That Testing Time of Year

 The sun is finally out in Washington State and the rain is subsiding for a bit.  As I walk to and from my portable, I notice the smiles on students faces, kids digging in the garden, and the excitement of spring ramping up.  It is the best time of year, but also stressful for students and teachers.  The SBAC is approaching fast and teachers and students alike are studying, planning, creating "boot camps" for review and mapping out the days and weeks ahead.

"What does that mean for SAGE and PEP?" the class I teach, you ask. Well, it means that we are also trying to ferociously wrap up units and review content before the tests hit.

When my students are testing, there are sometimes weeks where they miss instruction.  The tests matter when looking at class placement, as they are advised to take specific math or science courses depending on results.  They also can affect whether or not a student is allowed to sit for the CogAT test and appeal a result the following year.  The SBAC is used as a screener, and if students are not in the top 5% of the district scores, then they are not invited to test in October when referral season comes around.

Additionally, in the past, if a student showed that they were behind or struggling with content on a standardized test, then that individual was invited to attend summer school.  I do not believe that is the current practice within the district, but it was offered once upon a time.

The tests are long and tedious.  I remember watching my little eight and nine year old third graders writing five paragraph essays, typing away on the computer, honing their ideas, and trying to elaborate to the best of their ability.   They were tired and I was tired and everyone was exhausted at the end of the tests.  The days kept going and going and these little people had to be silent for so long.

Today not much has changed in that regard.  The kids get through it, and generally do fine.  

Differentiating: Knowing Your Student and Knowing the Standard

 There is no right or wrong way to differentiate.  

Today I threw a problem on the board for my first and third graders to attempt to solve and sat back and watched.  Some dived into it.  Some copied it. Others sat there with a deep frown contemplating where to start. 

There are many philosophies and ideas on the subject, but when it comes down to it, all it means to differentiate is meeting students where they are at. 

 Every person is unique and interesting and different and thus, they will need different things in math or any subject for that matter.  Just because someone is the same age as another individual, does not mean that they know the same content or need to work on the same logical reasoning process, thus comes the idea of differentiating.

If you really break it down, in order to differentiate you need to know two things.  A teacher needs to know his or her student and also the standards you are teaching.  

There are many ways in which a student can know a student.  She can get to know their interests through conversations, letters, surveys, get to know you activities and observation.  

A teacher can also get to know a student's constantly changing knowledge base through consistent use of pre-assessments and daily checks in through exit tickets and observation.   

Once a teacher knows the student, they can figure out what comes next.  If a student can only approach a problem and solve a subtraction or addition problem in one way, maybe a teacher move would be to dig deeper into the math practices and have the child make a model or draw a visual representation of the problem.  

If the child struggles with explaining his or her thinking, maybe as a teacher, you cut down the practice volume and ask the student to really show their work in depth and in multiple ways within one problem.  

If a child has difficulty working with peers, and this is a goal area, maybe that child has a partner for math daily and in conferences you are working on sharing the workload, listening, making eye contact and teaching the student to ask leading questions.

Additionally, if a student knows the grade level content, works well with others, can explain their thinking and show their work in multiple ways, then it is time to accelerate.  The student can then be exposed to above grade level problems.  The teacher might pull the student aside and give them a problem that is a little bit challenging and the student does not know how to solve.   The teacher can then ask what do you know about this problem?  What is a possible way to approach it?

The teacher does not show the student how to solve the problem and then ask the student to solve it exactly the same way, as that does not engage the learner in deeper thinking or problem solving but rather asks a student to merely mimic a solution strategy.   

Students need to engage in productive struggle and be pushed in order for learning to occur.   If a student does not engage in productive struggle then they will suffer as an adult or older student when a problem comes along.  Panic will set in.  Productive struggles helps students self regulate and adhere to challenges in the face of complexity.  

The Power of Starting with a Question

 Everyone loves a little mystery in life and most people like to think hard.  I have noticed my lessons go best when the learning target is stated at the end.  When I teach with an inquiry lens, and let the kids discover the math and science, engagement goes up, learning increases, and all students push through to learn at greater depths.

When I start the lesson with, "Today I will teach you how to add fractions," I notice that half my class tunes out and the other half already knows how to do it.  

In order to have students engage in productive struggle, we as teachers and parents, need to present our students with problems that they truly don't know how to answer.  They need to play with the numbers and explore concepts without someone telling them how to do it.  Students need to try and fail and be okay with that because later on in life, they will encounter problems that they need to solve, and they need to have the logical reasoning skills to tackle them head on.

Today, one of my students was trying to add fractions for the first time.  He has not been taught how to do such and I was watching as he logically thought his way through.  T. drew two models of fractions and then was trying to figure out how to cut them into the same sized pieces so he could add them.  T. told me that he had learned about equivalent fractions on i-ready and he was trying to use this concept to add.

I did not tell him any of this.  I watched as he crossed out numbers, sketched brownies on this graph paper, erased and tried again.  At the end, he was close, but mis-named the numerators because his sketches were not accurate enough.

At that point, we talked about ways to draw accurate diagrams for equivalent fractions and he eagerly solved the problem.  The teaching point was at the end and he was satisfied to have tried something hard and found a way to come up with an answer.

One of My Favorite Math Games for Kinder and First: Sneak Thief

 "Let's play Sneak Thief" cried M. 

"Yes! I love that game!" replied J.

I pulled out the train blocks and we started making ten stacks of tens. 

"We are going to have 100 soon!" squeaked M.  I watched as the students started making their rows of ten blocks.  Some rows were all white, others black, and some trains were multicolored.  It didn't really matter what they looked like as long as there were ten rows of ten.

"Okay! Close your eyes," I called.  I watched as my first graders turned their backs and covered their eyes.  I pulled 3 rows of ten off the table and broke apart another two blocks from a ten and quickly hid them under the kidney table in my classroom.

"Open them! Can you figure out how many the sneak thief stole?" I asked.

Hmmm... I watched as the students counted tens, considered how many were left, counted them again.  Soon they touched the remaining eight that we in the ten that I broke apart.  M. was deep in thought and J. was touching the table and then writing a number sentence down on his white board.

"You took 32!" J. called.

"How do you know?" asked M.

"Look.  There are eight left from one train and then there are six trains left as well.  So, 100-32 = 68.  There has to be ten tens."

We played this game again and again because it helped my students visually understand what was happening in a subtraction problem where you need to break apart a ten.  Often times my littles come to me and they have memorized an algorithm but they do not understand why it works, nor do they have a way to draw or build a model to explain it.  

This game teachers the base ten number system and uses models to represent large numbers.  Students start to understand how numbers are formed in a very visual way so they can decomposed and compose numbers mentally and logically.

Sneak thief can easily be adapted to meet the needs of more accelerated learners by using larger numbers, numbers with ones in them, or adapted for striving learners by just playing with a ten.   It is great at home and also as a rotation in your math block.  

The Stock Market Game

 I am always aiming to push my students out of their comfort zone and try new things.  This is hard for everyone, but can be especially difficult for gifted students.  This year, I tried to lead by example and taught a new unit on investing.  I was nervous at first, but figured I'd give it a whirl and now I am hooked.  

It all started, when I was sitting at my desk early September when a forwarded email came across my inbox.  It was titled, "The Stock Market Game" and run by Adam Wright through Western Washington University.   A friend of mine said that she was planning on having her students participate and try it, and after a moment of pause and hesitation, I decided that I would join too. 

 The students each get a pretend portfolio in which they learn how to invest.  Students can buy and sell stocks, mutual funds, and bonds just like the real stock market.  Their investments mimic the real stock market and they watch as their investments increase and decrease over time.  Every team got $100,000 to begin with and could borrow an additional $50,000 if they chose to do so.  

Initially, my plan was to have 4 groups at Briarwood play.  I would see how it went, and then maybe the following year I would include Creekside as well.  However, as soon as my Creekside students got wind of the game going on at the other school, they wanted to play too. "Please, Ms. De Jesus," they cried.  "I have been investing at home since I was little and I know how to do this! Please!"  (Mind you, this was said by 10 year old's.)  "I've been talking to my dad about investing since I was five," chimed in another student. Thus, I allocated three teams to Briarwood and then the last team was comprised of my fifth graders at Creekside Elementary. Off we went! 

We learned about diversification in a portfolio and the difference between mutual funds, ETFs, and Index funds.  We looked at balance sheets, revenue, and cash flow in businesses and read articles in Yahoo Finance that told how the politics of the day affect companies bottom line and stock prices. We examined how compound interest worked and created graphs showing how early investment can benefit a wanna-be millionaire, and also hurt a person behind on their credit card payment.  We watched youtube videos, videos from the Stock Market Game company and read.

The kids got into it. They talked about buying Tesla in early November and purchased a lot of it.  We looked at each other's portfolios and examined what was working and what wasn't working.  Students went home and chatted with their parents about what companies would be good investments and which ones should be passed up. They came with lots of ideas and talked eagerly about money and investing. 

Every week, after check in on the mood meter, my 4th and 5th graders anxiously opened their portfolios and cheered in joy (or groaned in dismay) about what they found.  Trades were made and the kids were ambitious. 

When the game was coming to a close, my students were succeeding.  One of the Briarwood teams placed first.  There were 28 teams in Washington for elementary ages students and all four of my teams came in the top 6.  We were also 5th out of 308 teams in the state, if you look at our competition against high schoolers and middle schoolers as well.   Basically, my kids kicked butt at investing and I learned a ton in the process.

Additionally, a side affect of the Stock Market Game was my own learning about investing.  The project made me relook at my portfolio and diversify some of my holdings.  I bought some stocks at opportune times and made calculated decisions based on all I had learned. I created portfolios for my own sons.  Students were so excited about TESLA, that it made me look into it as well and buy some in real life. 

In reality, this Stock Market Game was one of the best units I have taught in a while. It got me learning again, several of my students are considering finance as a career path, and there was a real life application to the work.  It was phenomenal and I recommend it to anyone looking for new math unit that pertains to life outside the classroom.  This is the unit I wish I had in school.  

Making Math Fun

 Last year, one of my most advanced 5th graders came to me and told me he liked my class but hated math.  

"I am so sick of it!  I have to do hours and hours of practice at home.  I can't stand math!"

Yikes, I thought.  This student was only 11 years old at the time, and while he was able to complete problems that an 8th grader could solve, he wanted to avoid math like the plague. 

"Yes, I've seen that too," a colleague of mine chimed in. "There was a student in my daughters class who won all of the Math Olympiad Competitions and awards and was the highest in math. But by the time that student got to high school, they didn't want to take any advanced AP or IB classes.  They were burnt out."

In SAGE class, I try to make math fun and engaging so my students want to try to problem solve and explore numbers.  A few ways I am able to do this is through partner work, problems with multiple entry points and answers, and exploratory learning.  We play games.  We write with whiteboard markers on tables, we build answers, and we talk.    There is no quiet learning in SAGE.   

Sometimes my class is loud, and other times it is messy with math tools all over the place.  Sometimes the students do not want to collaborate, but mostly students want to learn, play, be included and do deep thinking.

The "I do, you do, we do" method doesn't work well for math problem solving.  If a teacher just showed you how to solve a problem and mandates a certain approach, the fun is sucked out.  Who wants to do a puzzle when you already know the answer??

I love coming together and looking at various approaches at the conclusion of a lesson.  I love learning with others and learning from other people.  Math is a social subject, and should be approached as such.

I want my kids to have a lifetime love of math rather than an aversion by the time they hit middle school.  Maybe it is time to stop the timed tests, workbooks, and rote memorization and replace it with math nights, socialization, problem solving, and puzzles. 

Leveled Problem Solving

 The sweet third grade class poured into my portable after lunch today. They were still excited from recess and chatting about their holidays and plans and games.  After they settled down, and each took a seat, we started our day.  

The mood meter was on the board, and I heard about trips to California, games with brothers in the snow, and how it was hard to roll out of bed this morning. I like starting class this way, as in a soft start, because I get to know my students a little better and understand what their world looks like outside of my door. 

Time was limited and the learning levels in the class varied.  Students who were one or two years below grade level sat in the same room as problem solvers who were testing well above average.  How do I meet everyone's needs, engage learners and push my students all at the same time??

Today, my solution was leveled questioning and opening up models with builds.  The questions were a little difficult- but with partners, open whiteboards, and two teachers as scaffolds, structures were in place to support the on level kiddos. 

I watched as my on level students made connections between repeated addition problems and multiplication.  Students drew labeled diagrams and discussed representing math in meaningful ways.  The room was a buzz and the students were focused. 

One student, a reluctant mathematician, asked me if he could do the work in another way.  This student likes to think in objects and build ideas rather than show them on paper.  I opened up my science cabinet and he got to work.  I watched as this student poured water into measuring cups, and accurately measured out 250mL of water and carefully poured it into 5 cups.  He then verbally calculated the total amount of water in all the cups by explaining that 2 groups of 250mL made 500mL, and therefore, there must be 1L of water plus another 250mL.  He had a smile on his face, was focused and excited and eager to share his learning.  He even labeled some of his work with whiteboard markers on the table when he was done.  He leveled up and began thinking about 3 additional water bottles and continued his math exploration for the duration of the time. 

I pulled in the level 3 thinking into the debrief.  My gifted student explained to the class how a student could use the distributive property when calculating the cost of the water and cups.  He explained that he broke up $44.50 into 44 and 0.50 and multiplied each by 8 to find the cost of the cups.  My student walked us through how that would look as I added visuals to the board.  It was essentially a math talk at the conclusion on the lesson so my student could work on verbally explaining his logic and thinking to others.

Some days in teaching you walk away thinking, "Man, that lesson didn't go as I wanted it to..." and other days you win at teaching.  Differentiation and flexible thinking gave me a check in the win category today.  Thank you building thinking classrooms.