Category Archives: Uncategorized

Are stations the answer?

My time as a math coach taught me that stations are the bomb! I observed masterful first grade teachers regularly manage many different math levels without breaking a sweat. I experienced fourth grade teachers manage a room full of wiggly students during flex blocks and everyone was “getting what they needed.” Somewhere along the way we begin to believe that our students can sit for longer, focus for longer, and we don’t need to use stations to reach all learners.

A few years ago my district purchased the Connected Mathematics curriculum. I had used previous versions of the curriculum in the past and many of the problems were interesting and rich. The new version is clunky, disjointed, and difficult to use. Many of the problems are long, requiring several class sessions to complete with very little conceptual understanding. My students lose interest and are unmotivated by the time we finish a problem. The math they may have gleaned from the problem is lost in the euphoria they feel to be done.

As the year came to a close and I reflected on what went well and what didn’t, I was reminded of the times my students were engaged, challenged, and motivated to learn. The times this happened the most this year was when I was using stations in my classroom. They felt as though the tasks were interesting and at their level.

I began to think about my first unit in terms of stations using the math workshop model thinking about how I could use the best parts of the CMP curriculum. I came up with four stations including one where I will meet with students in small groups. These small group meetings will force both remediation and enrichment to happen within the station rotation.

Then I ran across this tweet….

After I read a little about responsive stations it seems like this is exactly what I need to add to make my stations even more productive. By first spending time to teach the necessary skills before starting a new unit I can really meet my students where they are. Looking at what students know and how to build off of that I can make all students feel successful.

So, my first unit is no longer my first unit. I need some station work before we start the first unit. The skills they really need to have solid are their multiplication and division relationships. I started planning my stations here. I think this will also be a great time to teach some of the classroom routines that need to get done at the beginning of the year so I’m only going to use three stations. More to come…

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The Past Year

This past school year was one of my toughest. There were a lot of reasons for this, I won’t go into all of them, but one of them was having access to technology. It was a lot to have constant access to technology. I love having iPads in my classroom, but I struggled to use them to transform my teaching without completely changing the way I teach. I need to rethink how my classroom runs and what I do.  Some thoughts….

  1. I quickly realized that I have the ability to run several different activities inside my classroom simultaneously. IPads make running stations or differentiated lessons much easier. I can distribute and collect work in a different way. We can keep unfinished card sorts or puzzles using the camera or explain everything. The paper everywhere problem is significantly streamlined. This class flow is very different.
  2. My students can and will collaborate to complete activities in different ways on the iPad, there is a different dynamic. Students are more willing to share ideas and engage in group work.
  3. Organization! Sixth graders struggle with organization. It just hard and the iPads are a game-changer. Things that used to get lost are easily stored in google drive. The sheet we use for estimation 180 was easily found and started every week, rather than handing out a new one every week. Students were able to see how they became better estimators as the year went on.
  4. Formative assessments! The world of technology has opened up my ability to quickly assess what my students are understanding. Formative and Pear Deck make it quick and easy to assess students without a lot of paper or correcting. I can bring students together and still have everyone participating and asking questions.

Now that I have seen the way the iPads effect my classroom I want to change the way I teach to match the new ways I have to reach my students.

A Day in the Life

5:30 am – Alarm…Snooze

5:53 – Peel myself out of the bed. Find something to wear. Go wake my boys. Dress Sam while he’s still sleeping and Ben’s talking to me from his crib. Dress Ben. Make lunch, pour cups of milk, make breakfast, make coffee, rush children out door…

6:30 – Take two trips to the car, one with bags, one with children.

7:15 – Drop both kids at daycare

7:30 – Get to work. Climb three flights to classroom.

7:40 – Finally get to classroom. Hmmm…maybe I should make some more copies, I never have enough copies. Go wait in line at the copier. Uh-oh, copier jammed, doesn’t look good. Oh well, hope I have enough for the morning.

7:55 – Change the date and day on the whiteboard, collect donations for Thanksgiving baskets.

8:10 – Listen to morning announcements, try to take attendance in Powerschool.  Won’t load, ugh, call the office with attendance. First class comes in…

Co-taught class – put on FM transmitter, make sure it’s on, and I begin. Collect homework, discuss multiplication of fractions, how do model one-half of one-third with the area model. Now with a length model…

Edcanvas of my lesson

8:55 – Bell rings, next class, “Uh, I’ve been absent for nine days, did I miss anything?” Multiplication of fractions.

9:46 – Bell rings, Prep. Tech guy comes in. Thank goodness, my LCD projector was knocked onto the floor Friday when I was out. It is working, but is it really okay. Seems to be.

Oh yeah, and my computer stopped printing fractions. I have to send all my files home in order to print them. That’s fun!

He finds the fix, no pictures on my problems…well that’s boring. When are we getting new computers, Christmas, maybe… Can he fix my clock? It was 40 minutes slow, but since daylight savings it’s 20 minutes fast. Nope.

10:37 – Next class…Multiply fractions

11:28 – Lunch, then directed study.

12:43 – Next class, multiply fractions

1:34 – Next class, multiply fractions

2:25 – End of the day. Students want to know if they are missing any work. Um, it’s the last day of the term.

Try to make more copies, do a little grading, start entering report card comments.

3:00 – Out the door to daycare. Pick kids up, both napped in good moods. Begin the drive home.

4:15 – Get home. Take two trips in, one with the kids, one with the stuff. Turn on the oven. Wash a chicken. Put chicken in the oven. Go play downstairs with the kids.

4:45 – What’s that noise? Oh yeah, the smoke alarm…

5:45 – Dinner’s ready, hubby walks in the door. Perfect timing.

7:00 – Ben to bed. Begin reading Twitter. Need to get caught up, need to get caught up.

8:00 – Sam to bed. Start writing….

9:00 – Go to bed.

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Excitement

We had a full day PD on Tuesday. They close down the schools to make it easier for everyone to vote. Some teachers dread these days… “What are they going to make us sit through now?” Not me…I secretly like them. I would never tell anyone this. I like listening to my colleagues teach me something they know and I don’t and I like listening to my other colleagues tell me about something they learned.

I have a renewed sense of excitement after PD. I’m excited to put into action whatever it is that I learned. I want to run back to my classroom and start teaching. This one was different. Ben Schersten taught us how to use Twitter for PD. I didn’t have to go back to my classroom… I could start right there. Twitter is an amazing tool for PD if only you know how to harness it. When Twitter was first introduced I couldn’t figure it out. What is this for? In the past three months I have become addicted I can’t stop reading. Thank you Ben for filling in the blanks. There is a lot to learn and there is a ton of information out there. Ben gave us people to follow, hashtags to search for and apps to use.

I have discovered another kind of PD as well. The kind I can sit on my couch in my PJs and enjoy. Thank you Global Math Dept I can learn something new every Tuesday night.

Blogging and twitter has changed the way I learn and teach. Thank you.

LCM, GCF, and Fractions.

We had a great time last week working with cogs and I think the mathematical thinking my students did is the kind I want them doing all year. Unfortunately, this lesson is not one of them.

My colleagues and I discussed whether we should even teach these topics. They are definitely not sixth grade topics, but we need somewhere to start and once we start simplifying fractions, we need some common language. I start out by reminding students how they usually find the greatest common factor, by listing out all common factors. I’m always hoping that someone will have a better method, using prime factors, maybe? I then show students the ladder method we used for prime factorization and how it can help us here.

Once again we ask ourselves the same question, “What is the smallest prime that goes into…?”

Using the same method we used for prime factorization we divide out prime common factors. What we are left with is the prime factorization down the left side of the chart, the LCM can be found by multiplying all the outside factors together and there are several other patterns in the chart as well. The bottom factor on the right multiplied by the number on the top left also equal the LCM. Here is the same page with a few completed examples.

There are obvious implications here for finding common denominators. Students can quickly find common denominators and the chart will give the factors that the denominators need to be multiplied by to get to that common denominator. There are a lot of patterns for students to see here and I think it gives a real understanding of how prime numbers can help us work with much larger numbers.

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Long Division

Long division is always a struggle at the beginning of the year. Many students do not know the process and even more students do not understand what they are doing. I’m afraid that long division will join algebra soon and mathematics education will only require students to learn how to multiply.

Long division is a multi-step process that many students struggle with to the point of making up rote memorization mnemonics. Students that have been shown how to repeatedly subtract multiples of the divisor don’t understand how this connects to the more efficient method.

My sixth grade classes today looked at me stunned when I asked them to divide 32 into a ten digit dividend. Does it matter? Have they never been asked to do something that is not printed on a worksheet? Something that might be challenging?

Several students asked if they could just do short division. This is something that really bugs me! Am I the only one?

I think there is so much math in long division that short division loses. Remainders are so important. Which remainders are repeating? Can we have a remainder larger than our divisor? What are the possible remainders when we are dividing by 32? These are questions that sixth graders don’t know the answers to. These are questions that are important to their understanding of division.

When I divided 132 by 11 today students couldn’t tell me what it meant to say 11 goes into 13 once. Why didn’t I put the 1 over the two? Why don’t I just subtract the 11 from the 32? These students have all seen their fourth grade teacher repeatedly subtracting multiples of 11’s. What is missing? Is it repetition? How do we help students “really” understand what they are doing?

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Mathematics

Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one county.

Howard Eves Mathematical Circles Squared (Boston 1971)

I have this quote hanging on my classroom wall, I always have. I don’t remember the first time I read it, but each time I look at it I feel inspired.

So many subjects are subjective based on a person’s perspective. Mathematics is different. Many people solve problems differently, but the solution is always the same. We all end up in the same place. I think that is what I love about this quote. We all get to the same place no matter our differences. It may take one person twice as long as another, but the solution is always the same.