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.Advancing 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

Two Great Math Resource Sites

I haven't been able to write much lately. We're in the middle of state testing - again - and now getting ready for that paperwork marathon known as end-of-the-school-year. Not a big fan of paperwork. Does anyone ever really read all that stuff?So I procrastinate. Which sometimes is not as much of a time waste as it sounds.This time, my procrastination(s) proved fruitful.  I've discovered two really useful - in my opinion - websites that I've already started using in math classes with students.Learnzillion is a video treasure of lessons started by a charter school in Washington, DC and recently opened to teachers willing to shared taped lesson snippets.  In addition to being tied directly to Common Core Mathematics Standards, a teacher can sign up for a (FREE!) account and create a playlist of videos. Teachers with more technology available to them that I currently have in my school, or than my students' families have, may find using a playlist with "homework" that confirms whether or not the students has viewed and understood the concept presented powerful. But even without this piece, I thought the video lessons were quite strong. Anyone who uses Lucy Calkins Units of Study will appreciate that the videos begin by addressing students as "mathematicians".Currently the videos support Common Core standards in Grades 3 through 9. And while not all standards are in the video library, there are plenty of visual lessons to help students understand math concepts.Another new to me site is K-5 Math Teaching Resources.  These are not video lessons but they are wonderfully constructed explorations of mathematical concepts. The activities are categorized by grade level, linked to the Common Core Mathematics Standards and, for the most part, are free.  The only for-fee sections appear to be the downloads of math projects, math vocabulary wordwalls, and math journal problems. Each of these downloads are $7 for a single-user PDF file. 

Daily Five Math, Common Core and Investigations

That's right, I am incorporating all three of these things in one classroom.  I've been a fan of the Daily Five and Literacy CAFE for a couple of years. Last year, I started to use the structure of the Daily Five in mathematics.  I did this for a couple of reasons - first and foremost is that I hate segmenting curriculum areas into compartments.  If something works well in one area, it should work well in another.  And it does.Admittedly, I have adapted D5 to suit my own needs as a teacher and the needs of my students.  This year has been a little tricky. The Common Core implementation ALONG SIDE continued attention to the 2004 Mathematics Framework makes me feel like I'm straddling a fairly fast moving river as the water level rises.This week - school vacation week here in Massachusetts - I spent some time getting my bearings again for what universal or landmark games I can rotate in and out of the Daily Five.  Here's what my current list looks like (this is on wikispaces, feel free to join in).

Using Daily Five Math to Support Common Core

This summer was partially spent in aligning Common Core Mathematics curriculum (Massachusetts-style) with the district's universally available materials and laying out a scope and sequence that makes sense vertically and horizontally. As anyone who has looked at the Common Core in depth can attest, it's an on-going process full of starts and stops.A particular challenge to 3rd and 4th grade teachers in this transition year - this year our students will be MCAS-tested on 2004 Curriculum Frameworks - is, while we work to transition there is a great  need to keep a close watch on those standards that have been moved from our grade level. Particularly the standards for which our students will be accountable but were not previously taught to mastery.To my thinking, this is where using the Daily Five in Mathematics makes perfect sense. I can still launch my core lesson - the Common Core-based lesson, have my students work for a period of time on the activity (notice I'm not saying worksheet!), reconvene for a summary discussion and refocus students on continued work using one of four categories: Strategy Games, Facts-Clocks-Money, Problem Solving, or Math Tools.Yes, I know that the Sisters don't use this terminology.  These are the terms that I use because of the mind-blowing task of straddling two curricula while transitioning to full Common Core implementation.As a third grade teacher, I know the bulk of my mathematics intervention - the dance to catch kids up on things that are now receiving more emphasis - will be on number sense and operations (CCM: NBT, OA) . Prior to this year, there was no explicitly spelled out requirement that students master addition and subtraction to 18s in second grade.  We've got some wood-shedding to do here.To keep things sane, and to allow me to meet several small groups, I have a few strategy games that I call "landmarks". In our current multiplication unit, those games include array cards, Marilyn Burn's Circle and Star game, as well as Close to 100 (or 1000) and Collection Card games (Investigations in Number Data and Space) we used to introduce 3-digit addition/subtraction. The teaching challenge is to pick out universal games where "rules" stay the same, but the ante is pushed to make it challenging for all students no matter what their level of mastery.As most students use the four choices to continue to build mathematical concepts and skills, I can meet with small groups of students needing intervention support  in place value, or understanding of addition/subtraction or some other yet undiscovered area of need.How can I do that? Because my students are Independent Learners, I know that when I attend to the small group, the rest of the class is engaged in some meaningful practice and learning. The same Daily Five expectations for Literacy - get started right away, do math the whole time, work quietly, work on stamina - are applied to independent explorations in mathematics.For me, the Daily Five principles applied to the mathematics class make this differentiation possible. My implementation certainly is not perfect, but knowing my students are getting what they need without the teacher being pulled away by monitoring what is going on in other areas of the classroom makes the work ahead possible. And definitely more enjoyable.

Another Look at the Daily Five and Math

How does that saying go? If you're not green and growing, you're rip and rotten. One of the key components of the Daily Five - teaching learners to be independent - is not only appealing, but imperative. After some false starts last year (based on my reading of both the D5 and Cafe books), I attended a Daily Five workshop. And the whole thing is becoming less muddled.Typically, my students don't do well with a million and one different teaching models thrown at them. We already have a Launch-Explore-Summary model in place for our mathematics instruction. There is a great need for small group/individualized math conferencing and intervention, particularly this year when we transition from the Massachusetts 2004/2009 Frameworks to the Massachusetts version of the Common Core Curriculum. There will be gaps, that is certain.To address both the transition to a new curriculum and my students' need for consistency, I have decided to make a go at implementing a Daily Five model during mathematics instruction. What are the five areas going to be? Well, here's what my current thinking is:

• Exploration activities based on the launched mini lesson (a "must" do)
• Strategy Activities. Through the use of games and other constructive activities, students will address computational and conceptual gaps.
• Problem Solving. All of my students, but particularly second language learners need practice in the structure of problem solving situations. This will be a weekly assignment with time built into our schedule for students to discuss how they solved the problem (rigor! perseverance!)
• Basic Fact Games/Practice
• Technology Tool (a chance to use the accompanying programs for our math program OR the interventions found in the Galileo program).

I'll need a minimum of 85 minutes; 90-100 would be better. That means getting back to class and started on our mathematics work right after recess. Hopefully the stamina-building and direct instruction in expectations for independence will give us greater success. On paper it looks do-able, in reality - I am hoping so.

Planning out the block comes next.  Suggestions welcome.

Common Core and Clarity

The Massachusetts Common Core Curriculum implementation starts this coming school year.  As a District Team, we've looked at how the standards are expressed with increased attention to Focus, Coherence, Clarity and Rigor.  In Lowell, we began our look at the new standards by defining exactly what these four terms mean. One idea that has stuck with me as we work on preparing materials for our colleagues is that  the standards are not "intended to be new names for old ways of doing business. They are a call to take the next step...."Where this becomes apparent is in looking at clarity as applied to the Common Core. I've been taking these standards apart since early June now, and each time it amazes me at how clearly each grade levels' responsibilities for student learning is spelled out.As a Third Grade example, our former Frameworks (2000, 2004) 3.N.10 asks students to "Add and subtract (up to four-digit numbers) and multiply (up to t2o-digit numbers by a one-digit number) accurately and efficiently".  This standard corresponds to the Common Core 3.NBT.2, "Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction."For me the new standard is truly packed with specifics. Fluently add should mean that no matter what the strategy, students can perform the operation without hesitation.Using strategies and algorithms based on place value does not mean the standard algorithm -- in fact the standard algorithm does not become specified until later grade levels (Grades 4 & 5).  What this standards tells us - clearly - is that all students need to be able to perform addition and subtraction within the thousands place using relationships - such as friendly number strategies - or using a process reliant on place value (decomposing and then adding partial sums for instance).While we may have students who are ready to record these problems using a standard algorithm, unless the student thoroughly understands and can explain the use of the standard algorithm - thereby demonstrating that the student is ready to use a standard algorithm - the student should use some other process for computation. Blindly applying a process without the knowledge of the what and why is no longer accepted.To me, this is refreshing - a recognition that understanding and comprehending a mathematical topic with depth, and rigor is of importance.  The wording itself of the standard is clear and direct.As we explore the Common Core, we discover that there is much more clarity about the level, or depth of thinking, to which we need to bring our students. And that is a good thing.

Fasten Your Seatbelts.....

It's going to be a bumpy night." I love this quote from "All About Eve"; and coming straight from Bette Davis' mouth - well you can imagine the delivery.The more thinking is done about the implementation of the new mathematics curriculum frameworks - the Common Core - the more it becomes apparent that this is going to be a major, that is MAJOR, implementation.Looking at it from a third grade teacher perspective - students will come to third grade with near mastery, if not mastery, of place value AND mastery (that is spelled out) of addition and subtraction facts --- all of them.  Historically, that has not been the case; students coming to third grade often have a shaky grasp of place value and most definitely we spend lots of the beginning of the year on addition & subtraction facts. Honestly, there are some children who do not leave THIRD grade having memorized/mastered these facts.  That's a post for another day though.What this means to me is that, for the next year - or possibly two - we will straddle two grade levels of work. It is clear what the expectations of students leaving third grade and going to fourth are. (Click here to download the PDF or Word version); but there will also be some catching up to do for second graders coming in to third this September.  I'm sure other teachers at grade levels above and below my own grade level will feel the same.And to add to the pressure, by 2014 the Spring testing will have completely transitioned to the new Common Core standards. Here's a link to DESE's plan to transition test items.  In other words, transition quickly and get working on mastery of the new standards.Will we be ready - I sure hope so. Because not only will there be new standards to be responsible for, the test results will be linked to my own evaluation as a teacher.I have a feeling that fastening my seatbelt isn't going to be much help here.

The Uncommon Common Core

Our District has a committee is working on unpacking the Common Core for Pre-K to 8 this summer. I volunteered - begged really - to do this and, lucky for me, I am part of the committee.Even with all of the expertise on this committee, there are struggles as we dig through seemingly simple standards only to discover that it's more complicated than it appears from the surface.  What will be important at one grade level may not be emphasized (notice I didn't say it wouldn't be important) at the next -- I have to say that the way these standards are built shows much thoughtfulness into the process of becoming mathematically literate.Here are some of the pieces that I think are strong:

• The standards are very specific. It is quite clear what skills and concepts each grade level will be responsible for.
• There is a place for fluency with computation and it is spelled out explicitly.
• Topics are explored in depth and students are expected to demonstrate understanding. Rote processes are not going to be enough; if a student is using the standard algorithm (for example), then that students needs to be able to explain how and why that algorithm works.

It is gratifying to see this committee complete the shift begun almost 10 years ago - the shift to thinking in terms of "standards" and not what page of a text is covered.  Finally a curriculum guide that recognizes the expertise of the teacher in choosing the appropriate materials to use when teaching -- which doesn't mean nothing is provided for those who want that support; but it is freeing for those of us who have felt hindered by a particular program or product being used district-wide.

It is going to be a massive undertaking to update guides, update assessments, and provide support for teachers who haven't had the opportunity to look at these standards in depth.  It is an uncommon opportunity.

Circle and Stars

I don't remember when I first came across this game -- I suspect it was during a Math Solutions Summer workshop week. For certain, it is included in several of the multiplication resources Math Solutions publishes, including the Third Grade Month-by-Month resource.It is empowering to find a game that children can just pick up and play. Circle and Star uses only a dice and a piece of scrap paper. Sometimes I get creative/fancy and use some wooden cubes that I have numbered from 5 to 10 so when the children play the game they'll have some larger numbers to work with.So here's what we do:1.  Roll the die once. The number that comes up is the number of circles you need to draw on your scrap paper.2. Roll the die a second time (or alternatively, roll the 5-10 die). The number that comes up is the number of stars to be drawn in  each circle.3. Write the resulting multiplication fact as number of circles times number of stars in each circle.  Compute the product.When we begin playing this game, I have students write the resulting multiplication fact 3 different ways:

NOTE: C = number of circles, S = number of stars

C groups of S equals ProductC S's = product (use the number words)C x S = Product

The students always are looking for this game on our Daily Five Math board. We both like it - the kids because it's fun, and I like it as a way to keep students practicing those important multiplication facts.

The Infamous 3N8

It is my -- and their -- nemesis:

3.N.8 Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money.

My students can perform computation into the thousands. We are pretty darn good at it. But toss a word/story problem in their direction and everything falls apart.  Why can't these kids figure out an appropriate equation and operation from the words? It is really quite a pain.Remembering the challenge of second language learners -- and the nuance of the English language -- partially explains why these kids have such a tough time deciding what operation and equation makes sense. I've resisted the urge to teach key wording because it doesn't always fit the situation. And the standardized testing we foist on these kids often doesn't follow the "formula." Besides, I want them to think and to know what they need to find a solution.So this week, I've started applying a teaching strategy we used to teach in another school for visualizing. Explicitly teaching students to visualize seems to me like the only way they are ever going to figure out if the answer - the result - should grow or shrink. Which I hope will lead the students to a reasonable equation for that computation they seem to do so well. It just so happens that the students are not very strong visualizers when it comes to reading either.What I do know is that unless I can convince the students to thoughtfully consider the action in a story problem, to visualize what the situation is, all the computational skill that they have acquired will mean next to nothing.

Daily Five and Math

This year I've made an attempt to follow the "Sisters" in implementing the Daily Five and the Literacy Cafe. So far, I'm happy with what is starting to take shape. Conferencing is more focused. Tracking those kids who need more than a once a month reading conference, keeping kids accountable through the Literacy Cafe Menu, all are clearly going to be helpful when presenting a case at an RTI meeting.Now if the Daily Five can help me with getting to those students who need some extra one-to-one support, maybe it can help with meeting the needs of students in mathematics.  The Sisters are way ahead of me on this one -- the Math Daily Five provides a way to organize "guided mathematics".  In my classroom, the five categories that I'm playing with are: Math Fact Drills, Landmark Math Games, Exploring Data, Problem Solving, and Featured Activity.  The math fact activities are games - electronic and otherwise - that provide fluency practice in addition, subtraction, multiplication and division.  Landmark Games are the "go to" games we teach throughout our third grade Investigations in Number, Data, and Space units and include games like "Close to 100/1000", "Capture on a 300 Chart" and "Fraction Cookies". Exploring Data is a new category -- our school has identified interpreting, representing, and constructing data as a focus for this year. Activities in these categories will provide students with activities for practice. I want my students to solve problems in context and I have been providing a problem for students to solve and later share solutions in this category. Finally, in the Featured Activity category, we will work on explorations that accompany the launches for the daily Investigations lesson.I want to keep the launches down to about 15 minutes - whether it's a model launch or a discussion. This isn't easy for me. But by limiting my talk, and getting kids actively involved in activities while I meet with smaller needs-based groups, we should be able to make some progress toward students meeting Grade 3 Math Standards.Will it be noisy? I'm sure it will be. Just like the Daily Five and Literacy Cafe, I'll need to build students' stamina for staying on task. But in the end it should be worth the time it will take - hopefully we can work smarter not longer.

Asking Questions, Forming Equations

Some part of the ARRA money allocated to the Lowell Schools is being used to give teachers time to look at assessments and collect data about how our students best learn.  Grade level teams and cross-grade level data teams have formed since late summer all with the purpose of methodically looking at our assessment data and making decision about what to do next.  We use the ORID protocols to analyze our data while the mechanism for assessment of our own teaching is the process of Learning Walks.My grade level, Grade 3, has been contemplating a mathematics inquiry that will help us improve our instruction and, ultimately our students' learnings.  The development of the question has taken us in a circuitous route through methods for comprehending a particular operational skill (multiplication) to the question we've agreed upon this morning: What does best practice look like when we are teaching our students to generate or identify a correctly constructed equation matching a word problem situation.We've noticed that our students, particularly our ELLs, meet the standards for whole number computation.  However, many students, regardless of whether or not they are ELLs or native speakers, cannot for the life of them select a reasonable equation to match the word or story problem.  This is critical mass for our kids -- the bulk of the MCAS testing that will take place in the Spring requires students to decipher story problems in just this way.Those of us who have a strong background in Constructivism dislike the very idea of teaching students "key" phrases:  for example, in all means to use an addition equation. Personally I feel that there are other ways to get kids to comprehend the problem and generate equations from their understandings.  I want my students to visualize the events in a story and be able to logically create an equation that will get them to an answer.But what about of kids who have so many language issues that visualizing is not a strength? Is there another, better way? The data analysis tells us there has to be - at least with the students we are currently working with. As my colleagues and I work through this cycle of inquiry, we will be peeling away our preconceptions; this can be pretty scary.Our next meeting will begin the process of researching what might work with our students, and maybe, we'll invent something new.  Now that would be something!

WNYC - Radiolab: Numbers (October 09, 2009)

WNYC - Radiolab: Numbers (October 09, 2009).This broadcast from PRI's Radio Lab on number is pretty interesting if you can stay with it.  If the interviewees are to be believed, I should have taken that Calculus course I failed in high school sometime around age 2.  That's right. The researchers interviewed assert that babies are logarithmic and they cite several sources and experiments to try with 2-year olds. (Sorry, I don't have a toddler so I can't prove or disprove the theory with the pennies.)How does this impact teaching? I have no idea; I'm still trying to wrap my mind around the South American people who have no counting system or number above 5!Thanks to Adrien and our discussions about mathematics -- yeah, we definitely are America's fun couple -- for the heads up.

Two Lessons From Master Teachers

Every year we scour our standardized test scores wondering what we can do so that our students look as good on paper as they appear when we are assessing them day-to-day.  I hate that standardized testing, in this case MCAS, is considered the measure for success.  I think of some of my colleagues who took the National Teacher's Exam -- does that test still exist -- a grueling all-day summative paper assessment by which prospective teachers were judged to be worthy or unworthy of hiring.  People I admired performed poorly on this test -- the single measure used to judge employability.  In the same way, I dislike the high-stakes tests that judge our students and judge our teaching effectiveness. Should one measure be the end-all of whether or not students are learning?Off of the soapbox now, the topic I'm considering is what magical intersection of ideas and conditions will help my students acquire mathematics?  And that's what this section of the blog is about.Once upon a time - at least 15 years ago -- I was a participant in a summer course designed by Math Solutions and developed by Marilyn Burns.  Marilyn Burns is not only a master mathematician, but she is a master teacher -- and unlike other experts/consultants in education, she puts her money where her mouth is: she actually teaches the lessons using the methods she advocates by volunteering in public schools in her area of California.  Right there she had my respect -- no theoretical ivory tower.One of the presenters said something sage that has stayed with me all these years.  When we are shifting the teaching of mathematics, or any topic for that matter, to a more constructive, meaning-based model, it can take up to 5 years for our students to "get it".  The presenter, whose name has escaped me, told how her school in Texas had adopted using replacement units for basal math texts -- unit based on deepening students' comprehension of mathematics. And while the test scores (remember them?) were disappointing at first, after several years, there was a delightful, vindicative jump showing that students had not only acquired math concepts, but were now flexible in applying them.Isn't that what we h0pe for? The current frenzy of testing and accountability of teachers for what students can and cannot show in a single-shot standardized high-stakes test, doesn't allow us much time for developing a program in a methodical way.  Lesson #1:  Things take time.The second lesson was an idea planted in my brain by a brilliant and gifted mathematician, Andrew Chen of Edutron.  I had the privilege of being a student in one of Andrew's Intensive Immersion Institutes, a mathematics class to strengthen/clarify/stretch mathematical thinking for teachers.  Andrew's words, that our students are just as bright as their suburban and high-achieving counterparts, were like a breath of fresh air.  Generally urban teachers are told either outright or through insinuation, that they can't be as good as counterparts in less troubled teaching environments -- or the students' test scores would be higher (how insidious is that!).  Here was an MIT mathematician telling us that our students (and teachers) can achieve much, but sometimes other things (socio-economic ills for example), get in the way.  Lesson #2: Don't give up on students or yourself.Both of these ideas have been in the back of my mind as I've been working with our Math Resource Teacher and Coach to tweak the third grade teaching resources this year.  As we develop materials that work for our kids, we'll use this space to document some of the things we've learned about teaching mathematics in an urban school system.