{"id":230,"date":"2016-05-17T20:38:31","date_gmt":"2016-05-17T20:38:31","guid":{"rendered":"http:\/\/www.coast2coast.me\/nate\/?p=230"},"modified":"2016-05-17T21:31:01","modified_gmt":"2016-05-17T21:31:01","slug":"still-going-strong-successes-on-the-homestretch","status":"publish","type":"post","link":"https:\/\/www.coast2coast.me\/nate\/2016\/05\/17\/still-going-strong-successes-on-the-homestretch\/","title":{"rendered":"Still Going Strong: Success on the Homestretch"},"content":{"rendered":"

Today in my Algebra 2 class we solved equations. \u00a0I started with a simple worksheet – solving linear and quadratic equations with one variable. \u00a0Easy stuff. \u00a0But as I looked around the room I was very happy with what I saw. \u00a0My students were all working diligently. \u00a0More importantly they were working together. \u00a0Many had left their seats to ask for help. Others were moving between groups confirming their answers. \u00a0At this point in the year, I was proud to see my students motivated and working hard. \u00a0I remember in my early years, as the year wound down, my students would become less and less willing to work and more and more likely to try to distract me from teaching. \u00a0I suppose I’ve come a long way. \u00a0Some thoughts…<\/p>\n

My students like easy work.<\/em> \u00a0This is somewhat bothersome. \u00a0I don’t blame them for liking what they are already able to do, but I would like to think they they would prefer a challenge, something that would lead to real thinking, new understanding and growth. \u00a0I often get the feeling that they would rather just practice math that they already know. \u00a0Like they just want to stay inside their comfort zone, all the way in the middle of their own personal ZPD. \u00a0Today’s class was engaging, not because it was a great mathematical exploration but because it was review. \u00a0This is frustrating for me.<\/p>\n

Opportunities to build confidence are important.<\/em>\u00a0 This is a counter to my last point. \u00a0I think it’s important to embed math that my students are already good at into my lessons. \u00a0For one, it’s always good to review. \u00a0Secondly, it gives students opportunities to share things they know with new people. \u00a0Third, and most importantly, it helps them remind themselves that there is some math they are good at. \u00a0As my students worked through the problem set, I heard them saying things like, “I feel smart!” and “I get this!” \u00a0That’s got to be worth something. \u00a0And I think it turned their brains on for the rest of the class period. \u00a0Like they got a little confidence\/adrenaline boost from completing the problems. \u00a0It also gave the students who typically struggle an opportunity to be on level footing with the ones who typically thrive. \u00a0Definitely worthwhile.<\/p>\n

My students have learned to work well together.<\/em> \u00a0This is huge. \u00a0As the students worked through the problems I saw groups of students sharing answers, freshmen helping seniors, and pairs arguing about solutions and debating pathways. \u00a0I see the collective effort of my class in a way that I haven’t seen in previous years. \u00a0I feel great about this. \u00a0It can’t be understated. \u00a0It got me back to this blog!<\/p>\n

Cancelling out is a thing for my students. \u00a0<\/em>Ugh. \u00a0Everyone solves by cancelling out. \u00a0I asked students to share how they answered the first problem:\u00a0\u00a02x + 7 = 17. \u00a0<\/em>Almost everyone shared that they had subtracted 7 from both sides. \u00a0Okay, good. \u00a0(I refrained from asking why both sides. \u00a0We’ve been over this many times.) \u00a0Then cancelled the 7.<\/p>\n

Okay, how?<\/p>\n

Huh?<\/p>\n

How did you “cancel” the 7?<\/p>\n

Huh? \u00a0That’s just what you do.<\/p>\n

But why does it cancel?<\/p>\n

*Blank stares. \u00a0Nobody knows.*<\/em><\/p><\/blockquote>\n

I think they know that\u00a07 – 7 = 0<\/em>, but I don’t think that’s part of the solving process for them. \u00a0I talked about additive and multiplicative identities for a bit. \u00a0I made a fuss. \u00a0We moved on.<\/p>\n

\"FullSizeRender\"<\/a>

Solving without crossing anything out.<\/p><\/div>\n

My students use procedures before thinking. \u00a0<\/em>After students shared the “cancelling method” I asked if anyone had done it another way. \u00a0Everyone was quiet for a while so I asked Ruben. \u00a0I knew he had a different method. \u00a0“I just looked at it, and I knew it had to be 5,” he said. \u00a0I looked at the rest of the class. \u00a0“Yes?” \u00a0Many of them smiled. \u00a0“Well yes,” their eyes told me, \u00a0“but that’s not how you do it!” \u00a0I disagree. \u00a0That’s how I do it! \u00a02x + 7 = 17\u00a0<\/em>? Two times what is 10? \u00a05. \u00a0Done. \u00a0They must have been taught that they shouldn’t do the problem that way. \u00a0It was as if they knew they weren’t allowed. \u00a0But why not!? \u00a0I’m a fan of doing easy mathematics the easiest way possible. \u00a0It’s efficient. \u00a0If a problem doesn’t require an elaborate strategy then you should only use one if you like that sort of thing, not because you’re a\u00a0robot who recognizes problem types and executes procedures. \u00a0Eventually problems will get more messy and students may need a more sophisticated strategy, but until then they shouldn’t be deprived of an approach that results in the correct answer.<\/p>\n

My students want to know why.<\/em> \u00a0Another huge win this year. \u00a0They expect this from me. \u00a0They know that I am going to talk about the whys. \u00a0They knew there would be more explanation for 2x + 7 = 17<\/em>, even when they already knew how to do the problem.<\/em>\u00a0 I hope they take this with them to their next math class. \u00a0I hope they demand this from themselves and their teachers. \u00a0Math is not the same without the whys.<\/p>\n

Random grouping matters. \u00a0<\/em>This will be another blog post. \u00a0I used UNO cards this year. \u00a0New seats every week. \u00a0My Algebra 2 classes have students from every grade: \u00a0advanced freshmen, seniors who haven’t been\u00a0mathematically inclined, and everything in between. \u00a0I mentioned earlier that freshmen were helping seniors. \u00a0In previous years, I’d keep them separate for fear they’d make each other uncomfortable. \u00a0But random grouping didn’t allow for that. \u00a0The result is a classroom where more groups and pairs of students are comfortable working together. \u00a0As the year has gone on I’ve become more lenient about students leaving their seat or even group to seek help and the results have been great. \u00a0Again, I will post about this later. \u00a0Thanks to Alex Overwijk and others at TMC15 for convincing me to do this.<\/p>\n

I’d like to share what I did next, but that is for another post. \u00a0Now, like my students, I need to stay motivated!<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Today in my Algebra 2 class we solved equations. \u00a0I started with a simple worksheet – solving linear and quadratic equations with one variable. \u00a0Easy stuff. \u00a0But as I looked around the room I was very happy with what I saw. \u00a0My students were all working diligently. \u00a0More importantly they were working together. \u00a0Many had […]<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/www.coast2coast.me\/nate\/wp-json\/wp\/v2\/posts\/230"}],"collection":[{"href":"https:\/\/www.coast2coast.me\/nate\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.coast2coast.me\/nate\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.coast2coast.me\/nate\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/www.coast2coast.me\/nate\/wp-json\/wp\/v2\/comments?post=230"}],"version-history":[{"count":10,"href":"https:\/\/www.coast2coast.me\/nate\/wp-json\/wp\/v2\/posts\/230\/revisions"}],"predecessor-version":[{"id":249,"href":"https:\/\/www.coast2coast.me\/nate\/wp-json\/wp\/v2\/posts\/230\/revisions\/249"}],"wp:attachment":[{"href":"https:\/\/www.coast2coast.me\/nate\/wp-json\/wp\/v2\/media?parent=230"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.coast2coast.me\/nate\/wp-json\/wp\/v2\/categories?post=230"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.coast2coast.me\/nate\/wp-json\/wp\/v2\/tags?post=230"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}