “Learning from mistakes is really what learning is.” Click here to see Leah and her students in action.
- Grading Practices 4: Share “my favorite mistakes” before passing out papers. After highlighting mistakes as described above, go through the papers again to look for trends and teachable opportunities. Select 3-5 of your favorite mistakes to discuss with the whole class prior to passing out their papers. This helps to glorify mistakes, communicating that mistakes are among the best learning opportunities we have.
I’m hoping that between last week’s homework post and this week’s grading post, you’re seeing ways in which teachers might shift their practice to maximize student learning without adding to the plethora of things they already do every single day. Simple tweaks in our practices can bring about tremendous shifts in student learning.
Please let us know how it goes by sharing your thoughts and stories in the comments box below.
Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.
Math, Professional Learning, Teaching and Learning
I remember math class as a child. As soon as we walked in the door, we would get our homework out and grade it as a class, usually trading papers to keep us honest. The teacher would read the answers, and we would simply mark each item that was incorrect, total the number of correct answers, and write that number at the top. And then we would give the papers back to the original owners.
As a good math student, I remember both the pride and fear associated with this practice. I was proud when my paper came back with 100% written at the top. However, anything less than 100% resulted in silent shame, the certain knowledge that everyone in the class realized I was a fraud, clearly unworthy of the reputation I had built. (And I felt even worse for my friends who struggled in math, knowing the humiliation they felt when they received their papers back.)
More importantly, we were unaware that our scores were not the feedback we needed. With no opportunity to understand why each answer was correct or incorrect and to self-correct, as needed, we simply looked at our score, proud with a good score and ashamed with a bad score. End-of-story.
Let’s take it a step further – even now, math homework often includes practicing the same skill 20-30 times. Although students need to develop automaticity, if they already know how to do long division, for example, they need only practice a few times before the practice becomes tedious. And, of course, if they don’t already know how, then practicing 20-30 times incorrectly is only going to reinforce bad habits.
If the point of homework is to see if students “get it,” then 5 practice problems is enough. If kids get it after 5 problems, and you ask them to do another 35, you’re just being mean. And if kids don’t get it after 5 problems, and you ask them to do another 35, you’re really being mean. – Matt Cwalina, Discovery Education
So, what can we do to improve students’ homework experiences?
The 2-4-2 Homework Policy
Steve Leinwand, the author of Accessible Mathematics: Ten Instructional Shifts That Raise Student Achievement and Sensible Mathematics: A Guide for School Leaders, suggests a new way of thinking about homework. Rather than assigning 20-30 problems, assign students 8 well-crafted, engaging problems using the 2-4-2 homework policy.
- 2 problems on the new skill (This is usually enough to determine understanding and, at the same time, avoids practicing and reinforcing) mistakes);
- 4 cumulative review problems roughly drawn from content developed the day before, the week before, the month before (think about being strategic with prerequisite skills for the current content); and
- 2 problems that require showing work or including explanation that supports problem solving, reasoning, and justification.
A Feedback Process That Promotes Learning
And then comes the most important part…feedback time. At the beginning of math class the next day, rather than asking students to trade papers to “grade,” the teacher posts the answers to these eight problems on the board. S/he provides students with five minutes to review their work in pairs or triads with particular attention to the last two problems. After five minutes of small-group discussion, s/he leads a group discussion of any problems that are still causing trouble. And here’s the kicker: homework is only to be recorded as completed.
This practice sure would have been helpful to me as a young scholar. As a matter of fact, as a middle-school student, I would meet with two of my friends before school to “compare answers.” For me, this self-created practice was especially about knowing that I know – going into class confident of my ability to do and understand the math. What I didn’t know then was that, someday, this would be the exact practice I would encourage in my own students.
Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.
After reading this post, please join in on the conversation using the comments box below! What homework practices do you currently employ? How might you reframe your practices to make them meaningful and useful for students?
Interested in learning more about KP Ten-Frame Tiles? Please check out Peggy’s latest Beyond Base Ten Blocks journal entry, Manipulatives First.
Game Play, Problem Solving, Professional Learning, Teaching and Learning
Years ago, I walked into a Weight Watchers meeting, shy, self-conscious, and unsure of what to expect. After signing my agreement and going through what would become my weekly ritual, I sat down to read through the stack of literature they gave to me. I read through many ideas, insights, and testimonials. Yet it was one very small side note that caught my eye. There, in an offset lavender box, were familiar words that resonated with me. “The Four Steps for Solving Your Weight Loss Problem.” Can you guess what those four steps were?
- Understand your weight-loss problem.
- Create a plan to address the problem.
- Solve the problem by following your plan, adjusting as needed.
- Reflect on your progress and check for new ways to address it.
Yes – these are the four steps I shared with you in last week’s blog post, So You Took Keywords Away – Now What? These four steps, immortalized by George Polya in How to Solve It, are the same steps for solving mathematical problems. It turns out that these steps find utility in all of life for beyond math class! And, interestingly enough, we were encouraged to move back and forth among the steps, reflecting upon and revising our plans from one week to the next.
Fast forward to today…I had some great conversations with several of you last week after sharing the problem solving template I use (click here to download again). One such conversation centered on the notion that Polya’s problem solving steps are not isolated, sequential steps. Rather, they are stages in a process that is both fluid and flexible.
Here are a few thoughts on ways to encourage and demonstrate flexible, fluid problem solving with your students:
- UNDERSTAND the Problem: This step has two parts. And you’ll likely revisit this step several times throughout the process as a way to monitor and adjust your progress.
- Understand the Story: Read the problem for understanding. Cover up the question at first, and relate to the context. Who is the problem about? What is happening? Where is it going? What story is being told?
- Understand the Question: Read the question to discover where the story goes next. What is being asked? Given this direction, what information in the story is useful? What are the quantitative relationships that emerge based on what the question is asking?
- PLAN a Course of Action: As with the Understand stage you’ll likely revisit your plan several times throughout the solution process, revising it as needed. Therefore, although you may be tempted to create a definitive plan, it’s likely that you will benefit more by coming up with something loose that you can revise as you go. The more flexible you are with your plan, the more likely you will be able to engage with the problem realistically, especially if you get stuck or need to back-track a bit. And remember that good plans includes both thinking strategies and a representations (see last week’s post for more on this).
- SOLVE by Implementing Your Plan: You’ll want to be flexible and fluid during this step of the process! Dive right in, knowing that you’ll be revisiting the Understand and Plan stages a few times to ensure that you’re on the right track. It’s okay to revise your plan once you gain new insights and notice new nuances within the problem itself.
- CHECK Your Solution and Reflect on Its Accuracy: This stage is so much more than using inverse operations to check for arithmetic accuracy. Did you really understand the address the original question? Does the solution match the original context? Does it answer the question? Did the plan work? Did both the thinking strategies and the representations help get to an accurate solution? Was the solution process messy or elegant? Might there have been a different plan that may have been more efficient or revealing? Does the final solution make sense? Does your solution need tweaking? Do you need to go back refine your process a bit more?
As you can see, problem solving is not at all linear, with siloed steps that happen in isolation. But, rather, problem solving is both fluid and flexible, allowing for movement in all directions throughout the process. Just as with real-life problems such as weight loss, job searches, or financial decision-making, moving back-and-forth among these steps allows you dive in, refine your understanding, revise your process. And even when you get to the check/reflection stage, you’re not necessarily finished.
Let us know what you think – we would love to hear your stories! Do you have any real-life examples of when this problem-solving process could be helpful? Have you had the chance to see students engage with problem solving that revealed flexibility and fluidity?
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PS – Beyond Math Blocks Teacher Institute is just around the corner – October 25-26 in Phoenix, AZ. My colleagues and I are super-excited about what we have in store for you. Have you signed up yet???? Click here to learn more.
PPS – Check out Peggy’s latest Beyond Base-Ten Blocks: A Search for a Better Solution journal entry and learn more about how base ten blocks may be problematic as manipulatives representing number and operations in our elementary classrooms.
Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.
Math, Problem Solving, Professional Learning, Teaching and Learning
I’ve done it. You’ve done it. We’ve likely all done it at some point…used a “trick” to help us find the answer to a math problem. And, like magic, we have no idea why we got the right answer. It was just there!
Much like teaching algorithms without conceptual understanding, teaching keywords as a primary strategy for solving word problems is not only problematic, it’s harmful. It undoes logic, intuition, and reasoning. Rather than trying to really understand the situation, we pull out the numbers, find a word or two to indicate the operation, and voila, we have a solution.
If the keyword strategy for solving word problems was really that simple, we wouldn’t even have to read the word problem. We would only have to pick out numbers and words and then operate. However, just like the rest of life, it’s just not that simple. Key words are inconsistent (e.g., “more” can mean to add, subtract, or multiply, depending on the context) and, often, nonexistent (sometimes they aren’t even present in a word problems). Sure, they work in contrived situations when “experts” write them to conform to a formula. But trying to apply an over-simplistic strategy such as key words will let us down in real life far more often than it will help us.
So, if using a keyword strategy won’t work, how else might we go about solving word problems?
Here are three strategies I’ve found to be highly successful. If you find that you, or the teachers you work with, are falling into the keyword trap, please share these strategies – they really work!
- Bet Line: Present a word problem, revealing only one line at a time. First, present the title of the word problem and ask, “What do you bet is going to happen in this math story?” After listening to a few predictions, reveal the first line. Then ask, “What do you bet is going to happen next?” After listening to a few more predictions, reveal the next line. Continue asking “What do you bet is going to happen next?” after you reveal each line until it’s time to reveal the question. Ask, “What do you bet the question is going to ask?” This has been, by far, the most productive process I’ve used to help children really understand the structure and flow of word problems. Want to learn more? Check out this article from NCTM.
- Target the Question: Post one reading passage each week. The passage should include several quantitative bits of information that can be used to answer a question. Then, each day, post a different question that can be answered using some or all of the quantitative information in the reading passage. This helps students see that you don’t know what to do with a word problem until you know the question. And different questions will require that you “do” different things each time. For a commercial version, check out the Lone Star Learning website.
- Write Me a Story: Asking students to write their own word problems is a powerful way to help them grapple with the structure and syntax of story problems. Begin by providing an equation such as 24 x 6 = 144. Then, leave it up to the students to find a context that makes sense for the number set and operation you gave them. They need to be sure to include a statement of context, a quantitative scenario, and a question that makes sense. You can differentiate for students by giving them different numbers and operations. You can also make this more difficult by asking students to include additional information that won’t be used to answer their questions. You might also ask students to write multiple word problems that use the same equation.
So, there you go — three ways to move beyond a keyword approach for solving word problems. Next week, I’ll share an amazing template that provides students with space for working out their word problem solutions…so stay tuned!
Please join the conversation. What are your favorite ways to help students grapple with word problems? And please let us know how it goes if you use one of the strategies mentioned above!
Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.
PS – If you’ll be in the Phoenix, AZ area at the end of October, please consider joining us for the Beyond Math Blocks Teacher Institute. This unique opportunity is designed to support K-5 teachers and coaches as they reimagine mathematics teaching and learning. Learn more by clicking here.
