I’ll start with the goods…student and collegue comments:
This is great.
I could have never done this alone. (from an uber high level student)
Can we finish with the same people on Monday?
I feel really good about this.
I want to see this with your OpenUp students. This a great. (my principal)
Did you hear what they are saying? They are really talking math! (curriculum facilitator)
Telling them they can kick a kid out of the group if they are not part of the process is gold. (math coach)
Did you come up with this yourself? (sixth grade teachers that came to watch)
So here’s how this came about.
I was in math club this morning and we had a group competition where each team of 4 had two problems and 6 minutes in there rounds. (Modified @mathcounts target round combined with team round) With math club you need the time con-straight because you are preparing for competition. I stole the two questions per sheet idea, the score only one sheet, and the group collaboration. I added…use 1 calculator for the group if you need it, graph paper and patty paper are permitted as are compasses and protractors, sadly, no desmos. Students choose the tools though. Tools are in the room, but students need to get them. They are figuring out what tools they need. That’s a mathematical practice, you know.
I bought a book at a used book store last weekend called something like The Humongous Book of Geometry Problems (I left it at school soI don’t have the exact title.) I was attracted to it because it had problems as well as solutions. Thank you. I modified some problems from there and used some pretty much as given. I also used problems from the quiz bank I was recently turned onto by David Wees. Thank you.
So, each group got a pack with two problems per sheet. Each student had their own sheet plus a colored sheet that had to have the final solution on. Group stapled all work papers to the colored sheet and turned it in as which time they got another pack with two questions. I had a total of three packs for 6 questions. There was notice limit. Here’s a copy of the instructions posted for the class.
Here’s a pic of the problem packs. I’ll attach the files if you want them. By the way, we are studying transformations.
The students were more engaged than I have seen them all year. I know part of it is that these students are motivated by grades. That got them going since it was a quiz grade, but the learning and the sharing and the teaching one another is the goal. I hate grades, but these students will work for them. This quiz was actually getting them ready for their unit test as they taught and reviewed with one another.
My last class ends at 3:50. This quiz had kids engaged at this level at 3:45 at the end of a week where they had county interim assessments for three days.
Her’s a montage of photos from the two classes.
At my principal’s request I am going to try this with my Math 8 students (they are using Open Up Resources). They are motivated in different ways than the groups I show here. I too am curious at the levels of learning and engagement I will get. I am hopeful.
I feel like a first-year teacher drinking from a fire hose. A couple days before school started, we were offered the opportunity to pilot the Open Up curriculum in our county for mathematics in grades 6 through 8. Because I had taught math 8 with zero resources for the past 12 years, other than what I harvested or created myself, I jumped at the opportunity.
There are many things I love about the Open Up Curriculum.
I love that I have to be more organized, focused and deliberate.
I love that I learn and see math differently each and every day.
I love the warm-up and learning routines and structures.
I love trying new things.
I love that the materials are already prepared.
I love that my kids are challenged and then they still have second chances if they don’t get something the first time around.
I love that they finally respect my kids and me enough to develop some real resources.
I cannot get ahead. I barely keep up. Each day I rush to get ready for the next. I prepare a PowerPoint to keep the class and me on topic. I snip screen shots into a PPT and prepare Student Task Sheets using what Open Up provides. Problem is, I frequently have to heavily edit so the information fits nicely onto a printable document. Mastering Textboxes has helped enormously in this area. I am saving all of these edited documents, so hopefully next year will be better. If that holds true, it will be the first year I have ever used what I made the year before. I have always created everything new each year in response to what my kids need.
I know that Open Up is integrated with OneNote and I even spent a couple hours being trained on how to do that. On my own, I cannot for the life of me figure it out though. I have to get ready for the next day. I don’t have time for trial and error where it is mostly error. I want to learn how to do all of that, but I also must be ready for the next day. I cannot sacrifice my kids for my learning curve. I also know there are Google slides for many of the lessons, but I have no idea where those are. I had them in the last unit, but can’t find the link now. There’s just too damn much to keep track of. I have to use what I know I can pull off now. I must survive.
I am working on pacing myself and my class based on the recommended time estimates for each activity. I have a hard time not getting each and every comment and contribution out of students before I move on, but a timer is helping me. I hate leaving a kid unheard, but we need to move.
Many kids are used to waiting you out. They will copy what you do, but they will not venture out on their own. I am now waiting many of them out, but I can’t wait them all out. There just isn’t time. I love mistakes that kids learn from, but too many won’t even try until the bitter end. Working in extra supports and re-teaching is tough. Where? When? With what?
I struggle with formal assessment as well. I hate grades and love learning. Unfortunately, we are required to take a minimum number of grades a quarter. On what? There are only end of unit formal assessments, but that is not enough. There are no quizzes. I collect daily work and cool downs periodically, but are they really formal assessments or are they just part of the learning process? I started the year doing my own quick quizzes, but have gotten away from that. I need to get back to that. Now.
The formal assessments created by Open Up are really great, but they are a bear to evaluate. If we were doing standards based grading, I could see where this type of assessment would be really helpful. We are not though, so making the grey into black and white is a challenge for sure.
Misconceptions about conceptual understanding:
For years I was told to dig deeper to get students to better understand. Problem was, nobody showed me what that meant. I was left to my own devices. I thought I was doing that when I insisted students understand why certain math algorithms worked. Turns out, I missed the mark. I am finally starting to understand what conceptual understanding means. If somebody was writing about it, I wasn’t reading it. Open Up Resources is actually showing me what it means to have/get/show/teach conceptual understanding of mathematics topics.
What I worry about now, is what my NC Math 2 kids are missing along the lines of conceptual understanding. These are the kids who have done well so far because they have been able to get away with memorizing stacks of mathematical algorithms. My only evidence that I am actually teaching for understanding in Math 2 is that I have a few kids that have historically gotten all As now struggle to get Bs because they do not truly understand what they are doing. I digress. This is about my experience with Math 8, Open Up Resources. I long to crack this conceptual understanding nut though.
I confess, I tell my Math 2 kids everyday how excited I am about what I just learned in Math 8. The ones that truly listen to what I am saying are very curious and want to know more. How I wish I could teach them this Math 8 goodness as well. I know next year I will work much of this into the Math 2 warm-ups. I do a bit know, but not like I wish I could.
I want to share with others, but I am slow. I know I should put all my stuff on Google Slides and share that way, but I haven’t learned all of that yet either. I need help figuring out how to efficiently share my stuff. I am re-creating all this and I am not sharing. That’s not who I am. I need help figuring out how to do that without spending an additional thirty minutes a day. My biggest problem is that I stink at asking for help. I will do anything for anybody, but I am not good at asking for help for myself. I’m getting better, but I still have a long way to go.
Goals: (These are actually wishes because I do not have actionable steps for them—yet.)
Create a Desmos activity of each lesson. I experimented with a cool down, but I want more. I think the tasks could be adapted pretty easily in Desmos.
Figure out how to use the parent resources created by Open Up. I am not even sure how to show parents that they are available. What I print stinks, so there must be a better way.
Figure out how to get students to utilize the reflection piece created by Open Up. That looks pretty deep and by deep I mean valuable.
Design a notebook or filing system for students to organize work papers so resources are available for review.
Figure out how to work training into my schedule. I teach Math 2 second and last periods. Math 8 is first and third. Trainings are half days. This takes me out of half of each of my classes. We have a dozen cross-teamed kids so adjusting the schedule is not practical.
I want to find or develop a group of learning tasks that show kids that their efforts matter even if they don’t get to the end. Too much of math is about the end and we need to start to praise and celebrate the middle because that is where the learning happens. I think this will help that perseverance piece a great deal.
I hope I don’t sound like Debbie Downer. I am really digging this curriculum. I even showed my pharmacist brother-in-law how cool it was over Thanks Giving. He said, “I don’t fully understand, but I can see how it would be exciting for a math teacher.” Now, granted, he is above average intelligence. The point is he appreciated what Open Up is trying to do for kids’ understanding. He also enjoyed how excited I was about it.
GOAL 1) I really wish I had blogged more and slept less last school year. I need to change that this year. My goal is to blog at least once a month.
GOAL 2) I will to become a better planner. I have my daily class structure ready. Once the dadgum pacing guides come out I will see how they stack up with what I have planned. It’s just two preps and I’ve taught both classes before, but this year is going to be very different in the most awesomest kinds of ways. I’m getting super excited. I am doing a self-study along with my language arts partner and that has already helped me plan and organize.
GOAL 3) I am going to do everything I can NOT to waist time at school as well as at home. Time wasters to keep my eye on are: doing jobs students can do, redoing things that don’t meet my standards but are certainly adequate, going down rabbit holes looking for lessons and tasks, starring into the refrigerator and pantry with no plan.
GOAL 4) I want higher quality resources and I want to come by them more efficiently. I’ve already gotten into some of this with my wade into Exeter. I need to get through their maths 1 & 2 materials since my smarty-pants Math 2 classes are a blend of some of both. I’m going to take my Math 8 kiddos into the Exeter world some as well by way of some of their math 1 problems. They can do it.
GOAL 5) I am going to enjoy time with my husband and myself daily. We will deliberately relax, exercise, talk or just sit there silently doing for at least fifteen minutes each day.
So that’s quite enough. Have a great week party people!
I was surrounded by greatness and for that I am grateful. I didn’t show up at TMC17 with my A game, but I improved as the week progressed. Why is that?
Attitude—After leaving Greensboro late because of a doctor appointment that came with unexpected news topped off with car trouble, I got to Atlanta three and a half hours later than expected. It all worked out rather well as I ran into some very nice MTBoSers in the hall and they invited a first timer and me to join them for dinner. Great restaurant. Great company. Thanks Steve Weimar, Megan Schmidt and Benjamin Walker.
Comfort level—I left TMC16 thinking I would not bother to come to another TMC. I got into writing proposals to present back in January and they were accepted and so I came. I attended the Desmos pre-con this year so that was nice. I read comments that non-amateurs were not very open to new folks at that point of the camp and that is unfortunate. I will say, though, that TMC non-amateurs were super great at speed dating the next day. Perhaps it’s because they were held hostage by a downpour, but regardless, they were there. They were participating and they were welcoming and I think they actually enjoyed meeting new people. That was a real turning point for TMC17. Somebody really needs to schedule rain for TMC18. I wonder who is in charge of that.
This year’s TMC was my 2nd so I had a point of reference. Last year I over-PDed, if that’s possible. This year, I came hungry. I enjoy My Favorites and the Keynote speakers blew me away. If you haven’t done so, please check out their presentations here. I chose good short sessions this year. Then I hit the mother load when I made the right choice for my three-day session. I was excited to meet and learn from the well respected @cheesemonkeySF. Boy, did she deliver. See separate post.
Along with friends, I presented so I also came to TMC17 vulnerable. Little did I know that vulnerability was the theme of TMC17. Last summer’s marching orders were “be intentional”. This year I heard loud and clear to be vulnerable. Take risks. I see vulnerability as a teacher’s Zone of Proximal Development. Learning and progress happen for teachers when they open up and take chances and then reflect and refine.
Have a great, vulnerable school year party people!! May you learn and grow exponentially.
This is MY reflection and summary of my three day Twitter Math Camp (TMC) session with @cheesemonkeySF, aka, Dr. Elizabeth Statmore. This is my interpretation. I apologize if I misconstrued anything Dr. Statmore put before me. My intent is to honor her and to document my learning at the same time.
A goal to be met in the first three weeks of school is to build a culture where students exhaust all they know and have available to them before asking for help when problem solving.
In order to get students to own the problem for themselves, make it personal to them. Change the names and places to be relatable to the earners. Put a story behind the problem.
Teach students how to approach a problem. This is the Know—>Notice—>Wonder sequence.
Use readers’ theater as a way to establish procedures and protocol for classroom routines such as Talking Points, Vertical Non-permanent Surfaces, and Number Talks. Elizabeth has done this through a script she has created called deleted scenes.
We actually got to practice this as a class and this helped me understand the purpose as well as the procedure. I had read Elizabeth’s blog on this, but never truly got my head around it. I am now ready to give this a shot. There are at least a couple people in the class that are going to give writing a script a shot. I hope these get posted and shared widely. Each member of a table group (4 students or so) has a copy of the script. (reuse for all classes.) Characters are assigned and the script is read, with each group simultaneously working through the script. Doing this as whole class leaves too many inactive learners. Up engagement and participation at every turn.
Use Talking Points to illicit emotions and access prior knowledge when moving into a new topic. Choose statements that are debatable and students have opinions about. The number 1 rule to adhere to and teach and monitor is: No comment, no emotion, no body language as the talking points are going around the table. As teachers we must model this. By doing so, we honor learner space and inner thinking. I repeat: NO snarky comments. Listen. Be silent and listen. In a circle, Talking Point 1 is read. The only person in the group speaking is the person holding the Talking Stick (or whatever article you choose). The talker states their reaction to the Talking Point and gives justification for their opinion. They then pass the talking stick to the next person who then gives their comment and justification. This continues all the way around the table group. Round two is the same procedure with the same Talking Point only this time the talker keeps or changes their opinion and gives justification. When all have completed the second round, opinions are tallied and the next Talking Point is run through the process. Some groups may get several Talking Points from the list completed and others may only get a couple. That’s ok. Front load the Talking Points so the important points are covered first. Shut it down and channel the emotion into learning the math at this point. I see this as peak interest and passion and then shift to content.
Day 2: The theme of today was Radical Differentiation and this was addressed through problem organization and people organization.
Challenge for all
Practice & support—more problems and challenges for speed demons
Make sure the beefy problems are up front so all students get these
Challenging learners does not mean stumping them
Every learner deserves a win.
Group speed demons together so they do not rob the other learners
Group the “katamari” together. These are the thoughtful, careful, deliberate learners, not strugglers, but rather the learners who know speed is not the end game.
Group free-loaders together.
If writing as a group, the talkers do not write and the writers do not talk. Trade devices when necessary.
Day 3: The final day, we were all in awe of Elizabeth and just wanted to learn everything we could from her. We asked what a day looked like in her class and she delivered.
She uses a broadcast clock to plan her class period, regardless of the length of the period. (I know I read about this someplace else, but I forget where, but it is genius.) Her clock looks something like this. broadcast clock Details below. Please note, unlike a real broadcast clock, the sectors in my clock are not proportional to the total time. (I simply do not know how to do that in Word.)
Open class with a PowerPoint slide that has students self-managing. Do now, check “Home Enjoyment”, aka, homework, with table mates, identify burning questions with tablemates, and get any handouts or supplies needed for the day. This all takes about 4 minutes. Each class has a theme song that plays for the first minute of the opening slide. This helps learners shift into math class mode.
Burning questions that students have about Home Enjoyment are addressed. Reserve the right to deem a posed question as NOT burning if learners can get there themselves and merely didn’t do so. This segment is as long as it needs to be, and no longer.
Slide changes to a fanfare of sorts to reveal the EQ. Learners rely on the EQ for focus and grounding. Initial notes and direct instruction happen here. This is only 6 minutes. Tighten up. You get another chance at the end.
Productive struggle/guided practice/guided sequential flailing happen at this sector. Have plenty of chosen problems, but front load them so all students get rich materials, not just those who get there first, aka, speed demons. Never give problems you have not done. Intentionally choose the sequence. Stumping learners is not challenging them and vice versa.
If the situation warrants, have a close. Elizabeth does not see this as a nonnegotiable the way some instructors do. I appreciate that, but will try to get my head around when closure is helpful and when it is just a closer for the sake of that checkmark.
Set a timer so you know when you have 7 minutes (or whatever your experience tells you that you need) for final notes and marching orders and a calm ending.
The productive struggle sector could be handled in a variety of ways. One way is to use Speed Dating—one side moves, each student is an expert in one problem, see Kate Nowak blog for details. This could also be Vertical Nonpermanent Surfaces, aka white boards. Alex Overwijk is the expert in this area. This could be the time for Exeter problems thoughtfully and purposefully sequenced for maximum learning.
Phrases—these just stood out to me as brilliant insights made by Elizabeth and paraphrased by me and others in our session.
You can’t develop patience quickly. (teachers or learners) Practice and honor the process.
Your learning should never be a threat to others. When you share your learning you gain and kids need to experience this. A rising tide floats all boats. Everyone benefits when students share their learning and insights with one another.
Speed demons commit cognitive theft. Honor all learners and protect the Katamari from robbery of their learning.
We don’t “fix” struggling learners, but rather, we help heal the disconnection from their inner mathematical selves.
Guided sequential flailing leads to learning. Problems are sequenced to support learner success.
Kids have to be able to get a win. Challenged ≠ Stumped
If kids have been robbed of their confidence, lend them yours. (Believe in them and let them know.) Take that burden from them so they may focus on learning.
Seat for discourse and production (separate the speed demons, katamari and freeloaders) when appropriate.
Honor learning and respect the process for self and others. Talking points procedure can reinforce this culture.
Music may be used for unity; transitions; class identification; sharing about yourself.
Students can self-start and you need to set the stage for that. Have this structure in place from the start so students own it and can rely on it, even if you are absent.
The Tibetan Singing Bowl is a peaceful way to focus students in a calming way. Help students be fully present and you be fully present for them.
Listen at every turn. Sequence. Listen. Learn. Breathe.
(Note, this is not intended as my TMC17 archive reflection. This is yet to come.)
Kindergarten is my first recollection of school and with good reason. I had Mrs. Trout. She spanked me on the very first day of school. Me! We sat at tables. Someone was at the front of the room. I spun around in my seat so I could see. Mrs. Trout told me to turn around, so I did. The next thing I know, she tells me I’m not paying attention and drags me out into the hall and spanks me. This was a rural school in Marion, Ohio and we only had kindergarten in the morning so Mary Mantey’s mom picked us up in her dark blue station wagon before lunch. Three girls (Mary, Jenny Pitts and I) climb into the back seat, and Mrs. Mantey turns around and says, “So, did anybody get whacked today?” We all just sat there, heads down, not saying a word. I never told my parents, but they said they found out at a conference. That explained to them why I stopped wanting to go to school. For math, we had to take a piece of chalk and go up to the board and write over the top of a number that was already up there. Mrs. Trout did not like the way my dad taught me to make my 4s and my 8s. I also remember that we had to take turns counting. Mary went all the way to 100! I went to 80 something and then I sat down. I could have gone further, but didn’t feel compelled to. I wasn’t into pleasing my teacher.
One memory from first grade is Jenny Pitts had a snowball in her desk that she was saving for recess. That didn’t end well. Also, I fell from the top of the slide onto the cinders below and had to get stitches. Jenny was involved in the incident too. Mary went to the Catholic school with her three older brothers. I don’t remember who my teacher was and I don’t remember a single academic event. I do remember that I brought a giant bull frog to school for show and tell. It got loose on the bus. Jenny’s brothers were really scared for me because they were always in trouble with that bus driver. He just smiled as I lifted my frog from under the gas pedal. His name was Fuzzie and he liked me because he knew my dad.
We moved to Delphos, Ohio around Halloween of second grade. My first day was unremarkable. I do remember that Kent Brewer and I had the same birthday. We got to play his game, but not mine. I also remember that this is when I began to hate reading. We had SRAs, whatever that stood for. There were colors that indicated the different levels. I was always significantly behind all of my friends in color. They were purple and teal. I was tan and brown. My teacher’s name was Mrs. Hoverman and everybody absolutely loved her, except me. She was tiny, well dressed and grey headed and she preferred boys to girls. That’s all I got. Oh, and the art teacher grabbed the paintbrush out of my hand and put bars over the animal I had drawn. I had the bars behind the animal. She made them go in front. That’s not what I wanted. I was in the cage, not looking from outside!
Third grade I had Miss McClure. She was young and I liked her. I fell on the playground that year the day before St. Patrick’s Day. I know the day because I had on green socks the next day when my dad took me to get a silver cap on my front tooth. I don’t member who my reading teacher was, but I do remember that I had to miss recess sometimes to be in a reading circle with a couple other boys. That made me mad and didn’t make me read any better.
Mrs. Shade was my 4th grade teacher. She was sweet and took on the look of every character in every book she ever read to us. I don’t remember any other teacher ever reading to the class. We made valentine boxes and I stepped in dog poop on my way to school and I passed a kid’s lunch box up the isle one day, just because. I had never sat in the back of a classroom before and I just couldn’t resist. Somebody else got blamed for it. I still feel bad.
We went to the middle school for fifth grade because there wasn’t room at the elementary school. A new high school had just opened so the middle school got moved into the old high school. It was the best building ever. It had three floors and a secret hallway that served as a fallout shelter and went over to the gym/auditorium. I don’t remember my main teacher’s name, but I remember I liked her. I wrote a lot of poetry. I wasn’t good at spelling though and we just had spelling bees constantly. I was always out early so I just sat there. I didn’t care about stupid spelling anyway. I had a different teacher for math. It was cool to switch classes. I was good at math, except when we had to match shirts to skirts and determine how many different outfits could be made. I totally disagreed with the teacher because, you see, two of the outfits she claimed were possible didn’t match. Other than that, I liked math. I got in trouble during study hall and got detention. Mr. Policki was the 8th grade math teacher and he was in charge of detention. I had a terrible cough and he yelled at me and said, “What’s the matter with you Baumgardner? Do you have whooping cough?”
In sixth grade I had a lady with only one hand for my reading teacher. I liked her. We did projects about what we read and I made a ukulele with my dad’s help. I got to play it for the class and I still have it. I had Mr. Morris for math and he was my first male teacher. Seems like he always had the book in his hand though as if he had no idea what he was about to do. I think he was new.
I was in trouble in 7th grade too. I remember having to stand at the chalkboard in study hall holding a penny to the board with my nose. Seems like the Reds were in the World Series that year. I had Mrs. Wager for social studies and we studied South America. I remember making a green bird out of dyed rice that I glued onto a board. I probably copied something right out of the encyclopedia and we called that a report. I may have had the one-handed lady for math that year.
My first authentic use for math came in 8th grade. Mr. Polocki had moved away, thankfully, though my sisters said he was a really good math teacher. I had a lady with long black wavy hair. She taught us how to balance a checkbook and how to actually write a check. That’s the only time I ever learned that and I use those skills regularly to this very day. She had power of attorney for her dad and so she had to do all of his bills and she just really thought we needed to know this too. That was a good call. We had Krotzer for history and he was a legend. Mr. Fleming taught science and he was fun and we got to build a bell that ran on a battery we made ourselves. I remember girls cheating in that class by memorizing answers. I thought that was crazy. It was so much easier to just learn the material rather than an ordered list of 20 ABCDs.
High school was much better. I quit getting in trouble so much, or at least, I stopped getting caught. I remember only one English class. I had the football coach and I was tired of getting not-so-great grades in English, so I wrote a story about a football from the perspective of the football. He loved it. I had finally succumbed to playing to the audience rather than being my own person. I was a sellout and I felt dirty. I took chemistry and civics a year early because I got out of Spanish 2 by doing poorly my first year. I was such a clever girl. I did not like Spanish 1. Math was the best though. I ended up having Mr. Wolfram for all four years of high school. We had algebra 1, geometry, algebra 2 and then trigonometry which was really pre-calculus, we just didn’t know it. I remember proportions and then mixed rate and mixture problems in algebra 1. That was fun when it finally clicked. Geometry was fun because it was like putting together a huge puzzle. By the time we got to trig, there were only 9 of us left in the class. Me, Kathy, Paul, Big Drew, Pacco, Trevor, Bruce, Sam and somebody else. I had a bookmark that I made that had trig identities on it. I used it all through college. Except for Pacco, I still see these people once in a while when I am in Delphos or on Facebook.
So, what finally made math fun and memorable? It was a challenge. I was pushed to think. Mr. Wolfram was full of energy. He loved what he was doing and it showed in how he did it. We did a lot of work at the board, getting feedback and helping each other. We loved helping each other understand. It was absolutely the best part of high school.
In college, I worked hard and made Bs and Cs. The only As I recall were in Managerial Accounting (the prof said I couldn’t get an A since I got a C in Financial Accounting so I had to prove him wrong) and Basic. The final was to write a program that had to do with rounding numbers. I wrote four lines of code and turned in my paper. The prof looked at it, and said, “Oh. I never thought about it like that. You can go.” I may have gotten an A in Money Credit and Banking just because somebody told me it couldn’t be done. I got As here and there in math, but mostly Bs and I was ok with that. I learned and I understood and that was all I wanted out of it.
In graduate school, I loved learning and being around other people who were enjoying school rather than enduring school as I had done twenty years earlier. Graduate school was the first time I ever recall a teacher actualy wanting me to succeed. It was like this big secret, that all of my teachers in the seventeen prior years kept, was uncovered. Teachers want students to succeed. They really do. Who knew? I seriously saw most teachers as an enemy that had to be defeated and that is how I got through. I finally got better at this reading and writing thing in graduate school–in my forties. I did ok in college, but reading was a real struggle that I did not enjoy.
Take-aways…adults need to take the time to see and hear a kid’s perspective. Now, as a teacher, I need to understand situations before I react. The actions of teachers matter, even after many years. The extreme actions of teachers are the most memorable. How do you want to be remembered? Is this different from how you will be remembered? Make an action plan to reconcile any differences. I know I have some fixing to do!
I was inspired to go through this exercise as I am reading Tracy Zager’s [@tracyzager] Becoming the Math Teacher You Wish You’d Had. Tracy takes me into so many classrooms and it stirs up many memories. Some of these memories are funny and some are painful, but they are all just part of what makes me, me.
If you’ve made it this far, thank you. I encourage all teachers to take some time to think back grade-by-grade and see what sort of memories you have. What sorts of experiences had lasting impact on you? Do you ever teach the way you were taught? Yikes!
My favorite topic to teach is completing the square. Weird, right? I just love it. I start by having kids solve radical expressions. I say “what cha gonna do?” and then say “square both sides!” We then move to solving equations where we need to square root both sides and I catch them in the chant! “what cha gonna do?” “Square both sides.” Really? Then they think. And then they think some more. “Oooo,” they say. X squared = plus or minus the square root of x. Major deal of course. So now the chant becomes, “what cha gonna do?’ and they say, “square root both sides.” Many forget the plus and minus no matter how many we do it. I do this before solving quadratics, which may be unconventional, but it works.
We solve equations with a squared term, a linear term and a constant or two and we discover how to complete the square in order to be able to take the square root of both side after some massaging. It’s awesome. It’s magical. It has absolutely nothing to do with quadratics as far as students know. We are merely balancing equations.
Then we do go into quadratics. There is always some smart alec that wants to dive into the quadratic formula. I hate this, but soldier on. They may NOT use the quadratic formula until they can prove it. End of story. We go into vertex form of a quadratic. They dig the structure and can assemble the vertex form of a quadric if they know the vertex and the multiplier. We then look at discovering coming up with a quadratic equation with far less information. We know the structure of vertex form because that is taught in Math 1 (supposedly). Of course the structure is re-taught. But, now we have a reason for knowing how to complete the square. Yeah! It’s so similar to coming up with the slope intercept form of a linear equation. Plug in what you know (what you are given) and chug away. That there must be a perfect square trinomial to make the square root of both side s of the equation is the secret weapon. All must balance. No illegal moves. Taking the multiplier into consideration is a challenge, but we get there.
Because I introduce completing the square multiple times and early, it sticks by the time we prove the quadratic formula. It gets revisited when we do geometry and prove the Pythagorean theorem. The sparks and light bulbs that go off are so fun!
I tell my kids when we first complete the square that this is a skill that could make them a hero some day. When I first started teaching algebra 7 years ago, my daughter was in a college chemistry class. Her class had a problem that looked unsolvable until a student suggested that they complete the square. That student was a hero. I tell my students that some day they too can be a hero with completing the square. They are instructed to notify me the day this happens. Sadly, no notifications so far.
I think that success in teaching completing the square comes from students being exposed to it over a period of time, even before they really need it. If you wait until they need it, the mind is too clogged with other ways to solve quadratics. I tell my kids, too frequently solving a quadratic via the quadratic formula is like taking a barge down a river. Completing the square is a kayak. Have fun! Use it. Be a hero!