Formative Assessment and Feedback in Math (General K-12 session) – John Scammell
My morning session choice was difficult for me. I had 4 choices I was debating over. When it came down to it. what swayed me was that this session would be applicable and usable in all of the classes I teach. If I’m going to spend 6 hours in a session, I want to get the most bang for my buck. John didn’t disappoint me here.
Takeaways from this session for me included:
Growing our own practice: How mathematics teachers can use social media to support ongoing improvement – Lani Horn
Thursday’s keynote was one I was looking forward to. Lani does a great job to push our thinking. I was so intent on listening that I didn’t jot down many notes. I really want to keep in mind her three things that distinguish great teachers from good teachers:
Planning Units using the MTBoS – Bree Pickford-Murray
I really liked how Bree planned this session. She spent about 40% of the time talking about she plans: Finding the resources, Collecting them (she uses Evernote), and Organizing them. She then gave us the rest of the time to do some of this. I have been struggling with Evernote for a while, but she convinced me that this is the way to go and I left with some tools to better work with it. I also spent some time with Matt Vaudrey and learned a tiny bit about spreadsheets. I realized that I have so little knowledge of how to effectively use spreadsheets and I need to work on that. I think it would help me in many ways to organize stuff. In the near future, I need to get my Evernote under control and that will most likely be one of my first projects before school starts.
Why Number Talks in Elementary Classes? – Chris Harris
Even though the heading had elementary in it, this session was on my radar because Number Talks were briefly mentioned in a session I attended at the county level in June. I had thought it may be a good thing for my Applied Algebra students to help boost their confidence in math. However, I didn’t have a whole lot of information about it and I thought this would help me better understand Number Talks. Chris did NOT disappoint me. I was so glad I went. I was reading someone’s blog post (I can’t remember whose) and it talked about starting the year of with Number Talks and dot problems. I had no clue what dot problems are. Chris fixed that. Yes, I will be starting with dot problems in the fall. I actually got to participate and experience how Number Talks work and now it makes so much more sense to me.
Math from the Heart, Not the Textbook – Christopher Danielson
Like many people, “Find what you love. Do more of that.” hit home with me. He then posed the following questions:
It was really hard to answer #1. I know I love the MTBoS community. That does extrapolate to community as a whole. The relationships I have within my church, family and school communities I treasure. But when it came to what do I love about mathematics, it was much harder. I think what I love is puzzles and figuring them out. Somehow I need to figure out how to better incorporate that into my classroom (especially when it comes to application problems).
Exploring Opportunities (or Obligations) for Leadership, Advocacy and Stewardship Without Leaving the Classroom – Peg Cagle and Levi Patrick
Friday for me was not as much about classroom stuff. It is about classroom stuff, but trying to make things better in my classroom. This session helped but some things into perspective for me. Bullet points of what caught my attention:
“If you call people educators it validates their other roles.” A teacher not only teaches but plans and grades and mentors. –@_levi_ #TMC15
— Tina Cardone (@crstn85) July 24, 2015
Advocacy is continuous. There are so many ways to engage at so many levels. –@pegcagle #TMC15 — Tina Cardone (@crstn85) July 24, 2015
This isn’t advocating on behalf of teachers, it’s advocating on behalf of teaching. We are the voice for our students. –@pegcagle #TMC15 — Tina Cardone (@crstn85) July 24, 2015
This session gave me a lot to think about and how I can be a better teacher leader and advocate for the profession.
Join a Conversation with NCTM! – Matt Larson
I really respect Matt Larson and Bob Doucette for wanting to be at TMC. It could not have been easy for them to come and I honestly hope they got a lot of food for thought from attending. This happened:
.@themathforum joins #NCTM! Its online resources will become a part of @NCTM #TMC15 #mtBos http://t.co/HsRp0TOxXj pic.twitter.com/YUNFZ5QQ6d
— NCTM (@NCTM) July 24, 2015
This was incredibly significant. For NCTM to announce the merger here provides legitimacy to TMC in other people’s eyes. We know it’s legitimate, but the establishment at large doesn’t get it. The Math Forum was the math education internet long before Twitter, Blogs, and the MTBoS existed. To me, thinking about that makes it very natural to announce the merger here. I am thrilled for The Math Forum folks and very relieved that there will be a place for them to continue to grow.
Teacher Woman, Because Teacher Man is Taken – Fawn Nguyen
Again, many have tweeted what they have gotten out of Fawn’s keynote. I was so enraptured in listening to her, really listening to her, that I did not pick up my phone to tweet AT ALL. Points I wrote that I wanted to remember:
That last piece really hit home with me. I am not a seek out approval type person. However, it does get frustrating that you feel like you are doing a good job and no one seems to recognize it. It was even more obvious to me personally how little recognition I get at times because SO many people wanted to take the time to thank me personally for TMC. I have gotten much better at accepting those thank yous graciously. What Fawn said about “nobody cares” and stopping asking for affirmations really hit home with me as far as my own classroom. Focus on what’s important.
What Do I Do with all this Cool Sh!t? – Matt Vaudrey and John Stevens
I kind of thought this session would be along the lines of Bree’s with organizing what we have in the MTBoS and how to better use it in my classroom. Instead, it was an hour of chatting with each other of how to make it work in our classrooms. Way better than I envisioned and much more valuable. I got to have time to talk to other teachers about getting this back home. It could not have been more perfectly scheduled in the schedule (at the end of the conference when you’re thinking the question they posed) and it was perfect.
Flex Session – AP Calculus Roundtable
This was a small and mighty group. I teach Calculus, not AP, but I still learned from this discussion and got some questions of my own answered. More importantly for me, I made some connections with Eric Martin, Liz Pursel, Jim Doherty, and Jonathan Claydon that will help my Calculus class be better in the long run. Now I’m trying to figure out how we can continue the conversation in a fluid way throughout the school year. May have to look into Slack.
Conclusions
Yes, I learned a lot. I think I did a great job of finding the “right” sessions to help improve my teaching. I have a lot to reflect on and decide how I am going to get it into practice. I am grateful for all of the gratitude shown. I had some wonderful conversations over the course of TMC. Thursday night dinner with the Spring crew was wonderful and exactly what I needed at the time. Actually, every meal I shared with someone was exactly what I needed at the time. The BBQ on Friday organized by John Stevens, Matt Vaudrey and Jed Butler and supported by Mathalicious was amazing. I am so grateful for my tweeps who check in with me to make sure everything is okay. You all know who you are and I love you. Last, but not least, I am grateful for all the people who make TMC great. Without the people, it’s not the same.
]]>So as I reflect on the wonderfulness that is TMC15, I keep coming back to one thing: Community. Many times, when TMCers sit down with me with any length of time for conversation, the question usually that comes up is “How did TMC start?” And I share the story, which for brevity’s sake, I’m not going to share now. But the question that is pretty much never asked of me is “Why do you do this?” The answer to that is quite simple. “It’s about the community, stupid!” (apologies to President Bill Clinton’s 1992 campaign – it’s the economy stupid. If you don’t know / remember – Google it)
When we started talking about meeting face-to-face 4 ½ years ago, Jason said to me, “You’re going to end up organizing this, aren’t you?” to which I said, “Yeah, probably.” He could see that this community was something that is important to me and it means a lot to me to meet people face-to-face. It’s about the community stupid.
As I go through tweets, these are some that I have favorited:
@PIspeak “’twas the night before #tmc15 and all through the country, not a teacher was stirring, except for @cheesemonkeysf “
— Mattie B (@stoodle) July 22, 2015
@stoodle the teachers are nestled asleep in their beds while visions of @samjshah danced in their heads
@PIspeak “the suitcases all packed stood by the door with games, in hopes that you’d meet all your favorite tweep names”
— Mattie B (@stoodle) July 22, 2015
Chris Luz @PIspeak Jul 22 And @jreulbach in Carolina and @stoodle from New York were texting sweet math terms, those loveable dorks
Safe travels to everyone making their way to beautiful Southern California for #tmc15, the math world’s family reunion. See you all soon! — John Stevens (@Jstevens009) July 22, 2015
#TMC15 Have a wonderful time. Ann and I will miss you all, but expect to rejoin y’all next year. Give Fawn an extra clap for us!
— Steve Leinwand (@steve_leinwand) July 22, 2015
Remember getting sent to camp as a kid to a place you didn’t want to leave? Great friends, life-changing conversations? That’s #tmc15 — John Stevens (@Jstevens009) July 22, 2015
To everyone off to #TMC15: May the road rise to meet you, the wind be always at your back, & may your dongles be compatible with everything.
— Chris Lusto (@Lustomatical) July 23, 2015
samjshah @samjshah Jul 23 @misscalcul8 two good things! I know the context is wrong, but what are two positive things from your trip? samjshah @samjshah Jul 23 Just posted on FB: “THIS PLACE AND THESE PEOPLE – THIS IS WHAT HEAVEN LOOKS LIKE.” g’night #TMC15, thanks for making me so giddy with joy!
It’s been less than twelve hours and @fawnpnguyen is already complaining that she misses @mr_stadel #TMC15 — Tina Cardone (@crstn85) July 23, 2015
200 math teachers that want to spend their time learning from each other is just… Awesome. #tmc15 pic.twitter.com/GyrjJ7EFXp
— Timon Piccini (@MrPicc112) July 23, 2015
#tmc15 goals: @jreulbach proactively sits by you
— Jonathan (@rawrdimus) July 23, 2015
#lifeGoals to teach more like @rawrdimus and @froynboy #tmc15 https://t.co/WDUWYPLLlM — Julie (@jreulbach) July 23, 2015
And that was all BEFORE TMC15 started. It’s about the community, stupid.
Then I came back to Christopher Danielson’s keynote. Find what you love. Do more of that.
He asked the questions:
What do you love? How can you incorporate more of that in what you do?
What do I love?
It’s about the community, stupid.
(there is something else I love as far as mathematics goes)
Pam Wilson retweeted this quote this morning:
If you want to go fast, go alone. If you want to go far, go together. pic.twitter.com/1jDXSTbipQ
— Alan Stein (@AlanStein) July 26, 2015
It’s about the community, stupid.
I think you get the point. So there are a few challenges I want to leave you with:
We all have a teacher that influenced us somehow as far as going into teaching. For me, that was Frank Monahan, my freshman English teacher. Of the many books he had us read, one of my favorites is Illusions by Richard Bach. In the book, there is something called a Messiah’s Handbook that always opens to the page you need. Here are the two quotes that I find apropos for TMC:
“The bond that links your true family is not one of blood, but of respect and joy in each other’s life. Rarely do members of one family grow up under the same roof.”
“Don’t be dismayed at good-byes. A farewell is necessary before you can meet again. And meeting again, after moments or lifetimes, is certain for those who are friends.”
But, you don’t have to wait until TMC16 to meet again. There is a huge local crowd here. You can follow the lead of NYC and Boston and arrange tweetups during the year. I hope that NYC and Boston and others continue to do the same. Plus, we all attend conferences throughout the year. If you’re at an NCTM regional or heading to San Francisco, you can meet up there.
But if that’s not in the cards for you, TMC16 will be Saturday, July 16 – Tuesday, July 19 at Augsburg College in Minneapolis, MN.
]]>Why I Go To Twitter Math Camp
-Jason Henry
It’s the question. In whatever form I get it, it goes something like this: “What do you teach?” And my response has become rote: “I don’t teach, and I don’t tweet. I’m Lisa’s husband.” So the unasked question becomes “So why are you here?”. And the first year, it was simple: I wanted to help. I wanted to be supportive of what my wife was helping bring to fruition. And I got to drive to St. Louis, tour the Budweiser brewery, and take in a Cardinals game. And that answer, in some fashion, would work for the next three as well. And if you ask me, that’s probably what I’ll tell you. But that’s not the only answer. At least not any more.
I come to Twitter Math Camp for the same reason Lisa does. Well, not exactly, but it’s for the people. I come to support 200 math teachers because they make my wife a better teacher. And that’s important to her, so it’s important to me. She might not read your blog, and you may not tweet as proficiently or eloquently as some, but you help. Because it’s a community. It’s in the name: sphere. Yeah, there’s some other parts to the name, but to me it’s the sphere part – the inclusivity that brings you all together. And that together you make a difference.
And it’s not just math. Or even just teaching where you make a difference. I remember back in St. Louis sitting in on My Favorites to see what this thing was. And I still remember Elissa Miller’s. It was “Two Good Things”, which you can ask her to explain, but it’s not about math or the classroom, it’s about respect. And making her students better people. That’s making a difference beyond teaching math. That’s important.
And now I’m a parent. Well, I’ve been a parent for a few years now. OK, more than a few. And I want my kids to learn, but I want them to be better people. And now my kids are getting to the age in school where I remember my education. Yes, I remember elementary school, but not the way I remember middle and high school. And my kids are getting to an age where I can relate to their education. Both the good and the bad. I had good and bad teachers. They have good and bad teachers.
And I want the people to attend TMC to know that they are good teachers. Every year there are posts/blogs/etc. about how humbling it is to come and see what others are doing and how it’s hard to take it all in and go back to the same classroom, trying to figure out how to bring these grand ideas home. And it bothers me to see that. I don’t care how effective you are in your classroom. Really. If your students can’t add 2+ 2 but you’re here trying to find out how to better reach them, that’s what matters. And that’s the real reason I like to come to TMC. It’s a word that I bet few of you would attach to why you are here. It’s a word that didn’t come to me until I saw my daughter struggle in school in a way that I never did, and not know how best to help her.
As a teacher at Twitter Math Camp, you see colleagues and friends and so much more. As a husband at TMC, you are a support system and professional development to the N^{th} degree for my wife. But as parent at TMC, you are HOPE. When I look out at the room full of eager and anxious teachers who can’t wait to engage one another in discourse and better their craft, I see hope. I wish your administrators and the parents of your students would get to see you as I do – as HOPE for the future of education.
The highest compliment that I can give you is not to thank you for coming to TMC. Which I do. Or to wish you continued and greater success in your class room. Which I do. But my greatest responsibility is as a parent to my 2 children, so what I leave you with is this: that I would HOPE for my children to have teachers like you.
]]>This is my 12-year old daughter Grace. In April, while she and her brother Cade were playing in the backyard, he tackled her and, as near as we can figure, his head hit her left knee cap, dislocated it, and chipped a piece of cartilage off the bottom of it, sending it somewhere above her knee. Tuesday, she had outpatient surgery to remove the piece of cartilage and a microfracture to regrow the cartilage. Wednesday, her dad and brother left for 3 days of Webelos (Cub Scout) Camp.
We have been home alone, mother and daughter, for 24 hours as I write this. I’m pretty sure it’s been tougher mentally on me than her, and it is definitely tougher for her physically. As you can see from the picture, she is in a black brace that immobilizes her left leg. Under the brace, her leg is wrapped from ankle all the way up and around her knee is a blue cooling wrap that ice water is pumped through (the cooler is off to the side) to keep the swelling down. She’s pretty much on the couch all day, except to go to the bathroom, which is a 10 minute process from start to finish. She’s kept company by her iPad and new cell phone and occasionally the TV. Pretty much I hang out on the couch with her and do some reading and TMC prep stuff in between running to get her whatever she needs.
We have finally started to settle into a more comfortable rhythm 2 days after her surgery. The first day, she rested and as her dad was home, I ran to get things she needed that I hadn’t anticipated (thank goodness for Wal Mart with cheap shorts and close gas stations for ice!). Between trying to figure out how to best care for her and help get the boys for camp, the first 24 hours were pretty chaotic. My friend Beth graciously brought us dinner Tuesday night with enough to get us through another night or two. Her daughter has been down the surgery route before and she knew exactly what we would need that first night. A venting phone call with Elizabeth was needed as I came back from Wal Mart. Flurried texts between Stef, Steph and I saved my sanity a few times in that first 24 hours, even as Steph’s son was having surgery on Wednesday.
Then the boys left and it was calm and quiet. Grace decided she wanted to nap and I was able to do a few small things in that hour. We settled in on the family room couch after that and worked our way through the day as best we could. By last night, Grace was uncomfortable again but she couldn’t articulate how she was uncomfortable. Knowing I couldn’t give her any more pain medication was tough. I finally figured out this morning that her leg was spasming and I have medication for that I can give her. My father-in-law brought us 2 big bags of ice, so we’re set there. Ceil, a family friend, called last night checking on Grace and is sending meals for today and tomorrow. She brought me to tears with her care and concern for us. All of the support on Facebook has been wonderful. The exchange that touched my heart the most was from Fawn:
Although I was enjoying the quiet of not having the boys home, it is beginning to wear on me. I stayed up reading last night (still trying to clean out my Digg Reader, which is at about 1600 right now – EEK!) and probably was up a bit too late. Grace called me at 6:15 am that she was ready to get up and off we went. We are in a better rhythm today. After more texts with Steph and Stef, I figured out that Grace had spasms last night in her leg. I figured out that if I refill her cooler when she gets up to go to the restroom, it stays cold and the disruption of the cooling wrap is as little as possible. Grace is getting better about telling me what is happening so I can help her feel better. We ordered dinner and it will be delivered around 5 pm. My husband was able to call this morning and check in on us. We both are dressed – not that either one of us is going anywhere, but we’re dressed!
So why am I sharing all of this here? There are some of you who truly care about me and want to know what’s going on, so there’s that. You’ve shown your support via Facebook and Twitter, for which I am very grateful for.
In one of my few alone moments this morning, it dawned on me how much this is like teaching. (It’s not like I’ve never taken stuff from my everyday life and tied it to teaching somehow…) When you first start, it is incredibly overwhelming. You want to do it all yourself. After all, it’s what you have gone to school for. We’ve all been in school and you have ideas of what kind of teacher you want to be. Hopefully, you’re smart enough to take help when it’s offered to you. It’s not a sign of weakness or that you’re a poor teacher to take that help. In fact, what you hopefully figure out is that by taking that help, is that it will ultimately make your job easier and you will be better at it. You learn from your experiences and you get better at teaching. When something isn’t going well, you work on figuring out what the problem is and come up with a way that works. Eventually, you figure out what works and teaching seems to be running smoothly. That doesn’t mean that it stays that way, though. But as you gain more confidence in what you’re doing, when you run into problems, you know how to deal with it better.
Chris, you’ll figure this all out in good time. What I hope you get from this is that there is a learning curve to teaching. It’s not going to all be unicorns and rainbows and you won’t be perfect at the beginning. But you have a good heart and a strong spirit and you will work through the process of becoming a great teacher. You have a strong support system already (yes, I saw the pictures your mom posted on Facebook) and you will continue to find support if you look for it.
The other thought that ran through my mind is how much support this community we’ve dubbed #MTBoS shows each other. I know that personally, I would not be the teacher I am today without the MathTwitterBlogoSphere. I have learned so much over the last 5 1/2 years both directly and indirectly from Twitter and reading blogs. I still cannot believe how wonderfully helpful everyone is and it is because of that I been able to learn so much from you. The friendships I have developed over the years I cherish immensely and I am so glad that I am a part of this community. You all are my lifeline in many ways, and as Elizabeth is so fond of saying, you are my tribe.
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The difference between memorization and understanding is that students quickly forget things they memorized. How can I help them see that?
— Julie (@jreulbach) May 29, 2015
As we are preparing for final exams, I see a lot of this. Today, we were working on reviewing solving systems of linear equations and many of them had forgotten how to graph lines. And as I was walking around, helping students, it dawned on me why. You see, my students have just come off a section on solving quadratic equations. To be honest, it was a little rushed due to time constraints, but not as rushed as last year. Prior to solving quadratic equations by taking square roots, or completing the square, or the quadratic formula, we had spent quite a bit of time on graphing quadratic equations (here is a post on the start of the unit). While learning how to graph the quadratic equations, students used completing the square to rewrite an equation into vertex form. They also solved equations by either factoring or by taking square roots when finding the x-intercepts (depending on whether or not the equation was in standard form or vertex form). So when we got down to solving by these two methods, they had seen them used before and in a context. They did significantly better on these two learning targets than students had in the past, especially the completing the square learning target. When I finished grading their papers, I was pondering what had gone better this time around. Between that and today, it was pretty clear: the connection students had made while using these processes in graphing quadratic equations helped. In fact, the tweet Glenn Waddell responded to Julie with rang through my head today.
@jreulbach My learners are enthusiastic about math this year. I think one reason is they do see the connections. — Glenn Waddell, Jr. (@gwaddellnvhs) May 29, 2015
It is becoming clearer to me that I need to work on helping my students find connections between the doing of the mathematics and where it can be used and/or why it is used. Glenn has already begun to blog about how he does this in his classes and I am looking forward to reading more about it this summer. I think I have found yet another summer project for #summerlist2015.
]]>I can sketch a rough graph using the zeroes of a polynomial and other easily identifiable points such as the y-intercept.
I’m incorporating A-APR.3 (Identify zeroes of polynomials when suitable factorizations are available, and use the zeroes to construct a rough graph of the function defined by the polynomial.) and A-SSE.3a (Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.^{*} Factor a quadratic expression to reveal the zeroes of the function it defines.) from the Common Core State Standards. We have just finished solving a quadratic equation by factoring, which incorporates A-SSE.3a. This is the first of four learning targets in my unit on Quadratic Functions, which focuses on graphing. I had originally intended to also do transformations in this unit, which I hope to do in the future. I am running out of time in the school year and I want to make sure I teach how to solve quadratic equations that are not factorable.
My intention (since I start this tomorrow), is to do a mixture of students working with what they know how to do and additional instruction to teach the new information. The pages below are set for my students to add into their interactive notebooks, so they are 2 to a page.
(Pardon the formatting – the graphs for some reason don’t come out right when I PDF it. Here is the link to the Word Doc – it didn’t hold my page formatting when viewed in the viewer.)
The first page is actually 2 copies of the same page – students will begin by doing it on their own. The second page is part notes and part examples students will work on their own. The first half is notes where I introduce the terms roots and zeros for solutions and discuss the important parts of the first page, where students were asked to find the x- and y-intercept of a linear equation and then to try to do the same for a quadratic equation. I am connecting this to their prior knowledge from linear equations. The parts the students work tie back to solving quadratic equations by factoring, which we just finished.
The third page continues in this format, asking students to find the y-intercept for each of the equations and introducing the shape of the quadratic graph as well as how the graph can open. By the end of the third page, students should have enough information to start a graph of the quadratic equation.
The fourth page walks students through the sketching process, at least as I saw it. The last page is where they actually would graph it. I did not introduce the term “axis of symmetry” at this point. The next learning targets will introduce vertex form and at that point I will bring in the term. I wanted to use the idea of the fold line and mirror image with the hope that it would help my struggling students understand how the symmetry in a parabola works. The final learning target in this unit is for students to graph a quadratic function, identifying key features such as the intercepts, maximum and/or minimum values, symmetry, increasing and decreasing intervals, and end behavior of the graph.
The examples I chose were all factorable. The first one is fairly straightforward. The second one factors easily and has only one x-intercept. The third and fourth examples have a negative squared term, one with -x^2, the other with -3x^2. They are a little more of a challenge to factor, but can be factored.
]]>You see, I have been largely absent from the MTBoS this year. I was trying to put my finger on as to why. A lot of it has boiled down to life getting in the way. I’ve been trying to keep up with my kids and keep my daughter in particular on track with her homework (she has ADHD and it is a daily struggle for us). Most times, when she is working on homework, I sit and play some sort of game – the hidden picture games I play primarily, although Candy Crush has crept in at times. Sometimes I am grading papers. But mostly, I am playing some game that keeps my mind occupied but that I can drop quickly to help her with her homework or get back on task. I could be reading stuff on Digg Reader or Twitter, and the excuse I’ve given myself is that it takes too much thought on my part to give it the focus I want to since many times I have to drop what I’m doing to work with my daughter in one way or another. By the time we get the kids in bed, mentally, I just haven’t wanted to go and read stuff related to work. I’ve told myself I just need a mental break and back to the games I head. Or maybe I’m checking Facebook or something else. But heading to blogs or Twitter hasn’t been the first (or the second or third) thing on my mind.
School hasn’t been incredibly more difficult than last year (which was tough!). There’s been the added pressures of the PARCC exams, but I haven’t been overly stressed about it. But, when the time comes that I could read stuff that is math education related, I just haven’t felt like it many times. I thought maybe it was burnout for a while, and maybe that is somewhat true. But as I have gone through some things this weekend, I don’t think that is entirely true. Maybe I was being selfish and just keeping to myself, but I’m not sure that is entirely true either. I didn’t blog much and I felt like I just didn’t have much to say that would contribute to the MTBoS, plus it was tied to work. So I didn’t blog much unless something really jumped out at me.
And life continued to happen. There has been a lot going on in my personal life in the last few months. I don’t want to share all of that here. It’s not the time, nor really the place. But I will share that the last two weeks have been very difficult on many levels for me. My daughter injured her knee while playing with her brother (he tackled her) and has been on crutches for the last two weeks. There have been some family things going on, including the death of a close family friend unexpectedly early last week. I got sick and it was kind of tough to shake it. And life continued to happen.
Yesterday was incredibly full. The funeral for our family friend was in the afternoon and we had a Girl Scout commitment that was shortly afterwards. My brother was here for the weekend and a good friend of mine was here for the day. Plus my husband’s family was here for the funeral. I had to make a choice. After the Girl Scout event, I could either head back and spend time with his family or have dinner with my friend and her son. One kid wanted to hang out with the cousins, the other wanted to head out to dinner with our friend and her son. And I really didn’t know what to do. I was torn. My brother said something that made a whole lot of sense – do what will make you happy because there is no way to make everyone happy. It was a lot longer than that, but that was the basic message behind it. At the funeral, they had talked about our friend who had died and how she was so kind and really cared for others. She always had time to listen to you and rarely talked about whatever was troubling her. She would generally share what was going on if you asked, but she never began with it. She was such a beautiful person and had such a beautiful soul. And as I thought about my decision – head back to visit with my in-laws or spend time having dinner with my friend, I realized that if I followed what my brother said – to do what would make me happy – it would make me happier to spend time with my friend, who needed someone to listen to her. So, after our Girl Scout event, we went out to dinner. I had time to visit with my friend and enjoy time with her. I was able to listen to her and be supportive of her.
Over the course of today, I have exchanged texts with a couple of MTBoS friends. With one, I began the conversation because of a difficulty she was going through. I wanted to connect with her to confirm what I suspected. We had a brief text conversation and I was glad I reached out to her. Later in the day, another MTBoS friend contacted me about TMC15. We had a conversation about booking flights and a little bit about NCTM. I know I’m looking forward to seeing him this summer and I’m glad to know he’ll be heading to LA.
So as I was putzing around today (and my husband was working with my daughter), I decided to open up my Digg Reader. It has the lovely infinity sign, which means I have more than 1000 posts to read. And rather than declare bankruptcy, I chose to start reading. The first blog on my list I came to was Sarah Hagan’s and I had to go all the way back to August, 2014. I began reading. About the 4th or 5th post was titled “On Blogging.” In the post, Sarah talks about why she was struggling with blogging and why it was important to her. And a lot of it rang true for me. But most of all, the last two paragraphs are spot on:
I need to go back and remember why I blog, though. I blog for me. I blog because I process best through written reflection. I blog because I have a terrible memory. How did I teach this topic last year? Let’s go back and read the blog post about it. I blog because I desire community. My blog made me a part of the MTBoS. I blog because I have a desire to share. I blog because I believe that my sharing will lead others to share. I blog because I want my impact to expand beyond the city limits of Drumright, Oklahoma. I blog to connect.
From here on out, I will stop apologizing about what I blog about. I blog for me, not you. I will not feel guilty when I do not blog. My blogging will happen based on what I need. Dan Meyer told us to be selfish. I’m taking his advice.
She is completely right. I have lost sight of why I became involved in the MTBoS and stayed on Twitter, read others blogs, and blogged myself. I, like Sarah, began blogging for myself. It was a place for me to hash out my thoughts and figure out what I was doing right and needed to improve. Participating in Twitter was a way to connect with others and find other like minded teachers. It was a way to find other teachers who taught the same course or who had similar passions for teaching math and bounce ideas off of them. Through Twitter and blogs, to quote Cheesemonkey, I found my tribe. As I read the last paragraph that Sarah wrote, I remembered how Dan talked about being selfish and some of the conversations we had around that at and after TMC14. And I realized I had gotten away from that. Even though it sounds bad to be selfish, when I was being selfish – blogging for myself, engaging in Twitter and blogs, interacting in the community – I was also being self-less. By being self-less (and selfish), I was giving back to the community that has helped me grow so much as a teacher and as a person.
So, I am publicly going to say this (even though I am really only doing this for myself): I am going to work at being more selfish/self-less. It’s going to take some time, but I am going to go back and read the blog posts I have stored in my Digg Reader. I am going to make a better effort to be more active on Twitter. Hopefully, the inspiration to blog more will strike me and I’ll want to post more here. I have more Common Core / PARCC tables that I want to work through at some point. Doing these things does make me happy. I need to get back to that.
And if you made it this far through my selfish blog post, two things: thank you for reading and I hope you are able to figure out what makes you happy and do whatever that is.
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Throughout this unit, I have been talking about how factoring is un-doing the distributive process that we did when multiplying polynomials. We are looking for the factors that we multiplied to get us the answer we are given.
We are not all of the way through, but this is what I have done so far:
Days -2 through 2 – Introduced X-Puzzles (Julie references them) for students to work on finding two numbers that multiply and give one number and add up to another number (example – two numbers that multiply and give 48 and add up to 14: 6 and 8)
Day 1 – Taught how to factor using the GCF.
Day 2 – Taught how to factor four terms using 2 and 2 grouping.
Day 3 – In class practice factoring using the GCF and 2 and 2 grouping.
Day 4 – Taught how to factor x^2 + bx + c. Here’s how I explained it:
Let’s say you have x^2 + 10x + 21. We’re going to set up an x with the multiply number on top and the add number on the bottom, like we have been doing. To get the add number, we are going to take the coefficient (including the sign!) of the x-term, which is 10. We are calling it the add number because to have gotten it, we added. To get the multiply number, we are going to multiply the coefficients of the x^2 term (which is 1) and the constant (which is 21). 1 times 21 is 21. Now solve the x-puzzle – what two numbers multiply to give you 21 and add up to 10? 7 and 3.
We are now going to rewrite the 10x as the sum of two terms with the coefficients we just got. So now we have x^2 + 7x + 3x + 21. Since we have 4 terms, we can use 2 and 2 grouping like we did last week.
x^2 + 7x + 3x + 21 What do the first two terms have in common? (x)
What do the second two terms have in common? (3)
= x(x + 7) + 3(x + 7)
We should now have the same expression in both parentheses – this is our common factor for the two terms I have. It goes in one parentheses and the other parentheses has what is multiplied by each of the (x + 7)s.
= (x + 7)(x + 3)
Then I have them multiply back to check:
x^2 + 3x + 7x + 21 (Oh look – the same four terms we had a moment ago!)
x^2 + 10x + 21 (Combine like terms to get our original problem).
We have spent two more days practicing this in class. With practice, they have caught on rather well. We will start ax^2 + bx + c when we get back from Easter Break in a few days. I feel confident that they will catch on to that with practice as well.
I’ve taught with the boxes that Julie referenced. I think the biggest problem I always found is that students get confused on which term goes in which box. With using 2 and 2 grouping as part of the process, it ties to something they have already learned and it makes clearer to the student why they get the answer they get.
]]>As we have been working through the Common Core State Standards this year, I have really been putting a heavier emphasis on my students being able to explain why they are getting the answer they are getting or what something represents. At times, it has felt like I am pulling teeth to get them to do it. But slowly, surely, we have been getting better. I am starting to see more students being willing to contribute an answer. Discussion is improving a little bit at a time.
I am not sure if I can pinpoint exactly why today’s discussion went well. I felt good about the questions I asked. Once I reflected on the day, I felt good about the responses I received from my students. But could I pinpoint exactly why they had a better idea today? Not really. But what I think I can feel confident about is that my students are coming around to applying the Standards of Mathematical Practice. With perseverance on my part in teaching them, they have begun to come around.
So, if you are reading this, I want to offer you some hope. Keep fighting the good fight. Push the students to use the Standards of Mathematical Practice. Post them in your room, whether the actual ones or the student-friendly ones. Make the students recite them, a la Justin Aion (sorry – I can’t find the actual post where he shares that they do this, but he does!) Whatever it is you need to do to get them to understand and, more importantly, use the Standards of Mathematical Practice, DO IT! Will it be easy? No, not at first. But it will get easier and they will improve. As far me, I will keep fighting the good fight. I’m going to enjoy today for a few minutes first.
]]>I teach in Ohio, which is was (as of June 30, 2015) a PARCC Consortia state. When Common Core was first released in 2010, grades K through 8 had their own set of mathematics standards. There are 5 domains of standards at the high school level, but they are not arranged by course. In addition, as you read the standards, there is some overlap. An Appendix (A) was added with a suggested list of which standards should go with which course (Algebra 1, Geometry, Algebra 2 or Math 1, 2, or 3), but that’s as much guidance that has been given.
So Ohio was involved with both consortia at the beginning. Eventually, they decided to go with PARCC. My students will be taking the PARCC exams this winter and spring. As I was looking at my curriculum map this fall, I was trying to figure out the order I was going to put my units in, knowing that my students were going to take the PBA in late February. Once again, I was hunting all over the PARCC website trying to find the information for each test and look through the End of Year test, and getting incredibly frustrated. As I was getting frustrated, I kind of thought about putting together something that had everything in one place – the actual Common Core Standard and all of the table information from PARCC from every document they had on Algebra 1. As I began assembling it, it made sense to me to add in the End of Year Items and Sample Tasks that were already released by PARCC in with the correct standard. While I was waiting on PARCC to release the PBAs, I also did Algebra 2. Since I teach Algebra 1, it made sense to me to do the same for Algebra 2 so I could see where my students were going. The 8th grade standards are next on my list, so that I can clearly see where my students should come from. I will add the 8th grade once I have it finished.
Once I completed these, I shared them with a few people I know who could use them. I wasn’t totally sure what I wanted to do with them. There were some varying opinions, but the bottom line opinion was that they would be useful to other teachers and it was a good idea to share them.
I have copied and pasted the information provided by the Common Core State Standards and PARCC online. At the very end of the document, you will find the links of where I pulled the information from. All I have done is formatted and arranged the information in a way that made sense to me.
So, here they are. I hope they can help you out. Please share the links.
All the best, Lisa
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