Math training, days 2 & 3

After tackling my homework for math training, grocery shopping, and spending several hours leveling my library (such a daunting task), I didn't have the energy left to process what I'd learned.  

However, today I was home much earlier so I could reflect on yesterday and today's math trainings.

Days 2 & 3:

We talked about multiplication.  We talked about it...a lot.  Perhaps it's because I teach fifth grade and have taught inclusion, but none of the strategies mentioned were new information.  I grasped the concept right away and helped my neighbor make the same mathematical discoveries.

However, I did learn a few new things over the past few days.  Here are my "ah ha" moments:

The minuend is the first number in a subtraction problem and represents the amount you start with.  The subtrahend is the amount that is being removed or subtracted.  

This discovery raised an interesting question within our group.  Why is it that other math vocabulary terms (addend, sum, factor, product, quotient, etc) are well-known but minuend and subtrahend aren't?  Why can teachers (and hopefully their students) use the correct vocabulary for the other operations, but stumble on subtraction terms?  I know I'll be incorporating these terms into my math instruction!

"Give One, get one, move on" strategy

The page is divided into four sections.  Students solve the problem in the first quadrant, which is labeled "give".  After time to process the problem, students then will stand up and find three other people to "get" strategies from.  The students will work in pairs to explain their strategies to one another.  Not only does this allow for movement, but students can explain their thoughts to one another.  During this time, the teacher is monitoring as an informal assessment to see what students are grasping the content and which ones still need a little more practice time.

The next classroom tweak deals with these manipulatives:

Found in almost every elementary classroom, I always called these "ones", "tens", "hundreds" and so on.  Most teachers do.

However, in doing so, you're limiting students' understanding of the relationship (powers of ten) between the manipulatives.  

These will henceforth be referred at as units (smallest), rods (long ones), flats, and cubes.

By doing so, a teacher is able to stress the relationship between a value being ten times larger or smaller than the value next to it on a place value chart.  

Referring to these as units, rods, flats, and cubes also allows for the manipulation in upper elementary.  If my "one" is now the cube, I can use these manipulatives to represent a tenth (flat), a hundredth (rod), and thousandth (unit).  I can also regard the unit as a thousand, then have students prove the other values. (Rod would be 10,000, flat 100,000, cube 1,000,000).  

Finally, we played close to 100 (from Investigations).  While this game was not new to me, I did appreciate the discussion about its importance in the classroom.  In playing this math game (and others), students are provided the opportunity to practice many math skills such as estimation, reasoning, critiquing the reasoning of others, operations, and place value.  These games take minutes to learn, can be a good task for students if they finish early with an activity, and can be used as homework.  I know my students would much rather go home and play a math game as their homework then fill out a worksheet.  

Close to 100 also reminded me of another quick math activity:

What an easy way to get their brains working during the first few moments of the day!

Stay tuned for a recap of days 4 and 5!

Change can be a good thing

I'm halfway through year five of teaching and my oh my have things changed.

For the most part, I see the changes as a good thing.  I know to truly see a program or strategy's effectiveness, it should be consistent within a school for several years to be able to accurately measure growth.  That's something we're working on at our school.

When I started teaching, we followed a scripted reading program with weekly spelling tests and a story of the week.  I taught comprehension strategies, sort of, but we were expected to abide by the book.  I thought I was doing pretty well following the structure and doing the same things as the other teachers in my grade level.

This blind, naive attitude only lasted a few months and (with administrative approval), I'd completely abandoned the scripted program by my second year. I don't do well with scripted programs anyway.

I brought additional challenges upon myself by having to find meaningful content, but at least during my second year I was teaching standards and not just a story.  My students were becoming more engaged and I was enjoying teaching more.

By year three, I was feeling more confident in the classroom.  I'd finished my masters degree and my Teach for America obligation. I had taken a lot of district trainings and was on a task force to unwrap the (at the time, new) Common Core State Standards.  There were still lots of extra demands on me to find the materials I needed to teach with and lots of long weekends preparing.  I was also in conflict with veteran teachers in my grade level who were unwilling to try new strategies and envied my successes in the classroom.

Year four brought more confidence and a partner.  I was no longer pitted me against the grade level, but rather me and my ally against the veteran teachers.  Slowly but surely, our students rose to our high expectations and outperformed the others simply because we weren't teaching a bland, scripted program.  We were teaching (and reteaching) the standards with a variety of strategies.  Not all of them worked, but our students were rarely bored.  Their high levels of engagement translated into higher test scores due to what I believe was their interest in learning. 

Year five: my dream team.  I work with three other fifth grade teachers and my special education co-teacher.  We are on the same page 95% of the time and always supporting one another.  None of us follow a scripted reading program with a new story a week.  No one gives a spelling test with 20 words that students had to memorize over the week and regurgitate on Friday.

No no, I think we do something much, much better.  

We teach a weekly, grade-level phonics skill with explicit phonics.  We teach the patterns, practice sorting by sounds, encode and decode with text, then on Friday give them a quick formative assessment with five words to see if they can apply the skill.  I don't want to see if they can memorize basic facts, I want to see if they an apply their knowledge of word parts to spelling unfamiliar words because that's a much more true assessment of whether or not they got the skill.

For math, we are using the Investigations program which is far superior to what we previously used.  Based on over eighty years of research and partnership with NCTM, the program has students discovering math concepts through manipulation and discourse, which provides for a more meaningful understanding of mathematics.  They are constantly building their number sense through Number Talks and math games that rely on critical thinking.

For reading, we're loosely following another school district's pacing guide because it draws heavily from mentor text that is rigorous, engaging and within an appropriate lexile level.  Before choosing to go with their plans as our backbone, we read through their plans, double checked that all standards were covered and added in our own notes.  I think it's going fairly well.

We don't give a weekly reading test (thank goodness!).  Instead, we give a monthly one with longer reading passages (to build their stamina) with questions that cover several standards.  I'm not testing how much they remember of a story we'd read together and discussed in class five times (because at that point, it was regurgitation, not knowledge).  We're testing how well they can independently apply the skills we've been working on in whole and small groups to the unfamiliar passage.

I look back at my first year in the classroom and have the overwhelming urge to apologize to that group of students. 

 I did the best I could with what I had, but I would never go back to that way of teaching.  I would never rely on worksheets and a story of the week.  That's not what helps students learn.

As an educator, I'm constantly trying to learn new strategies and implement them in my classroom.  While this highly reflective process can be a tad frustrating when things don't go as planned, I think that learning and trying new things is far better than repeating the same thing over and over again.

In the past five years, I've implemented interactive notebooks and Number Talks.  I do explicit phonics three times a day (whole group and both small groups).  I have students interact with technology rather than me being the sole one to create things.  I have centers and literature circles with novels, something I didn't even attempt until my second year.  I've learned how to do the CORE phonics assessment to see where students break down phonetically and the DRA to determine their reading levels. (Although it's time consuming, I much prefer it to the old diagnostic tests I had to give!).  We're using mentor text for reading and writing, doing mini-lessons and having students publish drafts both on the computers and the iPads.  It's been a tough, uphill battle and I'm proud of the new things I've learned.  I'm appreciative of the trainings I received at my school, from my district and from outside educational entities.

I'm saddened by teachers who are scared or unwilling to try new strategies.  I don't have the same bunch of kids I did when I first started five years ago, so why should I teach the same lesson the same way?

(Poor Harry Potter, subjected to the old ways of teaching)

Change can mean better instruction for students.  Change can mean more engaging, thoughtful, purposeful, driven lessons.  Change can mean teachers have more flexibility and students have more opportunities to collaborate with their peers on projects and activities, rather than just sitting quietly and working independently. Change can bring joy back into the classroom.  I'm not saying every aspect of education needs to change nor that all change should be blindly accepted because that's no good either.  However, if change brings about higher student performance and helps create more critical, thoughtful, passionate young scholars, why not give it a try?

Change can be a good thing.  

Terrific Thinking Thursday

Our school is using Number Talks for math to boost our students' number sense, working understanding of mathematical concepts and critical thinking.  The philosophy behind Number Talks aligns perfectly with Investigations, which we are using as a tool to guide our standards-based instruction and assessment.  Through hands-on learning and discourse, our students are learning how to interact with math rather than memorize and regurgitate information.

Our grade level has tweaked our number talks:

Monday: This is our traditional number talk.  A problem is displayed on the board, students solve mentally then raise their hands to share their answers.  Emphasis is given to strategies and explaining their thinking.

Tuesday: Ten minute math from Investigations.  We are starting with quick images where students are looking for patterns, which is supporting the 8 math practices.

Wednesday: Word problem Wednesdays.  We are moving away from the traditional circling of the number and choosing an operation robotic routine.  Instead, we are focusing on criticial thinking and strategies.

Thursday: Terrific Thinking Thursdays!  We display a deceptively simple problem and let students solve individually before sharing out whole group.  

Fridays: Fast Facts Fridays.  Students are working on their individual goals for fact fluency (multiplication and division) in a fun, game-like way with their shoulder or face partner.

Since it's Thursday, here is an example of today's problem:

The problem states "You have $2.75.  What coins could make this amount?"

None of my students gave me an answer invoving dollar bills.  There were actually more answers they came up with later and I was impressed they used half dollar coins in their answers.  Not bad for eight am :)