If you’re not a teacher, you’re probably sick of the whining. Heck! I AM a teacher, and I’m sick of my own whining. I write this as someone who is consistently described by both her students and colleagues as a cup-half-full kind of gal–this year was TOUGH! I asked my teacher friends on Facebook and Twitter what exactly made this year so exceptionally difficult. My hope is to help our communities and administrators understand why our teachers are near broken and provide some space for reflection and healing for teachers. Continue reading
I have a friend who is an elementary teacher, and she’ll ask me for math review games on occasion. One day, I was sharing one and she said, “Seriously, you need to make a list of all these games/reviews.” So, here it is. Let me begin by saying, I believe MOST if not all of these were stolen from other sources. I’m simply compiling them nicely for you (and for me) to reference in a pinch.
All of the games below can be done with a question stack or a review sheet broken into four or five slips. For that reason, they are quick and don’t need a ton of prep.
Connect 4 – Place a grid on the board. As each team (I suggest 3-4 in a group) completes the required problems and checks them either with you or a key, they can select a spot on the board using a symbol or initials. The goal is for a team to connect 4 diagonally, horizontally, or vertically. This game gets competitive when a team has lost any chance to win so they try to “block” others. In the end, typically only one team wins. Thanks go to my co-teacher Kayla Shivley for this one!
Gambler’s Review – Similar to the previous game, you place a numbered grid on the board, students complete required problems and mark initials on a number they consider “lucky.” The only differences are I typically have students work in pairs on this task and at the end I use a random number generator to select winners. I think I learned this one from colleague Allison Tuleo.
Trashketball – Similar to the previous two games, students complete problems in teams or partners and then check them. Each team earns two points for an accurately completed problem set with a chance to shoot for 1 or 2 BONUS points depending on where they choose to shoot their trashketball from (close or far from the line). Watch Trashketball in action HERE. This is a FAVE among my students. It literally requires a paper ball, masking tape and two baskets and they’re thrilled.
Four in a Row – This game I took from Sarah Carter (@mathequalslove) which she gleaned from Fawn Nguyen (@fawnpnguyen). I took a review sheet and removed all the space for work. I wrote the answers on the back of the worksheet. On
a separate sheet there is a numbered grid with the same number of problems as on the worksheet. Students are paired and “compete” against one another. One student starts by choosing a number. Both students work on that problem. When they both agree on the answer, they check to see if it’s correct. If it is correct, the student who chose that number puts his/her initials in the box. Then, the next student selects a box/problem. The first to get four in a row wins. This is a review I used for an Algebra II Trig Unit.
The games below work best if you have a list of prepared problems on a PowerPoint for review or you can just write the problem on the board.
Risk – Students partner or team with a markerboard. After they complete the problem, they decide how much of the beginning balance of $100 they’d like to gamble that their answer is correct. At the end of the set of problems, the team with the most money in their bank wins. A few hacks: 1) I have students in tables of four. I pair them and tell them the team with the most money at EACH TABLE wins. This means that each half of the table will keep the other honest. Students are typically generous and say “close enough” when I wouldn’t agree. 2) If a team loses all their money, they can get a loan for $10 to stay in the game. This review is from Julie Morgan via Sarah Carter (@mathequalslove).
Unfair Game – This is a game I have NOT tried yet and just learned about from former student and excellent young educator, Kayla Lewandowski, at a professional development workshop. How cool, right? Anyways, this game is so unfair! The rules are all in this presentation, but I’ll give you the gist. After teams do the problem, they are randomly selected to share their response. If their answer is accurate, they can decide if they want to earn the points or give them to another team. The point value is then revealed and sometimes it’s positive and sometimes it’s negative. So unfair, right? 🙂
MATHO – Like the old staple BINGO, you create a MATHO board by randomly placing answers on your board BEFORE you begin. Then, you would place a problem on the board and students solve it. Next, they look for that answer on the board and mark it off. They hope to get five in a row horizontally, vertically or diagonally (you can also allow four corners).
These tasks require a bit more prep, but are powerful review tasks for their own reasons.
Speed Dating – I’ve tried this one in the past and it hadn’t worked well for me. But, I think I’ve finally got it down! I have tables now, so that has helped. I placed the tables in a circle in my room. On the outside of the circle I’d place students who performed best on the last
formative assessment and everyone else on the inside. On each table I place a problem for all four people to work on. Once all 4 students agree on the solution, they can look at the solution on the back of the paper the problem is on (I typically type all the problems onto a PowerPoint and print the whole slide to put on each table). I use an online timer and project it on the board–typically for 3 minutes, but it depends on the type of problems I’m asking students to do. For that reason, you may want to make sure you give tasks that will last approximately the same amount of time. For easier problems, for example, add more of them to take longer. Then, have everyone move right one table and complete the next task. Do this until all your task are completed. I have 8 tables and 32 students, so I typically have 8 tasks. One hack: I typically assign students to their first table since I found when I just told students to find a spot to where they were assigned (inside or outside), they’d sit by their friend and it wasn’t as effective as it could be.
Sum ‘Em Up – This requires the most prep work, but it really checks a lot of boxes: Differentiation, critiquing the work of others, accountability, and collaboration. There are several variations. My favorite is to create one task like this one. Students choose which task they complete based on the fact the problems are increasingly in difficulty from A-D. Then, they sum up their answers. They can self-check with the answer (which is the sum of their individual answers) on the back of the task (or the next task) or can check with you. If it’s not correct, they’ll have to look at one another’s work and determine which solution is incorrect. Often times kids will say, “I wasn’t super confident about my answer.” Once they get the correct sum, they move on to the next task. I typically color code the tasks so that I can see if a group is falling behind and needs redirection or additional academic support. Hack: You can find a bunch of these on Teachers Pay Teachers.
Also, here’s how I quickly group students–often assigning a “coach” who performed well on the formative assessment. I hope it’s helpful to have a “bank” or reviews. I’d love to learn some new reviews if you have any to share :). Please share below…
This fall, not only did I return to the classroom after a 2 year hiatus as an instructional coach, but I joined and led an Algebra II team that had agreed to launch Standards Based Grading. We were given a week over the summer to upend our current curriculum and start from scratch with the Common Core State Math Standards. With the help of our instructional coach, we had developed a strong curriculum map and began writing our first assessments, rubrics and lessons. We weren’t the first team to take the leap. The previous year, the Geometry team was not only the inaugural team to take the Standards Based Grading jump in our department, but also our school. While it wasn’t easy and took a great deal of time and effort to redesign the curriculum and assessments, it was deemed, overall, a success.
- Room for Growth At the end of the semester I had students reflect on our classroom norms as they related to themselves as a student and as a classmate and, of course, my instruction. On the back of the evaluation, I had them also share their thoughts on Standards Based Grading. I was particularly impressed with the thoughtful reflection of one student, “It favors the students’ education over their grade and the work they complete.” Yes! Another student wrote “(I like how) we retake the test we do to better ourselves.” They’re really starting to get the basic values that are the foundation of our practice: prioritizing learning over grades, and growth over time. But, in reflection, I’d like to continue to prioritize growth mindset language in my classroom. For example, I give pencils that say “Got an A with Mrs. J” for students who receive an “exceeding the standard” rating of a 3.5 or 4/4. I was thinking that I should also give a prize to those who’ve most improved from the first standard to the second in an effort to honor growth. My colleague, Patrick, also suggested that we call the second assessment we give for each standard as the “Growth Assessment.” I like that, too.
- Struggle with Student Motivation By far the biggest struggle that’s been voiced among my colleagues is the frustration over the lack of student homework completion. Math is a skill and, like any other skill, requires practice. I’ve told students more times than I can remember that mentally assenting to mathematics done correctly does not mean that you can perform the skill as well. You can’t just watch football and think you’re ready for the NFL. Nonetheless students think they can. We’ve talked about counting homework for points, but the teachers in Algebra I remind us that student work in their classes reflect little effort and, sadly, copying. They cringe at the thought of giving that caliber of work points towards their final grade. So, we return to making the argument to students about the importance of homework to improve understanding and summative performance. I would LOVE any insight any of you might have!
- Admiration and Respect for My Team I wasn’t the only one without experience in Standards Based Grading. On the team, which comprised 8 teachers, there was only one who was also on the Geometry team and he was a huge contributor, helping us to avoid pitfalls and encouraging us to focus on what he felt would give us the strongest start. That being said, everyone embraced the challenge and appeared eager to contribute to the major undertaking, which included a division of labor and group edits. While we certainly believed in the tenants of Standards Based Grading, that is, a student’s grade should reflect what they can perform, articulate and understand and not a student’s behavior, we had to be honest about the practical rubber-meets-the-road type pitfalls, such as student motivation. We also needed to reflect on the flow of curriculum, the shifts in our pedagogy, and our team dynamics. We didn’t always agree. In fact, often we didn’t. But, our team is professional, reflective and fun. We tangled until we could live with the outcome and may revisit it again. We are currently on the “act – reflect – new action” cycle of education and are content with that. Truly, I feel blessed to work with such a thoughtful team of educators.
Overall, I would deem semester I a moderate success with room for my personal growth. I hope to move forward in shifting mindsets towards growth and away from a focus on grades. I want students to know what they know and what they don’t know. I want them to learn the benefits of practice towards peek performance. And I want to continue the good work of a team that cares about what’s best for students, even if we don’t always agree on how. Also, I’m grateful to have the privilege to work with students. Teaching isn’t for the weak, but it’s the most rewarding job there is. It never gets boring, to be sure. Here’s to the future–have a great 2019!
“Anyone? Anyone? Bueller?!” That iconic line from the movie Ferris Bueller’s Day Off demonstrates the futile nature of asking unanswered questions to a group of disinterested students. But, we’ve all been there, haven’t we? We wonder if it’s the question, our instruction, the students? Whatever it is, it is not the Dead Poet’s Society classroom we had envisioned when choosing teaching as a profession. We’d like to craft the questions that draw students to engage in lively debate. How do teachers do that? What is the magic spell they cast over their students?
While I can’t promise to make your classroom performance Oscar worthy, there are some strategies that WILL get your students talking. Here are five:
- Ask questions worth asking. Oftentimes our questions aren’t that interesting or just rote drill. Ask questions that require students to explain concepts, their thinking or personal connection to the content. Questions that include verbs at a higher Depth of Knowledge level typically are “discussion worthy” and will lead to greater debate, discussion and engagement. Also, asking more open ended questions, for example, instead of asking “What is the first step here?” you might ask “How might you solve this problem?” which provides students the opportunity to make their thinking transparent to the class.
- Prime the pump. After asking a question, require ALL students to respond to the question with a partner, on paper, or in some way in order to commit to a response, and THEN pose the question for class discussion. You’ll find that your students will be MUCH more eager to respond.
- Declare a minimum. Wait time is important for students to formulate an answer (6-10 seconds is ideal), but saying something like “I need at least 8 hands” OR “Raise your hand when you know,” which implies that everyone should raise their hand at some point, often yields great results.
- Catch and release. When a student responds to a question, avoid the urge to either approve or disapprove of the response. When a teacher declares something right or wrong, the conversation is over. Rather, ask the rest of the class if they agree or disagree with that student’s response and explain their reasoning. You can also ask, “Does anyone want to add on to that or amend it? If so, in what way and why?” That keeps the discussion flowing and engages the class.
- Declare no student off limits. We want all students to formulate an answer to our questions, not just a select few. If it’s worth asking during class time, then it is a valuable exercise for all students. One of the areas that new teachers, in particular, struggle philosophically is calling on students who don’t volunteer. Often they share that they are worried that they might embarrass a student who doesn’t know the answer. I will encourage them with this, “If you allow students to prime the pump and ask open ended questions worth asking, students will be much more comfortable responding.” If you find a student answers, “I don’t know.” You can respond with, “What did you and your partner discuss?” or “Tell me what thoughts you had when thinking about the question.” If we create an environment that only tolerates correct answers and does not make transparent the conceptions and misconceptions around ideas, then students won’t risk sharing ideas at all. It’s up to teachers to make sure students know that it is natural part of learning to process to expose and refine ideas.
Like all new routines in classrooms, these questioning shifts will take a few days to a week to hone. But, if you are faithful in implementing them, you WILL transform your classroom discussions! If you have an instructional coach in your building, invite him/her to observe you and help you tweak your mad questioning skills. A second set of eyes always helps.
Let’s do it, “O Captain, my Captain!” Get them talking!
As always, I’d love to hear what works for you (and might for me 🙂 ).
Depth of Knowledge Wheel Webb, Norman L. and others. “Web Alignment Tool” 24 July 2005. Wisconsin Center of Educational Research. University of Wisconsin-Madison. 2 Feb. 2006.
I am a member of the #MTBoS (Math Twitter Blog-O-Sphere). If you are a math teacher, you are too! To find them, you need only jump on Twitter (@ExploreMTBoS) or search the #MTBoS hashstag and enjoy all that is available to you. #MTBoS teachers share everything from their philosophy on what is BEST Math Teaching PRACTICE to the details of the lesson they did TODAY. The #MTBoS has challenged its members to blog once a week for the next month. This week, the challenge is to blog about our favorite thing(s). Here are some of my FAVORITE THINGS I’ve learned about/stolen from this group.
- WODB (@WODB) or “Which one doesn’t belong?” has been a fabulous resource for eliciting high level discourse with students.
These WODB K-12 puzzles are low entry/high ceiling problems that will meet your students exactly at their level of understanding. Your job is to push their thinking by asking questions. I’ve shown an Algebra example to the right, but there are graphs, number, shape puzzles, etc. Enjoy them!
- Class Norms Signs – If you’re looking for GREAT classroom signs and resources, Sarah Carter (@mathequalslove) is your girl! She makes some SNAZZY stuff! But, these signs definitely served
two purposes in my classroom. ONE: They are darling and decorated my room nicely and TWO (and most importantly): They served as principles that guided the collaborative work in my group. I only had to say “Helping is not the same as giving answers!” or “Can you read the green sign I am pointing to? What does that mean? Please be a respectful group member and do that now.” I LOVED having them to point to!
- Sum ‘Em Up – This is a game/activity that requires both individual and group accountability from your math students. The idea is from #MTBoS’s Kate Nowak’s (@k8nowak)
“Function of Time” blog. For each skill, you make four problems of various degrees of difficulty and for students you’ve placed in a heterogeneous grouping. Each student works individually and then, students sum up their totals. At that time, they can ask the teacher if they are correct. If they are NOT correct, the students have to decide which student(s) made the error and why. This leads to great mathematical discourse and “critiquing the reasoning of others.” You can find more details to this fabulous activity in the link above.
Obviously, this is just a taste of what you can find from teachers on Twitter, but I wanted to whet your appetite for more. The treasure of #MTBoS is yours (and mine)…enjoy! Go, search #MTBoS and see what happens…
Okay, it’s time to face reality. Your winter break is just about over and in a few days you’ll be looking into the faces of your sweet students. If you’re like me, you’ve been dreaming about how you might do things differently next semester. Ah, where to start…
- Reflection is one of the most difficult but helpful practices for teachers. Nonetheless, a teacher who wants to make positive changes towards growth, should make it a regular practice. If you’re looking for a second semester change, ask yourself a few reflective questions about the first semester. Reflect on WHAT? How about…
- Classroom Management–This is easy! Ask yourself: what behavior is the most annoying? Is it students distracted by cell phones? Is it language? Is it off task behavior? Can you get students undivided attention when you need to? Do you have a “quiet signal?”
- Classroom Climate–Does your room have a positive or negative vibe? Do students want to or even look forward to coming to your class? Are students kind to one another?
- Student Collaboration–Are they really collaborating or just seated closely? Is there individual and group accountability? Do students hold each other accountable?
- Instruction–Are you bored by your own lessons? Is your instruction teacher or student- centered? Do your lessons require students to go beyond note taking? Are students invested enough to debate and argue? Are students given the opportunity to grapple with tough questions and space to problem solve?
- Assessments–Are your students given opportunities to think critically? Do your tests reflect higher order thinking? Is everything on your test “Googleable?” For more advice on creating questions that are not “Googleable,’ click here. Do your assessments give students opportunities to demonstrate what they really do know and understand? Are your assessments tightly aligned to your standards/targets/objectives?
- Curriculum–Are you “covering” too much? Does it feel like your students are only getting a superficial understanding instead of a rich understanding? Is it time to consider removing content that you’ve typically covered?
- NEWSBENJIVERTS. I’m not even sure how that’s spelled. I was introduced to this acronym while watching this episode of the Middle where Brick, the little brother, tries to coach his sister, Sue, for her audition for the school newscaster position. Brick starts with this small acronym to help her to remember key newscaster skills: NEWS; Natural, Eye contact and Winning Smile. But, Sue needs so much help it grows to NEWSBENJIVERTS. During her audition, she is so overwhelmed by her the huge acronym that she performs with huge eyeballs, an awkward smile and, frankly, looks ridiculous! All this to say we often look ridiculous to our students when we tackle more than we can handle. We end up back-tracking on our commitments, which only breeds a lack of confidence in our words and actions. Choose ONE, maybe two, things to tackle. Larger, sweeping adjustments can come next year.
- Ask yourself probing questions to problem solve. After you determine what you’d like to change, ask yourself how this student behavior, instructional approach, classroom culture, etc. has become a pattern in your classroom? What is the root of those behaviors? Come up with at least several causes beyond student motivation or administrative mandate to these problems. After all, you have no control over them. Look for causes within your circle of influence. Make a plan to address them. This is where the internet and your colleagues are great resources. If you have instructional coaches in your building like I do, you might want to elicit their help in brainstorming solutions or processing root causes.
- Everyone needs a pep talk. Okay, it’s your first day back. Imagine your classroom is a locker room full of athletes and they are looking eagerly to you, their coach, as you prepare to give them an inspirational half time pep talk. Don’t let them down, Coach! Remind students that you are there for them, care for them, and want them to be successful. Tell them what they, as a class, did well last semester and point out areas where they are growing but aren’t quite there yet. Tell them second semester offers a fresh slate. Tell them that you expect that second semester will be challenging, but that you’ll get across the finish line together. However you word it, speak it from your heart. Kids can smell insincerity a mile away.
- Take a moment to reconnect. Show pictures of how you spent your break. Give them an opportunity to share about their adventures. When we do this, we are creating a safe space for students and communicating that we care about them. It also allows them to open the doors of communication with a topic that is comfortable for them. This will make it easier when you ask them to engage in content related discussions.
- Honesty is the best policy. Okay, time to get real. It’s time to make a change. You don’t have to pretend with students. Unlike administrators they are there every day and know exactly what it is like to be in your classroom — for real! Share how you’ve reflected over your break and your plan to reset for second semester. One caveat: if you say you are making a change, you have to stand by it. Telling your students means they WILL hold you accountable–as they should. When choosing a solution to your problem, choose a plan that you can carry out. Avoid developing systems that will be difficult to manage. You’re too busy for that!
Who doesn’t love a fresh start? Let’s make a resolution to keep making resolutions. After all, the key to our growth as educators (and people) is reflection, plan, change, REPEAT. Keep fighting the good fight, my friend! The fruit of growth is always joy.
I’ve ALWAYS wanted to teach. Since I was a young girl. My dad had discovered a desk in the garbage at his work that was an exact replica of my teacher’s desk at school. I was thrilled. He also found a chalkboard which he mounted in the basement next to my recycled desk in my make-shift classroom. My sister was four and a half years younger than I. My curriculum, however, consisted of recouped purple dittos from my teacher’s garbage can. Therefore, as my pupil learning what I had just learned, she was well ahead of grade level. Her willingness to please her older sister made her a highly motivated student. Her kindergarten teacher reported to my mom that her writing was exclusively in cursive and could she be convinced to print, thank you.
I love it all, the lessons, the learning, the art projects. I was hooked. However, who and what to teach was still a question mark for me all the way until I entered college. I loved learning and typically I wanted to teach whatever subject I loved most and at my current age. Since my last stint in school was in high school, I selected teaching high school. After all the content was so challenging and interesting. I was torn, however, between History, Spanish and Math. You might be surprised that I selected Math. Well, at least based on the responses I get from EVERYONE I tell that I teach high school Math. I loved that it was so clear cut. I could clearly discern whether a student understood the content or did not understand the content. It was step by step procedure and seemed “easier” to teach. Since then, I’ve changed my mind about Math’s predictability, methodology and the importance of unscripted rich problem solving. But, that’s for another time–this is the BEGINNING of my story.
For approximately every 30 children in the US, there is a teacher. We are an army of face wipers, coaches, and empathetic ears. We deliver content, challenge, tutor and seek to inspire. But, what brought us to this point? What drove us to do, what I believe, is one of the most challenging and rewarding jobs? I’d love to hear your story! Please share in the comments below. Include in your response if you would have chosen the same age & subject if you could do it all again.
This post could also be entitled: “Stuff I learned from Twitter over Christmas Break.” One of the things I love about break is the chance blog binge and peruse twitter for ideas. I have a folder in my g-mail entitled “Read over break” and LOVE when I get to crack it open. I bore easily and without new ideas, (gulp!) even teaching might become stale for me.
1. Wingman I watched a great little video regarding a strategy called Wingman from the Teaching Channel. Here the most pensive and quiet student is asked to engage by observing the group and giving feedback later. I highly value student to student communication in the process of learning. That being said, I know that my class must be an introvert’s nightmare. This will allow the introvert to be an observer and still participate in the learning. The video demonstrated the Wingman strategy in an ELA class but I would give it a little twist in my HS Math classroom. I’d most likely hand the “wingman” a sheet to keep a record of when students apply one of the 8 mathematical practices and encourage groups to make sure they touch on at least four or five of them. At the end the “wingman” could give a report to the group on their progress and point out individual strengths.
2. Closure Strategies I found this great article on Edutopia on 22 Powerful Closure Activities by Todd Finley. While quite of few of them were either ELA or elementary in nature, here are a few I’d like to try:
Ask students to stand up, raise their hands and high-five a peer — their short-term hustle buddy. When there are no hands left, ask a question for them to discuss. Solicit answers. Then play “Do the Hustle” as a signal for them to raise their hands and high-five a different partner for the next question. (Source: Gretchen Bridgers)
Exit Ticket Folder
Ask students to write their name, what they learned, and any lingering questions on a blank card or “ticket.” Before they leave class, direct them to deposit their exit tickets in a folder or bin labeled either “Got It,” “More Practice, Please,” or “I Need Some Help!” — whichever label best represents their relationship to the day’s content. (Source: Erika Savage)
3. Kick me. The first rule of “kick me” is NO KICKING. Good to know. I found this great strategy on the Teaching Channel as well. I teach Geometry and this strategy allows me to help them solidify their understanding of the plethora of vocabulary associated with the topic. I would probably create a sheet that includes several figures that demonstrate the vocabulary word. Students would have the vocabulary words taped to their backs and would have to search out the matching vocabulary. This might be a great “beginning of the school year” activity that would allow them to mingle AND give me some idea what geometry concepts that they brought with them from middle school.
4. Better Quiz Corrections Okay, this one I THUNK up myself…well, sort of. It started when I began only highlighting errors on quizzes and giving students 5-10 minutes to make corrections after they were returned as a result of watching this fabulous video from…the Teaching Channel (have I mentioned how much I LOVE this Twitter follow?). I thought that I might make a half slip that students can fill out that might give them (and me) more feedback: You can view that here.
5. Reflecting on Student Work. This idea came also from a video from Teaching Channel but I can’t seem to find it. The idea is to take two students from the class and follow their work throughout the year. I would love if several of my colleagues could join me in this. We can see the types of errors our students are making and what antidotes we have, as a team, to counteract them. Since PLCs seem to be a major goal in our district and school this year, this sounds like a good place to start.
Well, here’s to a fabulous 2016! Wishing teacherdom all the best! What are your resolutions? Please share! 🙂
I wrote earlier in my blog about an article I had read on “Why Americans Stink at Math” by the New York Times (you can read both the post and the article by following the blog roll to the right) and how it just may have revolutionized how I teach. Well, I’ve been continuing to use this method and I’ve stumbled upon some happy surprises. Here are a few:
Everyone’s engaged. Yep! Everyone! I ask students to work individually on each problem and I walk around. This frees me up to see who is staring into space–which rarely happens. Most students have some ideas about where to start. They also want to be ready to share something with their partner when we switch to “You all.” It’s amazing! If students are stuck, I’m freed up to ask them questions about the problem that might trigger a thought. From my Honors Pre-Calculus class to my average Geometry class–it seems to put everyone to work. During the “You All” talk time, students seem to all be talking to each other ABOUT MATH. Awesome!
Problematic thinking is head off early. Because students generate the ideas, the most common misconceptions quickly come to light during our “We” discussion. We are able to discuss each of them and why the idea might not work. In addition we tackle, as a group, the points where students get “stuck” and identify why it is a difficulty. At that point, we generate ideas to respond to the difficulty until every student is satisfied with the solution.
I facilitate, they solve. By the time we finally get to the “We” discussion, I am able to direct the discussion so that students alone are able to (1) solve the problem and satisfy student curiosity about the problem and (2) flesh out all the faulty thinking and “stuck” points.
Obviously, I’m sold. The one down side is that each problem takes longer. As a result, I’m trying to find the perfect problems that generate the discussion I want. I end up doing about 3-4 examples only. In the past I would have done 5-7, but I don’t think I had the engagement or understanding I am getting now. It’s a trade off–one that I’m convinced I should take.
Have you tried it? What do you think?
If you’re thinking this is a Vanilla Ice fan post, you’ll be disappointed. However, “You’ve got a problem–Yo! I’ll solve it!” is the motto that my math team borrowed from the rap icon. No, this is a post regarding some of the collaborative methods I use in the classroom.
The first method is MAN OVERBOARD. In this activity I arrange students in groups of four and ask that they assign a “Captain.” I leave this up to them–it’s always interesting to me whom they choose. The Captain’s 1st job is to gather a marker board, marker and eraser for each member of his/ her group. I present a problem and have each student work “secretly” on his/her board. When the student has worked out a solution, he/she flips his/her board over. When the Captain sees that everyone has finished, he/she will say “Man overboard!” Then, the students flip their boards and discuss their responses until they can agree upon one. The Captain also has the responsibility to make sure that everyone is comfortable with the agreed upon solution. I’ve confirmed solutions for students in two ways: either discussing it as a group when everyone has finished (this takes longer because I have to wait for everyone to finish) or I present the problems on cards that contain solutions on the opposite side. Then, after the group has come to agreement, they have to reconcile their solution with mine as well.
The second activity is TAPS. My friend across the hall found this on the internet somewhere and, like most things I do, it is either an exact replica or adaptation of something I’ve stolen from someone somewhere–most times I can’t even remember the source. What I typically do is pose problems on individual slides in PowerPoint and print off the slides 6 to a page. I write the solutions on the back of the cards by hand. Then, I mass produce them so that each group has a set of problems. I ask students to assemble in their groups of four and tell them that the person next to them in on their team and the people across from them are on the other team. Students take one problem out of the envelope and all four of them work on the solution. Teams are allowed to collaborate. The first person to “TAP” the problem will have the opportunity to answer the question and check the solution. If he/she is right, the team keeps that card and earns a point. If not, the other team still has a chance. One caveat is that students who are strong in the subject matter, and quick, can dominate this game leaving classmates in the dust and without adequate review. I made it a requirement that the winner of each card present the solution to the rest of the group and answer any questions other group members might have.
Lastly I will present to you KNOTTY PROBLEMS. I found this on a DePaul University website I’ve attached under “links.” This activity requires a really difficult (AKA KNOTTY) problem. Students are given several minutes to solve the problem and identify key frustrations or difficulties they are having with the problem. Then, he/she presents the difficulty to an assembled group. They listen without interruption. After the student explains the difficulty, the rest of the group offers solutions.
I read recently that true collaboration really doesn’t happen unless the problem is too difficult/knotty to be solved by just one mind. Just a thought.
I’d love to hear what type of collaboration techniques that you’ve used, too–especially in a HS math classroom!
I have to tell you–light bulbs are going off here! My mantra for math instruction this year is “You, You all, We” and I’m amazed at the response from students. It’s absolutely fabulous! It’s amazing how many years of mathematical knowledge is inside those minds–yet, for many years, I approached my lessons as though they’ve never seen the concepts before (i.e. right triangles, Pythagorean Theorem, radicals, slopes).
For years I’ve followed the “Me, You all, You” mentality. By that, I mean I would model for students the appropriate technique (Me), have them practice with a partner or a group (You all), and then expect them to perform the skill on an exit ticket (You). While I’m still entirely a fan of exit tickets, I do think my philosophy of instruction may have yielded to a great paradigm shift.
It’s not that I haven’t take advantage of Professional Development–I have! I’ve gotten a masters degree in Teaching and Leadership, went to many conferences, but it is all coming together for me after I read this recent article about “Why American’s Stink at Math” in the New York Times. That simple phrase “You, You all, We” connected some of the pedagogical dots between my training in problem based learning (PBL), STEM and courses on collaboration and engagement.
The past two days I’ve posed difficult problems, knowing (okay, hoping) that there was some foundation my students could draw from. They amazed me! I gave them 1-2 minutes to work on the problem individually (You). I told them it was okay if they weren’t able to solve the problem, but to draw as many conclusions as they possibly could (for example, I asked them to write the equation for the perpendicular bisector given two endpoints–they could perhaps find the slope of the line, or find the midpoint, etc). Then, they were to spend 2-3 minutes sharing with their partners what they concluded (You all). I was thrilled at how quickly they engaged (even though it has only been days 1 and 2!). When the conversation seemed to die down, I brought their attention to the board and asked students to share what they could about the problem (We). In the end, I did very little more than facilitate. It was fabulous! The fact the some students were able to solve portions of the problem, but were stumped on others, highly motivated them to listen to the solution.
In year 10 of teaching–I think I’m finally connecting the dots–“You, You all, We.” That’s all it took!
Hope you are all having a great start to your year! So pumped to make this my #bestyearever!
It all happened one summer…last summer, actually. I was curious what all the commotion was about Twitter. I even felt like the administration at my school was encouraging the use of Twitter. Why? Would they encourage us to use FaceBook? There had to be something to it…and there was! Nothing has influenced me more in my 10 years as an educator than Twitter–more specifically, the #mtbos (that is Math Teach Blog-O-Sphere). I love collaborating with teachers, especially my Math Pal across the hall; but, imagine having the best educators in the country, no…world, across the hall?!? That’s what Twitter has done for me. I hope to share my new found love affair with the elementary and middle school teachers @CrystalLakeSD47s at their #translit47 conference tomorrow. I’ve attached the link to my presentation HERE. It starts very basic and builds. I’m no pro, but I can help you get started!
If you haven’t stepped off the ledge with Twitter, maybe you might now? Start by following me! I’m @mrsjtweetsmath . See you around the Blog-O-Sphere!
It’s been…um a few years since I’ve posted on this blog. However, it has been a personal goal of mine to blog regarding teaching, even if I am the only one who reads it. That being said, summer is a great time for teachers to retool, rethink and reflect on the year past. There are so many things I love about my job, but my favorite is a new year–new students, new methods, a fresh slate. Who would like a fresh start at their job every year? Well, maybe not everyone, but I do. With that in mind, I wanted to share some thoughts and reflections on things I love and things I’d like to work on this year, in particular. I’m sure I won’t hit them all, but if I make progress in just a few, that’s good too. A journey of a thousand steps begins with just one. Here are my reflections:
My classroom is a loud and noisy place and that’s the way I like it. I didn’t always like it. I used to be very uncomfortable with movement and talking–when it wasn’t mine. I felt like I might not be able to wrangle my students back to attention. Over the years I’ve picked up tricks that have given me confidence to unleash my student and know that I can corral them back in (3, 2, 1; music, online-timers; warning bells; etc). With that in mind, this is what I think works in my classroom:
Full Group Engagement/Accountability If everyone is not working and actively engaged then I’m not happy with it. I know teachers often play games (Jeopardy, etc.) where only one or two kids are battling it out for the win. If everyone is not busy, then I’m not happy. One thing I do to ensure student engagement is that I assign group roles or label each paper 1-4 and collect one for a grade at the end of the class based on the role of the dice. If everyone is engaged and working cooperatively everyone benefits. If everyone is not engaged, then everyone suffers.
Collaborate and Listen Research shows that students are more positive about school, subject areas and teachers if they work in a collaborative classroom (Johnson and Johnson, 1984). For that reason, I have several “go-to” activites when that involve active learning and cooperation, many of which I’ve shared in this class.
- Man Overboard
- Knotty Problems
- Speed Dating
- Challenge Me with Role Assignment: Scribe, Artist, Communicator, Quality Control
- “I say…, You say…”
- Collaborative Groups
Communicating Problem Solving Strategies Since the Common Core Standards for Mathematical Practice require students to “Construct viable arguments and critique the reasoning of others” and “attend to precision,” I require students to present at least one problem per chapter to the rest of the class. While this is difficult for some students, they increasingly grow in this skill and I have scaffolding in place for students who struggle to encourage them to speak. For example, I offer students the opportunity for me to preview their work before they present. This gives them them a little added confidence to present.
High Level of Differentiated Accountability I place students in groups often and hold them accountable either by giving students roles or by assigning them a number 1-4 and then rolling dice at the end to collect work for activities. Ina ddition, I have students work on “bellwork” and then collect each one, check it and separate correct from incorrect work. If it is wrong, I like consult individually with each student or ask an “expert” student to work with them. In addition, I ask students to perform the objective task with a “Ticket to Leave” so that I know exactly who understands and who doesn’t. These tasks usually have students at 100% engagement.
Direct Instruction with Pizzazz I say “pizzazz” because I do not directly instruct in a typical, “I talk, you listen” fashion. It truly is a discussion. I pose problems that might have a connection but have a twist to former learning. I ask students to walk me through the process, asking probing questions. In that way, we are “discovering” together.
TI-84 Graphing Calculator I use the TI-84 regularly for classroom instruction. I feel like I have a good handle on its uses for Algebra II (and even some of the quirky technological issues that may arise) and how to use it for both group discovery and whole group discussion. When we use the calculator as a whole group, I have found it really helpful to have a student model its use on the document camera. I notice when I try to model it, I go too quickly and students find it difficult to keep up.
What Needs Improvement in my Classroom
For the most part, I like what I’m doing but I also know there is SO much that I can do to improve. That is what I love most about our profession—there is ALWAYS room for growth! The classes I’ve taken this summer have taught me that I have several weaknesses. I will list them in order of priority of implementation.
PBL Problem Based Learning, rooted in Constructivist thought, forces students to go beyond gaining proficiency in algorithms and mastering foundational knowledge in mathematics, students in PBL environments must learn a variety of mathematical processes and skills related communication, representation, modeling, and reasoning (Roh, 2003). This is, in part, due to a reluctance on the part of my district to wholeheartedly embrace the Common Core. There is still a “drill and skill” mentality and curriculum to support it. That being said, I’d still like to make room for at least one 3 Act type collaborative problem solving experience for my students per quarter. This would allow students to draw conclusions for themselves making connections to former mathematical learning.
Scaffolding I LOVE using groups, but I have been guilty of throwing groups together without the appropriate scaffolding and find that students are frustrated. I need to assign roles and, even more so, teach the skills of active listening and speaking, supporting statements with viable arguments as stated in the CCSS MP Standard 3. These can be taught to students and practiced. Ideas for practicing these social skills can be found at http://www.edutopia.org/blog/deeper-learning-collaboration-key-rebecca-alber .
Variety is the Spice of Life I would definitely like to expand my toolbox of Kagan Structures so that I could create a more collaborative environment where, according to Kagan, students develop a personal interdependence and desire to help each other learn. Several structures I’d like to try in particular are Numbered Heads Together and Spin-N-Review so that students will have greater engagement and better performance.
Pit Stop In the middle of direct instruction I want to take a pause for students to “teach” one another or perform some other BRIEF collaboration like “mirror” or “think-pair-share.” For example, if I teach a difficult example, I might pause for each person in a pair to take 30 seconds to explain it to their partner and then switch. In doing so, students can reflect on their understanding.
Brain Based Learning Brain breaks are a useful tool for students to use to help activate, energize and stimulate their brains by improving information storage and retrieval. Research indicates that brain breaks also improve students’ concentration and relieve stress. I think it might be important for my regular Geometry students to have Brain Breaks and hand motions as well. I plan to use the website gonoodle.com and place them in the middle of the lesson.
These are just MY thoughts–share yours–how will you make this your #bestyearever?