Well, I made it through

Day One, and Day Two!

We’ll just have to see

about getting through Three!”

I love Dr. Seuss Continue reading “Green Eggs and Ham; I love them, I love them, Sam-I-Am!”

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# Category: CCSS

# Green Eggs and Ham; I love them, I love them, Sam-I-Am!

# Intentional Talk meets Inquiry Based Learning. Hello, Beautiful!

# Productive conversations don’t just happen; conversations do. Let’s turn the natural into “super” natural(-ly productive, that is!)

# When testing becomes superfluous…

# Sonata in C, and Fluency: there is a price to be paid….

# Some days teaching are just better than others!

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# How do you tell parents to expect less from their children?

# Teachers: the Land that Time Forgot (or what a raise would look like if teachers could design one!)

# A little creativity goes a long way towards getting kids to do their homework!

# I let the kids teach today. They (well, most of them, anyway) rocked it out of the park!

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#iteachmath I invite you to join the conversation!

Well, I made it through

Day One, and Day Two!

We’ll just have to see

about getting through Three!”

I love Dr. Seuss Continue reading “Green Eggs and Ham; I love them, I love them, Sam-I-Am!”

I teach math. I don’t want to teach it anymore. Instead, I Continue reading “Intentional Talk meets Inquiry Based Learning. Hello, Beautiful!”

“Conversations about learning take time” Evan Weinberg

Evan, I think you may have revealed the heart of why teachers Continue reading “Productive conversations don’t just happen; conversations do. Let’s turn the natural into “super” natural(-ly productive, that is!)”

So my colleague was commenting about another teacher complaining that the test was all procedure and no processing….

Let me back up a little. Formative assessment is constant, very informal, and is, at its heaviest, a quiz. Summative assessment, on the other hand, is very formal, comes at specific breaks in the unit and at the end, and is administered to all classes in the same curriculum. Once the curriculum summative is created, it is provided to each teacher. In the above instance, the teachers was complaining to the curriculum chair about the current test.

My colleague felt this teacher should have known the purpose for the summative: our summatives were just testing practice for the course final.

I admit I was caught off guard- I didn’t know this was the purpose of our summatives either!

The argument made to me was “we really shouldn’t need to “test” (summative with a capital S) children unless they were making up material or they were remediating…” Huh?

It got me thinking about the true purpose of testing. If we are truly teaching for understanding, then testing is really superfluous, isn’t it? They will use the knowledge regularly, without the need to answer poorly constructed, artificial situations that are designed to test what they don’t know, with trick answers that are designed with the errors that are “usually” made by “most” students. There is something stinky about assessments with test banks so protected that they are secured better than banks!

So let’s talk about how we, as teachers, can make summative testing truly superfluous.

I found myself grading mounds of worksheets, and a couple of quizzes (remediations, really), and I began to wonder if I’d turned into one of those worksheet, algorithmic, obsessed teachers that focus on skill and drill over understanding. And I was beginning to despair, just a little.

I thought about my students, and what allows them to experience success, because it is the successes that motivate each one of them to keep going, to persevere in the “icky, sticky, I don’t get this” parts where they struggle. Part of the reason my students struggle is the lack of fluency. Each concept, each set of steps, each decision they make to solve or simplify, takes a huge cognitive load. They exhaust themselves just remembering what they need to do to factor a number (“Mrs. M., what is a factor again?”)

These children are not fluent. Not in multiplication tables, not in knowing the difference between base and exponent – more than half of them will tell you, “a negative plus a negative is a positive, because two positives make a negative.” I remind them they are adding, not multiplying, and they bravely leap back in, “oh yeah, -11 plus -3 is 8.” And this is after they have laboriously put the computation in the calculator… And I draw another number line on the board, or we play the game where they move their token up and down a number line to the tune of positive and negative numbers.

These babies of mine are not fluent! But they will get there. And therein is my saving grace with the worksheet thing. You see, I learned to play the piano, and I took ballet lessons, and I was on the swim team. And I was good at them in that order. But each of those activities required PRACTICE! I knew what it took to swim 50 meters fast enough to claim the silver, the red, and the blue ( third, second, and first, respectively), but I was better at collecting the silver than the red or blue, because, well, practice was held in the cool early summer mornings – when I’d rather be sleeping, or reading, or doing anything else than getting wet and cold over and over and over…. Well, you get the picture! I never got “fluent” at the swimming thing.

Ballet was a little better – no water! But I wasn’t slender or limber, and I couldn’t lift my leg to the bar without a pulley! I loved the pliĆ©, and the costumes and the recitals, but my heart wasn’t in it, (probably because my body wouldn’t cooperate by being tiny and graceful – one can only take so much of that feeling like a cow among graceful swans!)

Then there was the piano. We had an old upright; beautiful and rich sounding tones would pour forth when my mother played. She could play everything! And if she couldn’t play it, she could sight read the music. I soon learned to love the sounds I could produce. I wanted to play the classics – Mozart and Tchaikovsky, and Bach and Beethoven. I wanted to play the rich beautiful pieces mom could play. I had heard them, I could read the notes, but I had to become fluent in the patterns. I would play the pieces haltingly, getting a feel for the notes, but then, to really learn the piece, I would have to practice small sections – bar by beastly bar, until my fingers would traipse the keys of their own accord, and the piano would yield up its beautiful tones for me, the way it did for my mom.

So, back to the piles of worksheets. I look at them: logarithms and exponentials; growth and decay word problems; breaking down the formula, picking out the beginning value, the ending value, calculating the rate factor from the rate; understanding the idea of 100% being expressed as one. My babies are practicing their fluency with the notation, even as we put details to the numbers on the page. While I teach for understanding, I really want to show them the beauty and the majesty of math’s rich and beautiful notes. I want them to want to produce the beauty that comes as they practice; as they practice the changing from exponential to logarithmic so that they can spot what they need to do when they have to calculate for time, instead of finding an ending balance; as they practice because fluency takes a lot of that cognitive, heavy, exhausting work and turns it into a beautiful smile when the light clicks on and the child yells, “Mrs. M, I got it, let me come up to the board and write the answer!” And so I will keep on with the practice, worksheet by beautiful worksheet. Success breeds confidence. Confidence breeds courage – the kind you need when you tackle something new, or when you persevere because you believe you can find a solution.

To cut down on the paper (and the grading) I’ll keep varying the tasks: physical practice, verbal practice, mental math practice, practice through competition, things like Jeopardy or Kahoot, because practice builds fluency, fluency builds success, and success is what keeps us trying.

I did finally learn to play a pretty mean Sonata in C, but there was a price I paid to gain the fluency I needed. And, while I am not as good as I used to be, when my fingers find a piano, they slip into the gracefulness that eluded me in ballet, and the speed my body lacked in swimming competition, and they can “fluently” find the notes that will make the piano, and my heart, sing!

This is a blog that got written, but not posted. This semester I have a different group of kids, and as I read this post, I was reminded of how much fun we had last semester. And I am thankful for all the days since this recorded day in September with these awesome kids!

Today, Monday, September 15, 2014, was a good day; a really good day. “Why?” You ask. I’ll tell you why…

Tuesday is a “Formative” assessment, a pencil and paper, constructed response. You know the drill… “The students will be able to…. ” Anyway, I knew from my informal formative assessments last week that I needed to make sure my students understood how to build a histogram from the data *before* they tackled this test.

So I had them set out to build a histogram with 3×5 cards on big posters. (I wanted them to understand that those bins contained real numbers!)

We had a set of data on the heights of all the students in my classes, in inches, so I decided to stick with the familiar. I scaffolded by asking them to create a stem and leaf plot of the data and we ended up with three lovely rows of 3 leaves, 25 leaves and 7 leaves.

I had them turn the stem and leaf plot sideways. “What does it look like?” I asked.

“A histogram,” said one young lady. “Oh yeah,” some said. “I see it now, ” said another. And just as they thought they had deciphered what I wanted, they were given the task of putting the numbers on 3×5 cards and sorting them from least to greatest.

Puzzled, they did as they were asked as I ripped huge sheets of paper from a pad and laid them on the tables. “Lay the cards out just like the stem and leaf.”

Once the cards were laid out, I had them add intervals across the bottom, and frequencies up the side. As they worked on the task, they began to realize, if they had not already, that they were actually building histograms, something we had been working around and with in various ways since the beginning of the year.

At the bottom of each column of cards students wrote the actual intervals, which meant that numbers were skipped, since not every number between 57 and 74 were represented.

I asked those students where the missing numbers would have gone if we had them. After a bit of discussion, they determined that if they had those numbers, they would put them in the same line of the stem and leaf, so they needed to make room for them in the same column with the other cards.

Not all students were clear on what we were doing, so I was pleased (an understatement here!) when a couple of students from one group went to other groups and started *explaining (!)* to the others why they needed to (1) change the bins to cover the missing link and (2) why the bins had to cover the same amount (range) of numbers.

That task accomplished, I had them find the bins with mean, median, and 1st and 3rd quartiles. They were a little disheartened to find them all in the same bin. (We had been working backwards from histograms to approximate these values for a MARS Project

problem based task unit which had proved to be a difficult task on a conceptual level for many of them.

To correct this, the students decided they needed to spread the numbers out, have more bins… Some students leapt right in and started spreading out the cards. Others couldn’t envision how to start, so I asked them to just start spreading the cards out into smaller groups. One group immediately divided the cards into four columns of ten cards (we had 40 values), and clamored to show me. I asked them to give me the ranges each bin covered. They soon discovered they had the same numbers in more than one column! More shuffling ensued. Ranges were computed. Students debated whether each bin had the same ranges. Maybe more bins were needed, different ranges were calculated, discussed and decided on. Some students had five bins, some had six. As the bell would ring, I had students leave their unfinished charts for the next classes to finish.

I get some students more than once, for classes called strategy class, so after first period, I had some new students and some students from first period. The first period students had to explain the task and help the current period students finish. I was also challenging them to find different bin ranges. If they grouped five bins, I would then ask them to calculate for eight. One group decided on 14 bins, with one number falling in each bin. After each group felt they had the best arrangement, the students would outline the cards to create bins, recalculate the frequencies, and remove the cards.

As new classes came in, the stem and leaf exercise was repeated, the card decks were distributed and the task would begin again…

Once we had the drawings up on the wall, I asked the students to tell me which groupings seemed to be the best distribution and summary of our heights. Which graph seemed to tell our story the most clearly. I’ve included some of the finished product here. I am sorry about the picture quality. Some students’ markings didn’t show up well.

Why was this the best day ever? Because my students were totally engaged and learning. I was blown away by the level of engagement shown for this task from *all my students, even those who were generally disengaged. The students who came to me twice were leaving and telling me they couldn’t wait for the next period! *

I wish I could bottle the elixir let loose today! I want every activity I introduce to generate the type of group dynamic, the peer tutoring, the calculations and the understanding that dawned as they calculated different bin groupings. Did I mention that I love my students this year! Each and every one of them! Today was definitely a good day!

A recent article on the upcoming Common Core assessments that will be administered in 39 states this spring (2015) predicts that student scores will suffer. The writer cites the experiences of Kentucky and New York, where the new testing took place this past Fall (2014), two very different places and two very different results. The difference? Continue reading “How do you tell parents to expect less from their children?”

I offer the following Press as my hope for the teaching profession. Thanks Andrew!

My students do not do homework. Okay, maybe the young man from Vietnam. And he does it neatly, completely. But he is the exception.

Homework should allow students to practice what they’ve learned. They have to see a reason to really learn (aka understand, put in context, synthesize…), so this year my students will be required to videotape themselves explaining to another person (or their dog, or to me) what they have learned that day. They will need to include one new problem to be solved, with the solution. Extra points for the originality in the WAY they deliver their explanation!

Once uploaded to our class website, they can be viewed, commented upon and used in class for discussion. I also anticipate having a way for my students to see growth in their learning over time.

A side effect I anticipate is closer listening in class, and an enhanced collaborative spirit: this will force new ways for students to “share” homework. (Students are the original Creative Commons licensers!)

There are lots of great tech innovations for collecting, sharing, commenting on this type of assignment. Feel free to comment if you have a better (free) way of setting this up. I am in a BYOD school, and I want to get my students involved in texting comments during an assignment (about the actual assignment!), blogging, and more. I feel that getting multiple senses involved, and having them more involved in teaching/creating their own lessons, will generate more learning.

As a side note, I also plan to have them create other assignments on line: a magazine page on a topic; a cited problem solving journal article on one or more of our math topics: online posters illustrating concepts, a word wall, and more. This way they can incorporate music, visuals, and color. I may have to purchase a monitor for letting their creations run in a constant loop, like one of those electronic picture frames!

I will track their progress. Algebra II, here we come!

#MTBoS I am going to try this 30 day thing AGAIN! Here’s my challenge: school’s out. No kids to write about!

Let’s just see what a teacher does with summer!

#MTBoS30 A simple review activity created positive energy in the classroom today.

This is a difficult week: End of Course tests are done, finals are a week away. Students tend to relax and give into the end of the year lassitude. There are still a unit test and a performance (writing) assessment to go before the finals, but the students are completely burnt out on anything with the word review in it.

To combat the blahs, I designed a student teaching assignment. Students were paired up and given three brief instructions: create a lesson, teach it to the class, and ask the class to perform a brief activity to show understanding. We assigned each pair a problem from the sheet of review problems for the unit (on probabilities) and gave them 15 minutes to create their lessons.

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Some students required help with their understandings, and as I walked around listening to the students planning their strategies (20 points for sharing the teaching responsibilities), I was able to discern which students needed help and which ones didn’t. It was an enjoyable day of formative assessment for me, and having them teaching freed me up to spend more time facilitating the learning.

It was fun to watch the students mimicking me (and boy did they!), but I also saw a different side of many of the students as they led their peers, answered questions, and walked around the room helping other students understand the problem. They were reviewing without a single complaint! (Well, maybe just *fewer* complaints!)

This lesson took a block period, which for us means two 50 minute back to back sessions (a regular geometry and a strategies class). This gave us time for a brief introduction to the types of problems that we were going to review, a setup of the task and partnering, and 15 minutes for the pairs to plan. The students really needed about 2O minutes to plan, and we were able to give each pair about 5-7 minutes for lesson presentation and follow up.

Assigning the problems was made easier by taping the problem number to every pair of desks. As students came in, we sent the students where we wanted them to sit, which streamlined both the pairing and assigning problems portion of class.

The photos show the wide range of visuals the students employed to teach their lesson. They also used the smart board, however, that was more an electronic chalkboard for them!

Patterns in Practice

the blog of the Mathematical Practices Institute

vlogakavaughnlog

. Teaching maths and feelings mostly

occasionally optimal

high school math teacher in nyc interested in school transformation, discovery-based learning, equity/inclusion & grading reform

Graphic maths

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Gaming the Classroom

Using games to teach in and out of the classroom

Math Dyal

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