Archive for September, 2011

I really liked the way I introduced square roots and it was completely stolen from Dan Greene (and all of his awesome Algebra 1 lessons can be seen here).

The course I’m teaching (11th grade PSSA prep) is basically a “review” that helps kids pass the state test. How I’ve decided to teach the course is a “problem solving/critical thinking” course and I’m allowed to do this because most people associate any problem with words with critical thinking *not true*. The cool thing is since I’ve deemed this as a critical thinking course and the students are required to actually take Algebra 2 concurrently I’ve requested to simply teach concepts and reenforce understanding rather than memorization/procedures. So far I’ve gotten the green light from my co-op.

So, right – square roots. Most students should know this by 11th grade but the truth is these students didn’t. They had heard of a square root, they’d seen the symbol and some even could list the perfect squares (not from understanding but by adding consecutive odd numbers) but they didn’t know what it was, why, or where it came from. Enter Student Teacher Molly.

I taught this lesson over 2 days and introduced square roots by relating finding area of a square with given side lengths and looking for the inverse/opposite, what if I give you the area of a square – how would you find the side lengths?

I started with the side lengths of 3, which gave us an area of 9. Then after doing side lengths of 3-5 I put up a square and said the area was 9, so what must my side lengths be? Since we had just done this they knew it must be 3. We did this a few times and I introduced the new notation saying that the side length for the square with area 9 is the sqrt(9) = 3, and I wrote that along the side of the square. We did area of 25 together and wrote it as sqrt(25)=5 on the side length. Then they did the 3 squares on their sheets alone. I easily saw the misconceptions of side length being sqrt(5) and so I was able to walk around and address that discussing area etc.

(**My only issue here was the introduction of the square root symbol which felt a little forced like, hey this is a quick little shortcut symbol we use to denote this idea and this is what it means, I would’ve liked to do some history or something else on the symbol in hindsight**)

Then we filled in the proper way to say square root of A and what it was, “the length of a square whose area is A” (most of the students actually did that on their own). Then we talked about perfect squares and how they get their names and we made our lists. We began to talk about estimation and what to do when it’s not a perfect square; the first day we just left the side lengths in square root notation (before we got ‘2 answers sqrt(9)=3, but now we just get sqrt(10)) but the second day we started to estimate what they would be between.

The next day we talked about estimation which was actually a breeze. I started by actually drawing the squares next to each other so they could see porportionally what perfect square was bigger and smaller. After we did it with the phsyical squares, I just used our new notation and placed the question on the board, filling in the small square root above the one in question and the bigger one below (like a smush sandwich) and voila, you can find the whole numbers it lies between.

And the students really got it. When we went back to the PSSA book that asked questions about square side lengths and area the students were able to answer them easily (or maybe easier is being more honest) than if I were to have to introduced the square root more abstractly with all symbols and no squares. Thanks @dgreenedcp!

Here is the worksheet taking almost exactly from Dan Greene with some changes based on stretching the lesson and a few other things.

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Yelling… the road to respect?

I was told never to yell to get kids attention. Many methods have been suggested such as talking quieter so students have to lower their voices as well, flickering the lights or making a silent signal (and practicing it the first day). Okay at my school – these kids respond to yelling and discipline. I realize this is not the “right” thing and there’s a part of me that doesn’t even want to blog about this for fear of judgement and criticism but you know what, a silent signal doesn’t friggin work. Maybe it would with the freshmen or sophomores perhaps even my juniors would be kind enough on a good day to let me be that hokey but the seniors – FORGET IT.

I overhear the seniors making fun of other teachers all the time and today they were particularly cruel to a new teacher at the school. He apparently uses a silent signal and guess what, it doesn’t work. What did I hear this lovely student suggest he do? “He should just tell us to shut the F up, I mean he puts his hand up like some idiot like that’s gonna work.” And honestly she’s kind of right because that’s what many of these students respond to since it is what they know.

One student has been giving me a hell of a time, shouting extremely disrespectful and disruptive things at me during class. Finally he walked out of class so my co-op told me to write him up. After class the student came up to me and lost it, I mean I thought I might get punched in the face. But I stayed calm (despite my terror) and told the student he needed to respect the rules of the classroom or else there would be consequences. Today he was an angel, will it last? Probably not, but today he didn’t call me any names so that was nice.

These students do not respect authority inherently. If you talk quieter, they don’t care. You have to earn the right to be heard. If you talk about something interesting sometimes lowering your voice does actually work but it’s when the engaging intro or classwork has ended and the procedural work has begun that the students can often tune out. I have to be tough but kind.

What I have noticed works really well is talking to them like adults. After class saying thank you for listening or please try to stay awake tomorrow or I really like your input so please keep participating. Individually addressing issues both good and bad to let the students know I’m noticing and I’m interested.  I think the more students realize I am teaching them for their own learning and not for myself will lead to earning their respect and less behavioral outbursts. The new issue (isn’t there always one?) is how to get them to see I respect them, I’m tough and I can help if they let me.

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I’ve already had a bone to pick with the system but DAMN do I have a bone to pick with the system and it has to do with assessment (shocker). Friday was supposed to be quiz day for both Mr. M’s seniors and my juniors but due to electrical issues we closed (oh the irony as we are an Electrical & Tech vo school). We decided to give the quiz on Monday but allow students 10-15 minutes individual and/or class review time.

Let me explain what happened during the seniors quiz time. Mr. M reviewed EVERYTHING that would be on the quiz and completed quiz-like problems on the board. Then students requested we leave all the worked out problems, procedures and solutions on the board to help with the quiz, and so we did! Now I was already balking at that, how is this testing their understanding of hourly and overtime wage if they’re just switching out numbers left on the board?  However I was asking the wrong question since the information on the board was barely used. Students were raising their hands left and right and demanding procedural help as well as answers from me and Mr. M.  And let me tell you, they were so pissed when I refused to tell them how to do the problems. I mean, it’s a quiz – right?! As I sat back I watched Mr. M go around and help each student as if it were homework, pointing out the important information then just telling the student what to do; Also every student asked at the end of each problem, “Is this right?”

I was completely dumbfounded at the lack of “test etiquette” these kids showed. When I talked to Mr. M he explained to me that if he didn’t help these kids would fail and there is no point in failing these kids because at the end of the year the principal is going to come up to him and ask, “What can we do to pass them?” He also argued that those failing students get discouraged and disruptive since they usually adopt the attitude, “What’s the point I’m failing anyway.”

Still I’m concerned this is all wrong. If quiz grades don’t matter or reflect meaningful information, why give them at all? Is there a better way to asses learning, maybe in school projects? What is the point of all this if it’s not even vaguely accurate?!

Both the juniors and the seniors have severe learned helplessness and I keep going back to this idea of the gradual release of responsiblity that I wrote about before. For the seniors I think my goal needs to be more life-centered rather than school-centered.  I need to encourage individual thinking and problem-solving skills to help them become successful humans in the world not better test takers because for many this will be their last year in a school environment.

But most importantly I think this whole idea of a “quiz” needs to be scratched. If the information gathered is bogus, inaccurate and at the end not even used, why do it at all? And now more importantly, what can I do better instead?

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I need a new plan for Monday

There are so many little things that matter in teaching that I knew but didn’t really know. One of those things is homework; assignment, collection, grading, and answer checking. Another is warm-ups/do-nows because for some reason in my mind they go hand in hand.

At my school students are not used to having homework. They have become accustomed to 5-10 extra minutes at the end of class that is optional time to do homework (or hell it’s just not assigned at all). All last week when I was passing out worksheets (remember they don’t have textbooks to take home) the moaning and groaning was louder than any participation or disrespectful name calling I’d heard all day! But here’s the issue with homework – they copy, they cheat or they don’t do it. I realize none of this is in my control exactly but I’m wondering if I can provide meaningful incentive to complete this (hey, like knowledge?! no, bad – that’s bitter).

Since Monday is a new week I was hoping that I could start with new routines, expectations and goals since this past week I’ve been throwing together random routine ideas and seeing what works. I observed another teacher who collects homework, grades for completeness and returns the next day. She also has 4 problems very similar to the assignment on the board as a warm-up. Students complete the warm-up each day, go over the answers as a class and on Friday turn in their sheet with all their days work for credit, “Easy points to earn, easy points to lose.”

I have been putting warm-ups on the board but they do not always lend to the previous nights lesson (for example, does my text message count as a warm-up?).  Also, I have not been asking students to complete these for credit and I’m wondering if that would increase the number of students actually doing it. I don’t want to impose points on the warm-up to set these kids up to fail or to threaten them and I’m not sure if credit is enough incentive anyway (But maybe worth a shot!).

The procedure I’ve been implementing is taken directly from Mr. M. I have students do whatever I have up on the board while I go around and check the homework for completeness, not correctness. The problem with this is I do not get to see the common mistakes, I do not get to see what is tripping up every single student and I’m wasting time by going around to each student and marking done or not done. Plus, the last kid I check always gets more time to scribble some stuff down and make it look like he’s done his homework (I watch them do this). Then I’ll go over the warm-up or ask about homework questions. This whole procedure seems like a time-killer and ineffective. I read this post by square root of negative one about homework and providing solution banks to students and I think she’s onto something.

So basically this is what I want:

  • Meaningful homework assignments that are used as practice and assigned almost every night (Do you give homework on Fridays?)
  • A fair way to grade homework that allows students to get credit for effort and allows me to identify common misconceptions
  • A meaningful warm-up – NOT busy work so that I can finish checking homework. I don’t know if I want it graded or not.

One thing I was thinking for a “warm-up”  for this upcoming week is a challenging root/irrational problem to put on Monday’s do now and have the kids work on it every day for the first 5 minutes and get further and further as we move along in the unit. They would use what we’re doing in class each day to help them get closer on the warm-up the next morning. But to grade it, not to grade it… oy vey…

Most importantly I would love to outline my routines and expectations on Mondays so these kids can kvetch when I hand out homework but already know it’s coming. I don’t want to surprise them with challenging do-nows and I don’t want to collect homework one day and not the next. I really want to provide them with structure.

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“Success” from @mathhombre

Taken from here. Thanks for sharing @mathhombre!!!!

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I don’t know what I would do without you guys. As I explained a couple posts ago my goal is engagement, engagement, engagement. I am teaching a lot of dangerously boring procedures in these test prep classes with students with short attention spans and not a lot of respect for authority and mathematics. Basically a recipe for a student teacher meltdown.

I searched and searched and searched and finally SUCCESS. I stumbled upon this set of postings (with worksheets) by  Mr. K and then I hit the jackpot by finding an amazing introduction by @ddmeyer here. He introduces the idea of scientific notation by asking students to write down names of states which ultimately leads to a discussion of common abbreviations of states. He also gives students a bunch of insanely long numbers and has them kind of invent scientific notation on their own. That’s amazing but I only had 38 minutes of awesome to provide to kids who barely want to listen to me (and no tech to display said long numbers) so I had to modify slightly. Luckily this woman Amanda commented on dy/dan’s post and offered the suggestion of using text messages abbreviations and VOILA I knew I had a winner.

I placed this on the white board.

Students got really excited, “I can write whatever I want?” Yes, absolutely, as long as it’s appropriate knock your socks off. So as I went around and checked homework students wrote their new text message, abbreviating whatever words they wanted. I gave the following lead off example, “I know you all probably say ‘hey’ instead of hello.” Then I asked them to raise their hand and tell me a word they changed. This was the result on the board (summary from all 3 periods):

Then I asked them if everyone would know what “wsp”  would mean (or whatever the odd man out was up there), most said maybe (it means what’s up) which transitioned beautifully into a conversation about abbreviations, usefulness, standardizing for understanding, etc. One student even said she added extra vowels for emphasis, her example, “I don’t knoooooooow.” This was awesome because that led right into abbreviating large words/text messages or making small words larger. Then I talked about how in mathematics we do the same thing – take the distance to the sun .. and so on.

It went great! The kids were talking and completely engaged. I kept emphasizing raising their hand in order to contribute to the board so it was reasonably controlled chaos. They even paid attention to the somewhat lame procedural lecture that followed when we discussed the previous nights pattern homework worksheet from the Math Stories blog. (*They could use a calculator until they found the pattern. It was assigned as a pattern hunting worksheet rather than a scientific notation one).

Love when plans go well, I know it’s rare so I’ll savor this moment.

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Strippers don’t pay taxes

What seems relevant isn’t always relevant; this is one of the many things I am learning in this student teaching experience. The senior course “Business Math” that I will be teaching consists of all important and “relevant” math these students will need when they graduate. We cover hourly wage, overtime, savings accounts, writing checks, taxes etc. Now this is that “real” math those students are always asking for while they’re factoring or playing with quadratics. So imagine my surprise when these seniors show they could care less about this course. They are bored, uninterested and find this content extremely non-relevant.

After a grueling 5 days on hourly wage and overtime pay my co-op made the comment that, “Hey – this isn’t even what you get to take home, but we’ll talk about taxes later.” A couple of students groaned and one student called out, “Yea, well strippers don’t have to pay taxes so…” And about three other girls started nodding their heads. Now, I don’t even care if these girls want to be strippers or that one student did divulge to Mr. M last year that her dream in life is to become a pole dancer my honest reaction was, “Shit, this is just as irrelevant as Trig.”

I need to always remember the student context when creating my lessons. I don’t want to take this course content for granted – just because it seems more practical they should want to learn it for the sake of learning it. I am starting to realize that this class may be even more challenging than my PSSA prep class but I’m looking forward to finding (appropriate) and engaging ways to hook these students.

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