Whose Property Is It?

There’s a thought-provoking article in EdSurge this morning. Just who owns a teacher’s intellectual property? My husband, a former software engineer for several large tech companies, always had to sign over his rights to any ideas that he created as part of the hiring process. But educators do no such thing – at least until now.

2014-11-25-lincoln-024Advancing technology is going to make this an essential question for every school district to grapple with. Our lesson plans, reviewed regularly, are shared electronically not only with administrators but with colleagues. Documents and resources geared toward teaching, in fact, the teaching guides themselves, are often created by groups of teachers. It may be just a matter of time before enterprising schools, looking for new sources of revenue, want to monetize lesson plans or other teaching ideas developed by teaching staff.

An example of this is sharing classroom plans with Special Education inclusion partners who need to know what the classroom language and content goals are in order to make learning accessible to students on individual education plans. This past year, I’ve had my lesson plans copied into another teacher’s plan book without permission or attribution. When asked to stop, the person did; however, she continued to copy my “I can” or language/content goals again without permission. Was this a violation of my intellectual property?

In the age of Teachers-Pay-Teachers, intellectual property is about to become a huge factor. Pay attention.

Math, Flexible Thinking

My fourth graders had a burning question all year long: How old are you?

I’m not so much embarrassed by my age, as I am shocked at how quickly I got to this ripe spot in my timeline.  However, having said that, I do not directly answer that question.

Instead, I always give the students an equation on the last day of school. It usually involves a cube root. “But you didn’t teach us that!” they complain. And my reply is, “When you learn what that means, you’ll have earned the answer to your question.”

This year one of my fourth graders told me she didn’t need to know a cube root to figure out my age. Curiosity engaged, I asked her how she proposed to find the answer to her question.

Easy. You told us you were in sixth grade when John F. Kennedy died, so I can figure it out without a cube root.” And off she went to find a JFK biography in our class library.

Which reminds me of two things. One, be careful what personal facts you reveal. And two, being flexible thinkers in math is just as important as working through an equation.




A Lesson in Discussion in Mathematics

It wasn’t exactly where I had anticipated directing the discussion yesterday. And as it turns out, that was not only a moment of revelation, it was a glimpse into good things that can happen to mathematical discussions.

Have you seen a problem that is something like this one?

31 students are going on a field trip. They travel in cars holding 4 students and a driver. How many cars will they need?

With second language learners, I expected that we would have a discussion about what should be done with the remaining students.  We never actually got to that.

At the Summary point in our lesson, I asked volunteers to explain their thinking and computation for the problem. Three student volunteers stepped up to the document camera and explained their thinking: student one divided 31 by 3; student two divided by 4 and student three divided by 5.  Which one was correct?

The rest of the students kept turning around to me to see which of the three students had the right – as in which student had the one correct solution.  I’ve been working on this area of my teaching for a while now, and fortunately I did not take the bait.

Because had I stepped into the discussion as “teacher as the holder of all things correct” , I would have missed one of the all-time great moments of teaching — the time when the students follow all those discussion norms we’ve worked on and have a debate about which student had the most logical interpretation of this word problem.  I wish I had filmed it!

What did these fourth grade mathematicians decide? Although student one’s  interpretation made sense to him, there was general agreement “4 students and a driver”  did not mean divide by 3. Student two pointed out that bus drivers don’t go inside on field trips, so neither would car drivers; if the students were fourth graders, divide by 4. And student three? Student three is steadfastly holding the position that if the students were high school aged, one of them might be able to drive; therefore, divide by five.

And my question – what to do with the remaining students? Well, we’ll work on that one on another day.

Well, That Was Ugly

I have always thought it important for students to learn to work cooperatively. When I worked in the private sector, we worked as teams or groups – almost never without some kind of interaction with colleagues.  Kids need to know how to work in collaborations, too.  

And so, we set out this week to work in cooperative groups to create “rules” for defining two-dimensional polygons.

I modeled the expected outcome (a chart listing the attributes of the four polygons each group was investigating). I semi-randomly created groups of 4 students with one eye on creating a heterogeneous group. Defined and had students take on group jobs – recorders, materials, etc. And sent the groups on their merry way to focus on the task.

Which failed miserably. Why? Because despite our attention to polite dialogue (one student ended up telling her group to “shut the hell up”), the task of working with others needed to be broken down further. Even the simple – or so I thought – task of choosing one out of the four to record on chart paper was unattainable. I ended up spending much of the period on how to choose a recorder, what the responsibilities might be for the materials manager, etc.

Clearly, this is something my students and I need to work on aggressively. After we re-gathered in our meeting spot to talk about what was not working, I knew we needed to work much more diligently on getting along in a group so that the task (remember that?) actually is completed.

Yes, this is a very egocentric group; many try to have private conversations with me at the same time! But we need to learn how to get along in a group and how to negotiate working under group dynamics.

And that, my friends, was the take-away from that math lesson.



Daily Explore plus Four

The start of school is looming and I am spending some time thinking about how I’d like to change-up some of our learning activities. With all the attention on the Common Core in our District, and with the commitment to Launch-Explore-Summary lesson structures, I am once again tweaking Daily Five for math.

The basics of the philosophy and research behind the Daily Five, whether it is in math or literacy, always are there.  Clearly stated and modeled expectations (10 Steps to Independence), choice, brain research-based lesson structures (thank you Michael Grinder!).  Now, however, we are fitting this into our Launch-Explore-Summary lesson structure.

My newest iteration of the Daily Five for math is the Daily Explore Plus Four.  Using Launch-Explore-Summary, the target lesson follows our District curriculum modules in mathematics.  A focus lesson, approximately 10 minutes long, introduces the day’s math exploration.  Students can then begin to work on that exploration while I monitor who is able to persevere through the problem or activity and which students needs some additional support.

After about 20 minutes of independent work, we will re-gather as a group.  For this focus lesson, there may be an opportunity to share solutions (or partial solutions), talk about what was uncovered in the Explore, or continue with another 10 minute whole group learning activity.

Before dismissing students to work on other math activities, just as we do in the Daily Five for literacy, students will indicate what activities they plan to participate in during remaining independent times. Here is where most students will participate in the ‘plus four’ activities (Strategy Games, Drills and Fact Practice, Technology, Problem Solving).

During the second independent time (another 30-40 minutes), while students work on their chosen independent activity, I will be able to meet with a small group or meet individually with students who struggle with a mathematical concept.  For teachers who are already deep in to the Daily Five in Literacy, think individual conferences with a mathematics focus.

At the end of the math period, we will once again, re-gather as a whole group to summarize what our math goal was – and process whether or not we feel like it was accomplished – and 3 or 4 days of the week I plan to implement a 5-10 minute “Math Talk” based on Sherri Parrish’s Number Talks book.  On the fifth day, I’ll use the time to check on math fact fluency (a requirement for 3rd graders in the Common Core standards).

This is a flipped version of what we’ve traditionally done in math class.  In the past, the planned lesson based on the pacing criteria took about 60 minutes and the intervention/small group instructional block was 30 minutes.  With the knowledge that some students will choose to keep “exploring” during the second independent session, the model has flipped so that launch and explore are accomplished within the first 30 minutes of math.

Why do I think this is a good move? Well, for starters, I know I will get a better use of time by meeting with smaller, focused groups – the same way I see improved focus during individualized reading conferences.  Secondly, by strategically choosing strategy games that align with the standards currently being taught, students will have additional opportunity to practice those skills in a fun way. Analyzing test data will allow me to target and  support additional skill and strategy practice where students need it in the ‘plus four’ as well. The flexibility is endless.

The start of a new school can be exhilarating and frightening all at the same time. I am definitely looking forward to a change-up of our math time; one that I think will be more beneficial to my students.

The New Math

It’s been a long, strange journey from where I started as a teacher to the present. I say this because I’ve just finished a month of work with some wonderfully talented third grade teachers on our District’s Common Core Math curriculum maps. When I think back on the way I used to teach, I’m reminded that the “old days” were not always the “good old days”.

When I started teaching elementary school in 1987, math was a matter of following the workbook pages from page 1 to page n.  One day, kids are doing the addition facts for 12, the next day (having mastered addition and subtraction skills, of course), on to subtraction with renaming in 3 places.  No particular mathematical understanding on the part of the teacher – or the students – was necessary. Just do it.

If there is one thing I’d like to ask a former student, it is “how did you survive?”  There is possibly a support group for my former students who either learned to be mathematicians in spite of me or despite my pedagogical “skill”.

One thing I’ve learned about mathematics over time is that there’s a huge difference between the ability to remember and perform the process and the comprehension of the skill. As frustratingly painful as it can be to build understanding over process, as many times as that fragile understanding is undermined by well-intentioned helpers, it is through understanding that students become mathematics thinkers.

Measuring up to the challenge of teaching mathematics, even in elementary school has gone way beyond the ability to eek a 40-minute lesson out of a teachers’ manual.  Teachers need to understand the math themselves and become empathetic to those who cannot do so. It is a heady challenge for one who was considered a math underachiever.

As we educators unpack new Common Core Mathematics standards and uncover what it is that students really need to know in order to understand the mathematics standards, we are challenged to go beyond our old ways of teaching. It it far more important to reach levels of understanding than it is to use up all the pages in a math text.

And that’s a good thing.

A Different Take on Math Daily Five

I started working on this a couple of years ago when I first was exposed to the Daily Five and Literacy CAFE.  Gail and Joan – the Sisters – have since published a different Math Daily Five. I’ve continued with this version because it seems to work for my students – many are not strong mathematicians so revisiting Power Standards and anticipating the gaps we normally see in number sense and operations makes the most sense.

The structure for teaching the Math Daily Five – using the 10 steps to independence, carving out conferencing times, expectations for student and teacher during work times – all of these are the same. For my students it is important to think in terms of practice with strategy games, math facts (as well as analog clock reading), solving a multi-step problem, and using the available technology for mathematical exploration.

So this year, I’ve begun to compile a list of activities that complement the Massachusetts Common Core framework and continue to allow my students to practice meaningfully while I am working with and conferring with students needing intervention help.

So here is my take on applying the Daily Five.

Daily Five Math Board