Friday, December 9, 2016

Let Them Make Mistakes

One of the pitfalls we find ourselves falling into as math teachers (I use the first person plural here because I have done this and I see others doing it too) is we facilitate our instruction with a goal that everyone gets it right.

It is easy to forget that the Everyday Math lessons we teach are structured in a way that allows and even encourages children to make mistakes.  In any lesson on any given day, we should expect students to make mistakes while they work, and especially when they think aloud.

Let's look at this in terms of the parts of a lesson.

Warm-up.

For the Warm-Up portion of Everyday Math lessons, Mental Math and Fluency is a check-in opportunity.  This is not a time to make sure all students get it; it is a time to check for mastery. That's why there are three levels of difficulty for the mental math segment of every lesson.  If most students appear to struggle with the first level, don't go onto the next.  Mental math is a chance for you to have a snapshot of your students' levels of math fluency before you get into the bulk of the lesson.  What you see in mental math might impact how you facilitate the rest of your lesson.  Mental Math is not the time to clear up misconceptions, or to keep providing more examples until everyone gets it right.  "What do you see?" when flashing a Quick Look card, or "How do you see that?" are great questions to ask that will elicit formative information.  But asking every student to share a strategy, or making sure every student gets it right will take too long and disengage students.

Mental Math.

Mental math is your students' opportunity to get their feet wet, so let them.  They might make mistakes.  Give them opportunities to make those mistakes, and then let them talk to each other about their mistakes.   The Teacher's Lesson Guide gives you a little suggested script to follow up after the Math Message. Notice it never says, Keep quizzing children until everyone gets it right.  Instead, it usually offers a differentiation strategy with suggestions for scaffolding.  Your scaffolds should not be "hints," but rather sentence structures to help them grasp a strategy, or visual aides to help them understand how to use a tool.  We still want to give them opportunities to figure out the problem for themselves (and to occasionally make mistakes, even with scaffolds).

Math Journal work.

They can make mistakes here too!  But now their mistakes are visible on paper.  The journal work is an excellent opportunity for students to work together, check each other's work, and compare strategies.  Two partners have different answers?  Wonderful!  Have them see if they can come to a consensus.  The "growth mindset" in math requires that students make mistakes, and do it fairly often.  Every time a student truly discovers the root of his or her mistake, that student has gained significant mathematical understanding.

Practice.

Mistakes are still encouraged here, while playing a game or working on math boxes. Here, mistakes are likely smaller and quickly resolved, but they still can and do happen.  This is where we want students to be able to catch and correct their own mistakes, either on their own or with the help of a partner.  If there are a lot of mistakes at this point of the lesson, that informs you that some extra practice or re-teaching may be necessary.

You may find that persistently allowing students to make mistakes actually saves you instruction time, because you are not so busy going from child to child making sure every student has gotten every part of the problem right, or demonstrated every strategy correctly.  Sometimes, that can postpone the entire class from proceeding to the next part of the lesson.  Instead, use those mistakes as learning opportunities, turn-and-talk topics, group consensus opportunities, and formative evaluation of their understanding for future instructional decisions.


Thursday, December 1, 2016

Whole Class Instruction: Know When To Say When

Much of our instructional time in math lessons is taken up with small group and partner work, which allows students to explore, experiment, debate and take risks with their mathematical thinking.  Whole group instruction is minimal in our Everyday Math lessons, but when it happens, there are some things to keep in mind.

Recently in a fourth grade classroom and I saw a masterful decision take place on the part of the teacher.  Students had been working on a task, and it came time to share out.  A student volunteered to share his strategy for dividing three 8" pizzas among two friends evenly.

"Well.. basically what I did was.. I started by taking the three pizzas, and then I.. well, they're each 8 inches in diameter but I don't think that really matters for this problem, but I thought I would mention that, and then I, um.. I cut the pizzas in half because then I would have a number of parts of pizza that I could distribute evenly for everybody, and then I had four pizzas instead of two, or rather four half pizzas... Wait... I think I made a mistake..."

The teacher then intervened.  Instead of asking the student to re-think his strategy, or to start from the beginning, or asking if there were any other students who could help this student with his thinking, or asking if there were any other students who had a different strategy, the teacher instead put a halt to the share-out and asked the rest of the class to turn and talk with a partner to share strategies.  After a couple minutes, students had another opportunity to share, and lo and behold:

"We both cut the three pizzas in half so there were six halves, which is also divisible by two, so there would be three halves for each person."

The decision to intervene in the initial student's share-out was masterful because of the timing of the intervention.  She realized the student had not fully thought out his conclusion, or was not yet confident enough in his strategy to present it to the class.  Sure enough, by the time the student had said, "Well.. basically what I did was.." he had lost most of his peers' attention.  Eyes started turning away, pencils were being picked up, body language across the room said, almost universally, "We're not paying attention anymore."

The student's hesitation alone had lost the confidence in his peers, and many had decided it was not worth their time to listen.  The class had been well trained not to be distracting when distracted themselves, so there was little noise or even whispering going on, but it was clear very few, if anyone, was listening intently to the student share out his temporarily confused thought process.

The teacher had masterfully gauged student engagement and transitioned to an interactive partner review of the problem.  We all know what would likely have come next if she had allowed the student to continue, or if she had called on another student to follow up.  A visible or audible distraction from somewhere in the room, perhaps a spoken redirection or two from the teacher, and a prolonged share-out with even fewer attentive students.   Instead, students turned to a partner and rehearsed their thinking out loud together, interactively.  When it came time for a volunteer to share out, the result was clear, precise and succinct.

We always want to elicit mathematical thinking from our students, and we have a tendency to want to hear multiple students share a variety strategies all in a quick whole group share-out, so that little lightbulbs might turn on around the room as new understandings are shared and discovered by all. Unfortunately, it is a challenge for elementary and middle school aged children, and even adults sometimes, to articulate mathematical thinking on the spot.  And listening to someone think out loud is not often that engaging, especially for those of us who are not primarily auditory learners.  If what we hear doesn't make instant sense, we shut down.

So a couple of important lessons can be learned from this that pertain to whole-group instruction.

Firstly, student attention is short-lived in a whole group setting unless the topic is purely engaging. Even though a teacher might not be lecturing, sitting and listening while student after student attempts to articulate a strategy or defend an answer to a problem will not yield a great deal of new understanding.  Moreover, it will often lead to distracted students and sometimes misbehavior. Masterful teaching moves I have seen include expertly timed turn-and-talks, whole class physical transition to a new location (such as moving to the floor from their desks or vice versa), and transitioning to the next stage of a lesson.  If students are not comprehending, they are not going to invest their energy in listening.  If they are bored, they are going to struggle to keep focused. Something has to change.  No matter how animated and excited we get in the front of the room, it still often feels like a losing battle:

"Oh! Great thinking!  Did everybody hear what Timmy just said?  Timmy can you say that again so everybody can hear?  Ok, everybody, listen to Timmy's awesome strategy.. Suzie, you too.. and Billy, that means you.. Ok Timmy, go ahead.. but wait until everybody is quiet..."  

Ugh.  Not fun for you, not fun for them.  Sometimes a student just hits the nail on the head and you want everyone to absorb the learning opportunity, but if it took too long to elicit that sweet morsel of demonstrated knowledge, beware.  We might expend less energy typing it up and inserting it into 23 fortune cookies than we would trying to get every student to devote his or her complete attention to it.

Another lesson to be learned about whole group instruction involves giving directions.  In problem solving tasks, directions are often complex and require considerable effort on the part of students (and sometimes teachers) to understand.  It becomes very important in those cases for the teacher to be the one to read or deliver instructions slowly and carefully, with all the right intended emphases.  We often want to give students opportunities to read aloud and take ownership, but instructions to problem solving tasks are not appropriate for those opportunities.  Even some of the best student readers still need work on their delivery and might not execute the right emphasis.  Some read very fast, others read very quietly, others read with a monotone, still others insert careful but perhaps awkward space between words.  All of these can make it difficult for their peers to understand, and thus result in students abandoning the effort of paying attention.  "Two.. brothers.. go.. to.. lunch.. and.. share.. three.. pizzas.. equally.. how.. much.. pizza.. does.. each.. brother.. get.." By the fifth word, chances are wandering eyes and body language will begin to present visible evidence that students are not eagerly anticipating the task.  A confident adult reader is important when giving instructions and sharing important details for mathematics problem solving tasks.

Whole class instruction can be engaging, and it can be effective.  It is important to be keenly aware of student engagement and to be practice teaching moves that maintain engagement or re-engage students. Then your energy can be more devoted to listening to what students are saying, gauging student understanding, and confidently moving forward with facilitation of learning.  Knowing when to say when will keep whole class instruction limited, and leave more time for partner and group work, as well as those all-important games and hands-on activities.

Thursday, October 13, 2016

Assessing for Understanding

So by now the school year is well underway and you are beginning to learn a lot about the mathematicians in your classes.  As we gather evidence that will eventually serve to provide a grade on the trimester report card, I've had a few questions regarding how to collect that evidence, and how we are scoring assessments this year.

What do I do if the student got it wrong, but I know they can get it right?
You'll see in the email response below that this will be a common scenario.  It's important to remember that we are always formatively assessing our students.  "Formative assessment" is an ongoing process that occurs constantly as you teach your lessons, observe students at work and the discourse they share, and review completed assignments.  Always be looking for evidence of understanding.  If a student makes an error in their journal, or even on an assessment, you can always give them more opportunities to show they really get it.  If it is a careless error, the student may simply need to see the error he or she made, and be given the opportunity to fix it.  If it is an error that is a result of a lack of understanding, the student may need re-teaching.  It might come back in a future lesson (see the spiral!), or you might be able to provide opportunities to revisit the concept and re-assess for understanding.

The items on the test are either correct or incorrect and cannot be given partial credit.  This is true.  Even if there are six answers to #7 (as in, there is a 7a,7b,7c,7d,7e, and a 7f), they ALL need to be correct in order for the item to be marked correct.  Why is this?  Here's how I answered this in a recent email:

If you think a student juuuust missed getting them all [the parts of the question] correct with a careless error, give him or her the chance to look over their work and make the fix.. If he or she can find and fix the error, then adjust the score to a 3.  The other option is to find more evidence elsewhere in the unit or upcoming unit to determine if the student is achieving proficiency or developing.  You can use items on the cumulative assessments for this, the ACIs, alternative test items, or other examples.  (The spiral in the TLG might help you locate where the specific standard is assessed again in the book.)

The more I have learned about scoring assessments, the more I lean toward this kind of scoring.  If the item has 4 parts, EM has essentially designed it that way to assess proficiency.  Students are not proficient until they can get all those right.  And if they don't but you feel they really should have gotten all the answers right, you can give students chances to provide you with that evidence.

Later, we got into discussing specifics.  The items in question were a 5th grade order of operations and grouping problem and a volume-of-a-rectangular-prism problem.  Should students be required to evaluate all for expressions correctly, and then answer the volume problem with the correct units of measurement (cubic centimeters)?  

For #3, the standard is 5.OA.1, "evaluate expressions that contain grouping symbols."  There are four expressions to evaluate, but andb go together and c and go together as they use the same numbers with parentheses in different places.   So if a student got a wrong but b right, that likely demonstrates a misunderstanding of what parentheses mean, as the answer to b would be the same even without the grouping symbols.  The four separate parts to the item help to ensure that the student understands the standard.  5.OA.1 is listed on page 8 (the spiral page) of the Teacher's Lesson Guide as a mastery expectation, so with this assessment item we want to make sure the student gets it.

With units of measurement pertaining to volume of 3D figures, I have mixed feelings!  Yes, it is important that they learn how to compute volume, but we also want them to understand how and why lxwxh=V.  Otherwise, they are just memorizing a formula which is susceptible to becoming confused with area and/or perimeter as they progress down the geometry/ measurement content strands... If the l,w, and h measurements are in cm, then the answer must be in cubic cm.  NOW... That's tough for 5th graders.  So the approach I like is to take those answers that are correct with the incorrect or missing unit of measurement, and bring them back to the student.  "Did you forget something?" ...or, "Is your answer just '40,' or is it '40 somethings...?"  Give the student a chance to demonstrate the unit of measurement.  If the student shrugs his or her shoulders and says "I don't get it, my answer is 40.." then they do not grasp how or why they are using that formula.  The CCSS language is "recognize volume as an attribute of solid figures and understand concepts of volume measurement."  But again, this is hard for 5th grade, so that's why I suggest giving students every opportunity to grasp the concept... You can always re-teach, and give students another chance to demonstrate proficiency.  

Also, there is certainly some subjectivity to scoring these items.  You know your students more and more as the weeks go on, and you will know who needs re-teaching and who doesn't.  The one thing I recommend as you make these judgments, though, is to keep looking for evidence of understanding when you score assessments.  And the more opportunities they have to explore and discover these concepts during the units (to problem solve collaboratively and independently by trial and error and with manipulatives), the more they will achieve understanding.

Lastly, we discussed what can be done in the event we want to find additional evidence to show a student is achieving the standard when the initial assessment item did not:  

Sometimes there might be a domain at the end of a trimester that has minimal assessment items represented... You can certainly base a student's domain grade on more than the two or three assessment items they attempted pertaining to that domain.  Use the items in the cumulative assessment if you like, or the ACIs, or alternative assessments to find more evidence.  I'm always happy to help with this too (and even adjust cover pages if necessary).

More thoughts on all this?  Let me know!

Wednesday, May 4, 2016

Don't Panic About Pacing

As we quickly shift into the home stretch of the school year, there is considerable anxiety regarding pacing.  Will my class finish all the lessons and units before the end of the year?

Despite the new Everyday Math units being somewhat more manageable in terms of how many lessons are taught and how much goes into each lesson, finishing out the year having covered every lesson is clearly a challenge for many.  This time of year, the lessons are getting more complex and dense, and with all the field trips, fire drills, assemblies and celebrations scheduled, it is easy to fall behind the pacing guides.

Here are a few important things to keep in mind that might help with pacing the rest of this year and next year too.  Before I get to the bullets, though, remember that for most of us, this year is the very first year of a program that is 80% new, so we are still in our learning phase.


  • The unit assessments are long, and are taking multiple days to complete in some cases.  If you feel your students need a little more time than one lesson period to finish the unit assessment, that is understandable.  But think of the unit assessment as a formative tool in addition to a summative one.  If the assessment is taking a long time, it may be best to prioritize items and cut the assessment short.  Learning is most important, and if students are not able to complete every part of an assessment, that is ok.  Remember there are extra practice and readiness activities in the upcoming lessons you can rely on to provide a little extra support for students who might not have been able to demonstrate mastery in certain domains of prior units.  Moving on to the next unit may be more important for your students than every student finishing the assessment.  For 2016/2017, we are looking at abbreviating the unit assessments some in order to focus more on assessing content standards, so the assessment process will hopefully become more efficient in time.  
  • Math boxes are an important part of every lesson, but they are intended to take up no more than 15 minutes of time.  If students are taking longer than 15 minutes to finish math boxes, they are either struggling with the material, which is important formative information for you to know, or they are distracted.  If students are struggling to finish the math boxes, it is ok to modify the assignment, to take one or two of them off their plate. If students are distracted, that is a behavior/disciplinary issue, and should be addressed as such.    
  • Don't be afraid to use a timer when you teach Everyday Math lessons.  When I teach, the danger lies in the warm-up.  There always seem to be so many teachable moments!  If you look in the Teacher's Lesson Guide, most Warm Ups (Mental Math and Fluency) are designed to take only 5 minutes.  These are also formative assessments.  The first part of the lesson is not intended for discussion or correcting students' thinking.  That's what the Math Message is for.  The Warm Up is a quick gauge of where your students are at before you start the lesson, and an opportunity for students to get their brains into a math mindset.  No real teaching is happening. Have them write their answers on their slates and move on.  It is ok, to tell them the answer, and answer a question or two, but beyond that, the Warm Up is not a time for justifying answers, clearing up major misconceptions, or having teachable moments.  It is hard, I know!  But for the lesson to be most effective, save the great mathematical discussions and teachable moments for the Math Message and the rest of the Focus portion of the lesson. 
  • Remember that the math you teach right now is foundational prerequisite knowledge for the math they will be learning later.  When tough decisions need to be made regarding pacing, work with your team to see what strategies your colleagues might be employing, and contact your friendly Math Strategist to help you map out your next lessons and units.  You are working hard to give your students the most meaningful math experience possible to prepare them for future learning and problem solving, so you don't want to misdirect those efforts. Together with your colleagues, you can carve a sensible path forward.
  • Next year your hard work will pay off; not only will your students go to their next year's teachers with a richer mathematical background, but your students will come to you as more capable learners as well.  And you will have a year (or two, in the case of grades K-2) of teaching this new program under your belt.  So have faith that good things are happening, and they are only getting better next year.
This has been (and still is!) a great first year with all grades (K-6) teaching Everyday Math 4.  I am very much looking forward to next year when we can focus even more on deeper understanding of concepts and mathematical thinking.  If your pacing hasn't been perfect this year, it will get better next year.  We'll all be working hard to make that happen.  While it is not necessarily reasonable to expect everyone to be teaching the same lesson on the very same day, it is helpful for teams to be able to collaborate when grade level classrooms are within a few days of each other in the unit.  This way, Open Response lessons can be taught simultaneously.  Wait!  This should be another bullet...
  • Teach Open Response lessons on the same day as your grade level colleagues!  You can teach these lessons out of order if you are not exactly on the same page as your teammates in order to coordinate the days when you will teach Open Response lessons.  The benefit to this is grand. You can teach day 1 of the lesson, and then bring student work with you to review with your colleagues between day 1 and day 2.  Then you collaborate to determine what day 2 of your O.R. lesson will look like.  This helps you to see a wider range of student work, which will not only help you see trends of confusion and misconceptions, but it will also help you determine what to look for when you are scoring Open Response assessments after odd numbered units.  
I hope this has been a helpful bit of information regarding pacing.  Please contact me if you would like to discuss any issues with pacing as they arise.  

Monday, April 4, 2016

Spring Classroom Reflections: How Great Visuals Help

For the last couple of months, I have been taking note of the excellent visuals I see on classroom walls that help students with their mathematical routines.

I've always had mixed feelings about math visuals.. In middle school, when the phenomenon of math anxiety really begins to set in for some, the last thing I ever wanted to do was scare my students every time they came in my classroom with equations and formulae all over the walls.  I'm a math teacher, someone who genuinely sees beauty in mathematics, and a room full of numbers sounds kind of nauseating even to me.  But over the years I have grown to appreciate carefully planned visuals that truly help students with learning.  I've learned that what those visuals are and how they are displayed is just as important as how they are utilized.



For example, some of the posters that I see in first and second grade classrooms display strategies for subtraction.  They are clearly visible and attractive, but most importantly, I see teachers referring to them.  A poster on the wall is just a poster on the wall until it is demonstrated and modelled as a tool that can be utilized by students at any time.




Word walls are another thing that can be useful if displayed and utilized intentionally.  Otherwise, it is just a group of words on the wall that might as well be in a foreign language.  In the Everyday Math lessons, unit vocabulary is listed in the Mathematical Background section of the Teacher's Lesson Guide, located just before the first lesson of each unit.  Building a word wall and evolving it with each unit is a great practice, but actually referring to it and encouraging students to refer to it is best.  Wall space is precious in most classrooms I visit, and one wouldn't want that precious space to go un-utilized. 

Many of the excellent visuals I see when I visit classrooms are interdisciplinary.  Most notably, posters and wall art that displays think-stems and sentence starters for writing exercises are perfectly appropriate for students who need help expressing their mathematical thinking on paper.  This is one of our students' biggest challenges, and having those visual aids on the wall can be extremely helpful to them.  Developing confidence in writing is a big deal, and I have a feeling it is going to be a major source of collaboration in RSU 5 among the strategists in both literacy and math in the future.






Both science and social studies displays can include mathematical components as well.  I have seen planetary displays (miles and kilometers), timelines (years, positive and negative numbers), and thermometers (also positive and negative numbers) displayed in classrooms



Most of the representations of classroom visuals I chose to include came from RSU 5 classrooms, and most of them are hand-made.  There are some nice math posters you can buy online, but you never know if it will pertain to exactly what you want on your wall.  Nice teacher-made wall art takes time and effort, but it can be used year after year, and can even be laminated.  Also, Every EM4 teacher kit came with a series of posters that display the eight Standards for Mathematical Practice, along with EM4's aligned Goals for Mathematical Practice.  These can be displayed all at once or rotated in and out to focus on specific practices.  The key, though, as with any display, is to refer to them often and model their use.  



It is great to see such carefully thought-out and smartly displayed mathematical wall displays in so many places.  I will keep taking more pictures and posting them as they are all ideas worth sharing.

Wednesday, February 3, 2016

Subtraction Strategies in grades 1 and 2, and how they impact learning in the upper elementary grades.

Subtraction is the first nearly universal struggle math learners stumble upon in the early elementary years, before division, fractions, and eventually algebra.  It doesn't work like addition, it is not commutative (i.e. the turn-around rule does not work in subtraction), the answer is called the "difference" (confusing word in math), and we use about ten different words to represent it (minus, take away, subtract, minuend/subtrahend, how many less, decreased by, how many left over, how many fewer,  how many more, what is the difference, etc!).

By the time students reach third grade, they have been introduced to a variety of different subtraction strategies (see grade 2, unit 3 for a list), but as the authors of the Everyday Math units tell us, we should not expect every student to be able to master every subtraction strategy.  Students are introduced to subtraction in kindergarten, and practice only basic subtraction in first grade.  By the end of second grade, they should have tried all the strategies introduced, and they likely will have latched onto a couple.  In third grade, we really want them to be considering strategies to use beyond counting on their fingers.

Third grade involves a lot of subtraction practice in units 2 and 3, where your students should be "building their understanding of place value to develop methods for subtracting 2- and 3-digit numbers." (<-- from the Mathematical Background: Content section in the grade 3 TLG)  Here, expand-and-trade takes front and center as a major algorithm for students to practice and use.  This is an important piece of their understanding for future computation and problem solving, and really tests their understanding of place value.

It is not intended to be an algorithm they latch onto for life; expand-and-trade is like training wheels for the more traditional vertical subtraction most adults are familiar with.  Parents may see their child struggle with expand-and-trade, and not have the faintest idea how to help them.  "That's not how I learned it," they may say to themselves, or express to you in a frustrated note attached to a homework assignment.  Unfortunately, the temptation is to just go ahead and teach the traditional vertical subtraction method instead, because it makes more sense to the adult.  But do what you can to prevent this.  Expand-and-trade is designed to slow down the steps and deconstruct the numbers so students can see precisely when they are subtracting ones, tens and hundreds.  When they eventually transition to more efficient methods, they are well-versed in what each step of subtraction represents, and are better equipped to catch their own errors when they happen and know when their answers are in the ballpark or not.  In short, they become more confident with their subtraction.

It is the confidence that we are aiming at, because that confidence carries over to the rest of their math learning.  If they can add and subtract with confidence, then learning how to multiply and divide will not produce as much anxiety.  When they can multiply and divide with confidence, fractions are less confusing and intimidating.

Subtracting numbers is one of the most important things your students will learn how to do while in first, second and third grade.  The more opportunities your students have to work on subtraction in the early years, the better they will do in the later years.  And your fourth, fifth and sixth grade teaching colleagues will really notice a difference.

Here is a link to the VLC with some resources related to subtraction:

Subtraction Resources on the VLC

Lastly, don't forget to access the Grade Level Resources option toward the bottom of the grey menu when you log onto ConnectED.  There are lots of tutorial videos and visual aides and other resources in this section that can help you provide subtraction practice opportunities for your students.  Contact me if you need help accessing these tools.

Tuesday, February 2, 2016

What's Happening in Classrooms: Fantastic Turn-and -Talks

Recently I have visited a lot of math lessons where turn-and-talks are frequent and intentional, and I want us to celebrate and encourage that practice.

Teaching math with intentional student discourse involves taking risks, but they are risks worth taking..  These are some of these risks and ways to overcome them:

It might be disruptive and might not work.  When you ask your students to talk to each other during a lesson, you run the risk of creating a noisy, disruptive environment.   For this reason, we need to have students practice a specific protocol for turn-and-talks.  Make sure they are using indoor voices.  It is also helpful to have explicit instructions for what to discuss, and make sure they only last a minute or so.  I encourage everyone to have students practice math turn-and-talks, because math is something students don't always feel comfortable talking about.  You could say, for example:

OK, friends, let's practice a turn-and-talk.  Here's what I would like you to discuss.  13 plus 12.  What is the answer, and what are two different ways to show or prove your answer is correct.  Ready? OK, turn and talk.

You might wish to add extra protocols, like making sure each partner has a chance to talk.

OK, one, two, three, eyes on me.  (Wait for all to respond stop talking).. Now I would like you to turn-and-talk again, just to make sure both partners had a chance to speak.  Turn and talk again now please.

Practicing and re-teaching protocols for math talk is really important during the middle of the year to maintain the most productive and comfortable learning environment.

I used to wonder if too many turn-and-talks might mean too many transitions and disruptions to learning.  Could Turn-and-talks could get old?  This is actually not something to worry about.  You can have students turn and talk repeatedly in one mini-lesson, three or four times in just a few minutes.  As long as you encourage them to use the protocols, if there are things to talk about, give them the opportunity to do so.  The more they do this, the more comfortable they will become communicating their thinking with one another, with you, to their class, and on paper.  The benefits of turn-and-talks are especially great in math classes and every class should be utilizing them (in my humble opinion..).  It is a good idea to insert a little space or discussion between turn-and-talks, but the actually risk of doing them too often is almost zero.

Not enough turn-and-talks is the greatest risk of all... When your students are not communicating with each other about their thinking in math on a regular basis, they are not getting opportunities to reflect on their work, to reflect on their own thinking, and to hear the thinking of their peers.  Critiquing and analyzing the mathematical thinking of others is an important mathematical practice, and turn-and-talks are a critical way to make that happen.

It's important to diversify students' conversational experiences in math.  Turn-and-talks, small group work, class discussions, peer conferences, partner work-- They all provide excellent opportunities for students to reflect on their own thinking and learn from their peers.  But Turn-and-talks are special, in that they offer students a chance to communicate directly with a partner about an idea that is right there in the moment.  They only take a few seconds, and they keep your students engaged in your lesson.  If you would like support from a colleague in using turn-and-talks in math lessons, chances are good you have someone right next door or across the hall who can help you... Or you can ask your friendly math strategist to come model turn-and-talks in math.




Tuesday, January 19, 2016

EM4 and How We Teacher Common Core Math

We are doing the right thing.  That is the most important message I can give you at this time.  When we teach for greater understanding of mathematical concepts, and coach our young people into becoming better problem solvers, we are doing the best thing we can for them.  So the questions we need to be asking ourselves when we  are faced with how to teach a lesson, a unit, or a concept, is: Will this help my students become better problem solvers?  This is one of the reasons we went with Everyday Math 4-- The emphasis is on problem solving and deeper understanding of mathematical concepts.

Common Core math is constantly under scrutiny in social media and even in the news, mostly because teaching for deeper understanding is not how previous generations were taught, as a rule.  We were primarily given instructions to follow, rather than a puzzle to work at, take risks with, and eventually solve, perhaps with some help from a neighbor or two.   Puzzles aren't always easy to understand, and they often involve making mistakes before a solution is found.  For some puzzles, it helps to look at them from multiple perspectives, which is why we often have our students problem solve with partners and small groups.  Other puzzles are best approached independently (have you ever tried to solve one of those nine-square puzzles with birds or reptiles or another such scene on them, with a group?  Unless one member is a very dominant type, it is almost impossible!*).

Let us remember that Common Core is merely a set of standards, and not entirely different than standards we've had in the past.  The major difference is within the eight Standards for Mathematical Practice and the content standards, there is greater emphasis on deeper understanding and problem solving.  This is not understood by some parents and other vocal critics, who see what looks like strange and unusual homework assignments coming home (and others, with questionable authenticity, posted on Facebook) they have trouble helping their children with, let alone understanding themselves.  While the Common Core math standards are the same in 42 states, how they are implemented is not always the same.  Different districts in these 42 states have different math programs, and within those districts there is a varying degree of fidelity to those supposedly Common Core aligned math programs.  As someone who has studied the Common Core math standards since before they were released, while still in draft form, my opinion is that EM4 has done an impressive job aligning to the standards and capturing the emphasis on understanding and problem solving.  As with any mass-published resource, we each will find the occasional weirdly worded problem, or curiously designed activity, but the mathematical content and instructional shifts that are the focus of EM4 are its major strengths, and teachers in RSU5 are doing a fabulous job in the inaugural years of using these resources.

I want to share a NY Times article that was published recently which attempts to address some concerns about Common Core math, just to help celebrate and acknowledge what we are doing.  I think you will read this short article and say to yourself, "I'm doing that," or, "that's already happening in my classroom."  So congratulations, you are doing the right thing.  I am confident that as the next couple years progress, we will see more and more great things coming out of the work our students produce, because I see the difference one year makes every day in the classrooms I visit.  Imagine what will happen when we all really get good at this.

Thank you for taking risks in your work, for allowing opportunities for your students to problem solve together, for shifting your instruction, and for putting so much love and hard work into your math lessons.

Here's the link:

NY Times Common Core Math piece


* There's a story that goes with this puzzle thing... I worked at the Spurwink School, among other intense alternative education environments, prior to getting my teaching certificate, and one day I pulled out one of those nine-piece square puzzles for a boy that was dealing with a lot of emotional issues and had recently gotten himself in some serious trouble at school (that would eventually involve charges being brought against him).  I brought in the puzzle because my wife and I had been working on it at home periodically, and it took almost two weeks for us to stumble upon the solution.  Intuition led me to believe this particular child might really focus on such a thing, and he was obsessed with songbirds.  This puzzle had songbirds all over it.  The first thing he did was correctly name each bird species, and then he went to town on the puzzle, quietly mumbling to himself as he rapidly swung cards around in different positions.  He solved it in less than 60 seconds.  Now one could come to a number of conclusions from such a phenomenon, one being that my wife and I are perhaps not all that sharp... but I prefer to use this as an example of not just a special kid (I have never seen anyone else solve the puzzle so fast), but of one of those situations where other perspectives actually complicate the problem solving process.  When my wife sat beside me at the table, she was looking at the puzzle from a different angle.  Every time she moved a piece in or out of place, it completely messed with what I was seeing, and I had to switch gears in my thinking.  When I would adjust the puzzle, my wife would let out a displeased sigh.  For the child I gave the puzzle to, it was just a matter of rapid-fire trial and error, in total quietude, without disruption, and bam.  Puzzle solved.  It didn't end up being a very lengthy distraction for him, but he did get to feel good about himself for a few minutes.

It just goes to show that while problem solving is a process most often benefitted from collaborative work environments, we should continue to still provide opportunities for our students to do some work independently.  Sometimes that is where their strengths manifest themselves.