Sunday, December 21, 2014

What is a Math Concept?

I recently received an email from an educator in North Carolina encouraging me to look deeper into the meaning of the word "concepts". Below are snippets of the email. 



This email stemmed from a category on my website Sensible Mathematics 
https://sites.google.com/site/sensiblemathematics/activities-by-concepts. The writer felt the category should not read "Activities by Concepts". 

Because I understand there's a constant need for growth which happens when new information challenges my current understanding, I'm open to your perception, understanding and definition of a mathematical concept. Here's my current knowledge:



Wednesday, November 12, 2014

Coach for a Day

I had the pleasure of filling in coaching shoes at the middle school level. After a conversation with our Title teacher about the lack of student reasoning happening within our classes, I introduced a strategy assessment called GLoSS. It originated in New Zealand and assesses student use of strategy in the domains of addition/subtraction, multiplication/division and ratios/proportions. 

What was great about this opportunity was it allowed me to put back on my coaching hat and model the idea of student-centered, conceptual teaching. This idea was foreign to the Title teacher who shared he's very procedural in his teaching because it was the way he was taught.

His classroom was set-up in rows and students sat at least one desk away from the nearest neighbor. The students only encountered math in the nude and only needed to worry about getting the correct answer. Manipulatives were never visible. These kids are considered the "bubble kids" with gapping holes in their mathematical understanding. GLoSS and the Numeracy Project http://www.nzmaths.co.nz/numeracy-projects would be perfect for this classroom. 

He seemed very open to the entire idea. I would model the assessment and implement a lesson based on the data gained from the assessment. I assessed all but three of his kids determining the strategy range for concepts relating to ratios and proportions within the 7 th grade class was as low as 2nd grade to 4th grade understanding.

The lesson implemented involved the use of manipulatives, context and math discusses of the concept versus the procedure. It's like a grand slam modeling lesson for a teacher who has never seen that in action. A great lesson in which the students were engaged and of which the teacher enjoyed being a part. 

I left telling him, if he wanted to discuss the lesson later we could. There was no obligation because I'm technically not a coach. My hope is that change was promoted. Any change...

As I walked passed his classroom to leave for the day I saw this...
Change.

Wednesday, October 8, 2014

C is for Cookie That's Good Enough for Me

That's the song of the Cookie Monster I remember from my youth. CM sings about the letter "c" and begins by saying, "Cookie starts with the letter c, what are some other things that start with c?  Who cares about those other things..."  This is what it sounds like when teachers say, "I didn't learn this way and it was good enough for me!"  

The thing of it is, you may have come to terms with the idea of robotically following a routine without understanding why you're doing it and why it works. But it should not mean you are to subject your students to the same misfortune. I know it's a harsh reality when you find out what you thought you know isn't exactly right. It's like finding out the guy you thought was totally into you is actually madly in love with someone else. If you continue on as if you and him have a future together you'd be living in a false reality. 

Now let's apply that analogy to math instruction. You've found out that the math instruction you've been using for the past 5, 10, or 15 years is not as effective as you thought it was. So are you going to continue on in the same manner even though you know the truth?  Or do you push pass the discomfort of not knowing and begin to develop your own understanding in order to meet the needs of your students?

The Cookie Monster song: http://youtu.be/Ye8mB6VsUHw

Tuesday, September 16, 2014

When Kids Don't Get It

http://youtu.be/KdxEAt91D7k I was first introduced to this video as a math coach. Like many others, my initial thoughts were, "Oh this is too cute, oh this is so funny". My perspective today is different. I see the truth behind the humor, as my husband quite other says, "The truth is in the joke".

What happens when kids don't get it?  As teachers, we are called to meet each kid where they are and bring them as far as they are capable of going. But as we are bringing them along, are we sure, we aren't  leaving them behind, bewildered by the lack of support and guidance from the teacher who has handed them a failing grade. When students don't get it, what clicks in your mind?

For me, when I am analyzing student performance, I mentally go through a flowchart of instruction. 
Was the concept introduced conceptually? If yes, what strategies were developed, discussed, and implemented to allow the student(s) to gain understanding?  If no, how can I guide students to begin to look at the content conceptually?

What methods, have I used to meet the students needs?  Have I tried more than one way?  If not, TRY ANOTHER WAY. 

When students don't get it and you find yourself using the same method every day for several weeks, there may be a flaw in your method. If what you've tried doesn't work, it is okay to say, "what I thought would be effective wasn't, here's how I will change what I did". This is why collaboration is so important.  You have the opportunity to bounce ideas off of other teachers. You find out what was effective or ineffective with their students. 

Like, shoes, clothes and underwear, education is not one size fits all. Math especially is not one size fits all. So if you have a one size fits all approach to teaching mathematics, consider the flowchart approach of reflection to ensure that when kids don't get it, you've done all you can do to ensure they can.  And chances are if you have, they will never receive an assessment with 6 out of 24 correct. 

Thursday, September 4, 2014

Lies My Teacher Told Me

I remember having to take a History course while attending the University of Florida (Go Gators). We were required to read a book titled Lies My Teacher Told Me. To me even the title of this book was so provocative, to even image that teachers would lie. As I read the book, it became more shocking to me as it discussed rtopics and ideas shared by teachers which were invalid or down right untrue. And a lot of this teacher misunderstandings came from dare I say, a textbook. 

If I were to rewrite this book based on math misconceptions I've heard from my students in the first 5 weeks of 7th grade I would include the following:

You cannot take a large amount from a smaller amount. 

A negative plus a negative ALWAYS equals a positive. 

When adding 36 + 47, 6+7 and 3+6. 

Adding means a number gets bigger, subtraction means a number gets smaller. 

When you add on a number line you ALWAYS go to the right. When you subtract on a number line you ALWAYS go to the left. 

And the one that takes the cake for me: when discussing absolute, the number comes out of jail and is positive. UGH!!

Rules can expire and tricks cannot be applied in various problematic situations. So is it truly worth the price students have to pay in misunderstandings?

Thursday, August 14, 2014

I Can Say I'm Sorry

Most times when you're on the outside looking in, you have visions of how things should be on the "inside". As a coach, I always had this vision of how things should be within the classroom. I secretly frowned upon those who were not implementing county initiatives or best practices properly. I hadn't been long out of the classroom so I used that as my stripes to say, "I know what I'm talking about, I know how this is supposed to work. 

Now I find myself on the inside. I'm on the inside trying to make my out of box thoughts about teaching and learning fit. Well I'll be darn! Those ideals in which on the outside looked like it would fit within the round hole carved out for the round peg have now become square. 

So yes, while I struggle to make what's best fit best for my students, I say sorry to myself. Sorry to each teacher I secretly judged even if for a second. Sorry for each teacher who was in the midst of their productive struggle and I didn't stop to ask how they were managing it all. 

I can say sorry...

Monday, August 11, 2014

The Power of Leading By Example

A good friend of mine passed on "Daring Greatly" by Brene Brown.  It's a book about vulnerability and whole-hearted living.  I'm currently on the chapter in which she is discussing how to dare greatly in parenting.  The statement that is resonating with me is "Be the adult you want your child to be when they grow up".  This is huge because it calls you out as a parent to lead by example.

Now as I look to relate this to being a teacher leader, I still hear the same call to lead by example.  Be the teacher you want your colleagues to be, be the leader you want your colleagues to be.  It's not about enforcing non-negotiables or hoarding your ideas and resources.  It's first doing what is best for kids, then telling others about what the students were able to do as a result.  This isn't done in a "I'm the bomb.com and this is what I'm doing with my student" fashion.  It's a "the kids were really engaged today when we did this..." fashion.  This is when you share student work, student experiences and provide the opportunity for others to use your resources.  You approach this humbly, so not to bring glory to yourself, but to shed a light on the goodness that is happening with student engagement and performance.

When you do things like that, you have the opportunity to get excited when a teammate decides the textbook isn't engaging enough for their students.  So they come to you asking for the very thing you wanted them to use from the beginning, rich and engaging math tasks :-).

It is my belief that when a teacher switches from the textbook to GA state math frameworks, a math angel gets its wings!


Saturday, August 9, 2014

SMPs According to 7th Graders

These 7th graders were asked to analyze and interpret the Standards for Mathematical Practice. Here are a few:





#Meaningful


Wednesday, August 6, 2014

Being a Teacher Leader

Just a quick thought on being a teacher leader. 

A teacher leader is anyone who can lead by example. Someone who shares their thinking without making others feel inferior. It's being innovative and not being afraid to fail because you know you are carving out a trail for others to follow. 

Our schools are filled with teacher leaders, many of whom don't think they are. They're the ones who are being secretly watched by their peers to see what great things are happening. 

I salute those teacher leaders who aren't in it for the recognition or praise but are simply doing what's best for the greater good!

Monday, June 23, 2014

We're Talking About Practice

When it comes to practice I kind of feel like Allen Iverson during his practice rant http://youtu.be/eGDBR2L5kzI. It is my belief that rich and meaningful task should be the emphasis. However many around me feel that the importance should be placed on practice. 

During a workshop this past year, @ddmeyer described practice using a basketball context. He said, "math practice is like practicing your free throws", it isn't something that you spend the entire time doing but it is something that's beneficial during the game. My thinking about practice began to shift at that moment. So my shift was from no practice to meaningful practice. 

Meaningful practice as defined by @turtletoms is the application of the mathematics once the concept it is understood and explicitly connected to understanding. @mikewiernicki says meaningful practice meets student where they are as it relates to their understanding. A great way to incorporate meaningful practice in your math routine is through games such as those found nzmaths website http://www.nzmaths.co.nz/number-knowledge-activities. These games are leveled based on strategy and number knowledge. 

The cutisie activities are okay, but you have to be careful that the practice activity does not undermine the strategy and concept development which took place prior to practice. I've come across a few resources for practice activities:
GA Frameworks have practice tasks
https://www.georgiastandards.org/Common-Core/Pages/Math-K-5.aspx
Choice Menus
https://sites.google.com/site/sensiblemathematics/ 
Symbaloo
http://www.symbaloo.com/startLogin.do 

I know there are tons more, so feel free to share. 

Saturday, June 7, 2014

The Beauty in Being Less Helpful

   I'm a controller at heart. I have to know what's next, determine how to handle the next steps and internalize the success and/or failure of my decision. This is simply because I must be in control. But I promise you, if you ever saw me teach,children or adults, you would never know it. How could such contradictory happen within one person?  I've learned the art of being less helpful or the art of losing control. 

   If you're anything like me, a controller, the thought of losing control is a hilarious and ridiculous one. Until you find yourself feeling beat down from doing, thinking and saying it all. You find your students looking at you with closed mouths and empty stares waiting for you to tell them what to do, how to do it and if they've done it right. You own all the knowledge and all the control. You haven't made impact on anyone's life but your own. 

   Well, what do you do?  You slowly stop telling answers but answer questions with questions. Students ask, "What am I supposed to do?"  Your response is, "What are you trying to do," followed by "What information do you have?"  And then you simply walk away. Your student is left with the very information they need to approach a task, problem or equation without you telling them a thing. So the next time they run into that same issue, they rely on this experience to help them solve another problem. 

   Don't look at it as not helping the student because you are, you're helping them make sense of problems and persevere (SMP 1), you're leading them to reason with quantities (SMP 2), you're guiding them to model with mathematics, look for patterns, use math language and more. You are creating mathematical thinkers all while losing control. You aren't  saying, "I can't tell you that," rather you're asking the student what they think (remember that metacognition phrase from your education college classes?). 

    In a recent workshop I facilitated, participants were working on a task. I overheard a lady inquire about a strategy she was planning to implement. The lady sitting next to her replied, "Well don't ask Jenise because she won't tell you."  As a controller, I had two options after listening to her question 1. Tell her exactly what she needed to move forward or 2. Ask her and her group members what they thought. I chose the latter. They were able to confer, own their understanding and continue on with the task. 

     I encourage you to try your hand at being less helpful. In each grade level overview of the K-5 math units for Georgia are lists of questions you can use to allow your students to own their understanding and control their math world https://www.georgiastandards.org/Common-Core/Common%20Core%20Frameworks/CCGPS_Math_4_GradeLevelOverview.pdf. Once you do, post a comment to tell me all about it. 

Saturday, May 24, 2014

Beyond the Test

As Georgia's standardized test scores have been released, the recurring question that flows through the air is, "How did your school do?"  I think there are two ways to respond to that question. 

The first way is from the perspective of stakeholders, administrators, policy makers and many teachers. They look solely at the snapshot of the test scores to say this school is a high performing school or this system is a high performing system. 
For those tests, on those days they make a superficial determination about the work of the teacher, the knowledge of the students and the effectiveness of the school's instructional practices. 

So this means, a school with disengaging practices, procedural mathematics teaching and learning, and textbooks with superficial understanding for the teachers and students can be praised for the work they've done based on their test scores. Conversely, a school with highly engaging problem based tasks, conceptual mathematics teaching and learning, and standards-based practices may be frowned upon for low test scores. 

This brings me to the second perspective. This perspective sees the whole picture which includes student growth and "out of our control" factors. For example, a 3rd grader can enter the year reading on a kindergarten level and with intensive work end the year on a 2nd grade reading level. That same student struggles with counting one to one coming in but by the end of the year they can use simple part whole strategies to solve addition/subtraction and multiplication/division problems. This student made tremendous gains throughout the year, but will not meet grade level expectations on the state test. That teacher's and student's hard work is now overshadowed by a "does not meet" on the state test. 

The second perspective also tells the tale of two worlds. On one end you have the population that has high parental involvement, funding for tutoring and a healthy overall home life. On the other side there's very little parental involvement, which leads to no additional tutoring outside of what the school offers, a high population of homeless and/or foster children, not to mention a spike in child abuse cases. The students on both side can receive the exact same highly effective instruction in school, but due to the factors outside of our control, the students begin in two different starting places. 

This is why I believe it's so important to look closely at the student growth versus the snapshot test score. I found myself making comparisons based on that snapshot score and I'm sure others of you have as well. It wasn't until @Math_HCS pointed out the perspectives mentioned above. It helped me widen my view again to see the student growth pieces that were being overshadowed. So I encourage you to do the same. Widen your view, analyze your student growth data and create your own celebrations and goals based on those. Don't write a biography on a student based on one moment of his/her life. 

Thursday, April 17, 2014

A Troubling Problem

   Solving word problems has been a thorn in teachers' sides as long as I can remember. We've all attempted to remedy this issue by pointing out key words, saying key information with heavy emphasis and even making students redo the problems until they get it right. With all of these efforts, we still end up with students who cannot independently solve a word problem. Ugh!!

   SMP 1 tells us students should always be making sense of the mathematics. As I compare that standard to the practices even I have implemented in my classroom, I realize if this is happening students are not making sense of the mathematics. No wonder when students are working with word problems they just spend the wheel of computation and does what "feels" right. So how can you get students to the place were they are exhibiting SMP 1 when solving word problems?


(Sorry for the sideway images.)

    This problem was solved by a 4th grader. When I asked how confident he was with his answer, he felt pretty confident. 

   I rewrote the problem on another sheet of paper minus the question stem and we started anew. I first asked him to read the problem. 

Me: What's the context of the problem?  What's happening?

Student: They're ordering pizza and there's pizza left over. 

   We read the problem again. 

Me: What mathematical information is there?

   We read the problem a third time. 
Me: What mathematical questions could we ask about this problem? 

Student: Do you need to add or subtract?

Me: Think again about the context. 

  I asked the student to compare his answers. He pointed to the 3 wholes and said, "This one is correct.  The questions are different."
Me: What's different about them?

Student: This one says 'How much pizza was left over'. 

Me: Well what made this problem easier (referring to the problem without the question stem)?

Student: I was able to answer my own question. 

  This 3-Read strategy changed my perspective on solving word problems. This idea was flushed out in the document Instructional Toolkit for Mathematics shared on Dan Meyer's blog http://blog.mrmeyer.com/wp-content/uploads/OUSDMathInstructionalToolkit2013-14.pdf. When asked was this strategy just for the kids who can comprehend well, I swiftly replied, "No!"  Don't limit this strategy to just some kids, expose all students to this strategy, especially those we have trouble with solving problems. 

Friday, April 11, 2014

So Who's Failing

It's that time again, the end of the unit. You pass out your multiple choice assessment, confident in knowing you've taught your students everything they needed to know. You've shown them everything you could to make them understand the unit's concepts. You even supplied students with a study guide mirroring the unit assessment and went through every question on the study guide prior to the test. 

After taking the time to analyze the data from your assessment you're stunned by the results. 

How could this be?! More than half of your students are not proficient on the unit assessment. You think to yourself, "They failed.  These kids just don't get it.  I need to assign more homework.  They just don't listen to me!" All while you are denying any wrong doing on your part. 

As an effective teacher, you watch for pitfalls, wrong way turns and plain out misunderstanding along the way. This is hard to do when you are cruising through the pages of a textbook, covering the content superficially. It's hard to do when the only assessments you administer come at the beginning and end of the unit. It's also hard to do when you implement 20 question tests which take several days for you to grade. 

What's a better alternative to ensure at the end of the unit journey you haven't left half your class behind?  Observation rubrics.  As students are working through a task, the teacher circulates listening to math discussions, looking at student work and asking guiding questions.  The rubric has predetermined expectations based on the standards and related to the task. Once the teacher has checked on a student's thinking, the student's name is recorded next to the appropriate level of understanding. 

In this example you can clearly see which students are on target to master the standard and which are not quite ready. You can vary the task students will complete the next day or pull small groups to remediate and accelerate students. This process is continuous through the unit and provides a better idea of how you adjust your instructional strategies to meet students' needs. 

If you come to the end of a unit and half of your students still lack understanding, you haven't met their needs. The use of informal assessments such as an observation rubric is an extremely effective way to gauge where students are and what you need to change about your instructional practices.  Because my friends, if half of your students lack understanding at the end of the unit, they haven't failed, you have.



Friday, March 14, 2014

It's Like Standing in Line For Your Favorite Coffee

As a coach, majority of my work is directed towards teachers, so my interaction with students is secondary.  When I get the opportunity to work with students, I realize how much I miss it. 

I had the pleasure of working with students on dividing with fractions.  Their teacher jumped into the action to build her conceptual understanding. From that experience I realized, "I miss this!"  I miss the excitement students have when they make connections for themselves.  I miss asking those guiding questions to help students get to their understanding. 
So I've made the decision to pursue a classroom position.  I personally know teachers who would scoff at that statement. But have you ever wanted your favorite coffee so bad that you waited in the Starbucks line for "I don't care how long it takes" amount of time?  Well for me, working in the classroom is like waiting for that coffee.  All of the paper pushing and evaluations will not keep me from enjoying the sweet brew of students thinking critically and making sense of mathematics.  

To start from the beginning of understanding and watch them as they grow is my goal for the next school year.  It's like waiting in line for your favorite coffee. 

Friday, February 28, 2014

I Believe the Children Are Our Future


Wednesday morning I awoke to a retweet by @Natasha_Neffy which read, "Georgia Senate has passed a bill to withdraw Georgia from Common Core". WHAT! 



 I spiraled into a tizzy thinking about all of the work we have put into getting students to a place of understanding in mathematics. I thought about all of the ineffective teaching practices that were on their way out of the door due to Common Core.  I thought about all the teachers who set aside their fear of change to do what's best for students. 

Common Core has developed a bad reputation. From people believing it is the government "enforcing its rule" upon us, to others believing it confuses students with the mathematics. Common Core has sifted fears and insecurities of many teachers to the surface, exposing them. Instead of admitting these things and having a sense of vulnerability, they have found excuses and remain misinformed. They passed on these fears to parents, who in turn are misinformed. With all of this, Georgia now finds itself in a compromising position. 

Do we compromise the understanding of our students to appease those who are afraid of change?  Do we subject our kids to a life of, "I was never good at math"?  Do we bow to the pressure of the misinform?  Withdrawing from Common Core does just that!  These standards were written to build understanding of math concepts gradually. You would not want to live in a house built in a day, because chances are it would not withstand any storm. So why would we subject our kids to such construction?

Bottomline Georgia Senate, if you believe the children are our future, which they are, what future are you creating for us all?  Have you considered the ramifications of removing critical thinking and understanding by changing from rigorous standards to those which do not allow the building of understanding?

"I believe the children are our future.  Teach them well and let them lead the way, show them all the beauty the possess inside. Give them a sense of pride, to make it easier..." - Whitney Houston

Monday, February 24, 2014

Lessons From Homeschooling

Like other areas of mathematics, teachers too often rely on memory to ensure students, dare I say, understand measurement concepts. We go to various lengths to find the cutest activities for students to complete and encourage them to "Remember the one time we...?"  Only unfortunately they don't remember, some yes, but we weren't aiming for just some.  The connections are not made for all. Why is that?

I have a friend who home schools her four girls.  Before you begin making your judgments about what homeschool is or is not, please hear me out.  One thing I've learned from discussing homeschooling with Dawn is, her girls have authentic experiences with math concepts on a regular basis. Her oldest daughter has a solid understanding of measurement concepts, this I know based on your demonstration of her understanding.  
The pictured tasty treat was made from scratch, by for 11 years old daughter!  From scratch meaning, she didn't drop the contents of a box into a bowl and mix.  She measured the ingredients using tools accurately.  She has adjusted the recipe for make more or less cupcakes, no seriously guys, she made 1 just one cupcake from a recipe meant to make many more.  

So what's my point?  It is the experiences with measurement that help to shape and deepen our understanding of its concepts. What does this look like in a classroom setting?


It looks like activities where students engage with the tools and connect the use of the tools to understanding the concepts. An experience measuring how tall you are compared to your friends or teacher and what you used to determine the heights are retained more than completing a worksheet on "Which item is taller" or "What tool would you use to measure..."  

An activity using student feet to help determine why we have standard units of measure and what they are will aid in students using rulers correctly more than completing pages in a textbook.

Many of these types of activities can be found within resources like Math Solutions' Investigations, Tasks, and Rubrics to Teach and Assess Math; John Van de Walle's Student Centered Mathematics or Math Solutions' Sizing Up Measurement.  If these resources are unavailable to you, take a lesson from homeschooling and create authentic everyday measurement activities to implement in the classroom. 
For more ideas, you can visit my webpage Sensible Mathematics https://sites.google.com/site/sensiblemathematics/.  

Friday, February 14, 2014

Friends with Benefits

Personally and professionally I like to surround myself with people who challenge me, who make me better.  I tend to shy away from the "yes" men and women whose constant approval will create a fixed mindset and leave me with a big head and overgrown ego. Thankfully, I haven't had too many of those relationships. No, I have friends who quite often call me on my nonsense and challenge me to try new things. 

The new thing I'm trying, courtesy of my friends Graham Fletcher, Michael Wiernicki and Turtle Gunn are 3 Act Tasks. I started with the Apple's Solar Farm task, shared in a previous post and since then I've been on a bit of a snowball effect. I've created five more tasks which can be found on  https://docs.google.com/spreadsheet/ccc?key=0Are6h0vMbntddGVlQkE2VzgyZkdJb3NBWWwtamhJQXc&usp=docslist_api. These tasks will soon be found on www.101qs.com. Not many coaches in my district have made the shift to this innovative teaching practice that I have. That's one of the many benefits of having friends that challenge you.

Wednesday, January 29, 2014

For the Nonbelievers

I like to surround myself with people from whom I can learn. Over the past five years as a math coach, I have been surround by people who are not afraid to step outside the box and challenge the ideas students and teachers have about mathematics. The new endeavor attempted by a couple of my coaching friends is the use of 3 Act Tasks within the math class. If you haven't heard of them, check out Dan Meyer's blog http://blog.mrmeyer.com/?p=16470.  

My quick and dirty version of a 3 act task- present students with a situation or a conflict with very limited information. Allow students to pose questions that come to mind. Students estimate an answer that is too high and too low, then using only what they have begin to find a solution to the situation or conflict. As they work, students find they need more information and are able to obtain the information by asking for what they need. Dan says this is creating an intellectual need. 

This type of approach was introduced to me by Graham Flecther. The examples I've seen were with the intermediate grades up through high school. So naturally, my original thought was to try my hand with this approach in a 4th or 5th grade classroom. In actuality, my first experience was in a 2nd grade class. If you are a nonbeliever in giving students as little information as possible and allowing their curiosity take over, if you believe you have to teach the concept before students in engage in a task or you believe only older students have the ability to do such a thing; let me make you a believer. 

The 2nd graders completely blew my mind. As I walked around asking probing questions, I became more and more excited.  This is the task in which they engaged. Their questions didn't go in the original direction I had planned. It looked like I was going to experience some set back with questions such as, "is it a wedding," "is it a concert". 
With the possibility of the lesson unraveling, I posed the question, "How many panels are in the noted region?"  At this point, students took off thinking and processing, until they realized there wasn't enough information for them to arrive at a solution. Information was revealed only after a student inquired about the information. 

The strategies the students exhibited to multiply double digits ranged greatly. Students had their choice of which manipulatives to use within their groups. 


This group created nine rows of ten, but doubled the quantity to represent 18x10. 

This group realized that 10 groups of 10 was equivalent to 100, so they used their counters to make 10 groups of 10 and 10 groups of 8 to model 18x10. What they really were doing was the distributive property, but that wasn't an explicit goal of the lesson. Wow! Creating the opportunity to make sense of mathematics naturally brings out the concepts some teachers believe they have to "teach" before students can do it. 

This student drew an array for 18x10 and used repeated addition to solve. 


This group created 18 groups of 10 and skip counted by 10 eighteen times to arrive at an answer for 18x10. 

As if walking around talking with students about their mathematical thinking wasn't exciting enough, we got together as a class to discuss how the different groups arrived at a solution. I posted two explanations on one of my YouTube channels. http://youtu.be/gtv039ktFkI



From this task, one of those 2nd graders made a conjecture most 4th and 5th graders struggle with understanding. For that very reason, I recorded this thought on anchor charts and hung them in the hallway. 

In the math classroom, there is a time and a place for lecture and practice. But if you spend most of your time doing these two practices, it's likely that your students will miss out on the opportunity to make sense of the mathematics in which they are engaging. 

Saturday, January 18, 2014

Dance

The Dance card
The card reads: Step into the light. Share your gifts and talents with the world.

I've pondered over this card for a while and how it connects to my life. Yesterday I was forced into the world of blogging, a place I did not want to be. I don't like those kinds of people who feel like they always have something to say. Maybe because I'm a words person and I try to think through my thoughts before blurting them out all the time. Maybe because someone else wants or needs a turn in the spotlight. Or maybe because I know my ego and how it can get out of control if I allow it to always be in the forefront. So I
put off blogging as long as I could.

But it seems blogging is connected to the card I pulled at my last counseling session. At the end of each session you pull a card from a box and journal about how it makes you feel, how it connects to your life or anything that comes to mind. I do believe I have a gift of teaching. Why? Because I honestly enjoy it, I see the impact I'm able to make and because I took a spiritual gifts test on more than one occasion and scored the highest on teaching. So if my gift and my talents lay here, why keep it to myself? That's biblical, you know the story of the one talent man. I don't want to be "that guy" or girl in my case.

I guess coming out of my "me against the mainstream world" fight is necessary and a part of the work I am purposes to do while I have time left on this earth.

Reminds me of a Kid President question posed in one of his videos. What are you teaching the world?

Friday, January 17, 2014

A Coach's Reflection

Reflecting on last semester as a math leader is very vague for me.  Inbetween my numerous stays at Children's Healthcare of Atlanta, I vaguely remember going to new PLs, engaging in exciting math activities or trying out an innovative math idea within a classroom.  One would think that I have had an unfulfilling first semester, but looking at so of my works I've planted good fruit. I've created technology resources for my teachers, changed the way some teachers think about my math among other things. Check out my website and see what you think: 
http://schoolwires.henry.k12.ga.us/site/default.aspx?DomainID=4011 


Legacy is important to me.  When someone thinks of Jenise, there are certain things I want to leave within their span of memory.  I'm not being morbid, I'm talking about leaving one place and going to another. How will I leave my mark.  With going through this school year with a chronically ill infant, going back and forth to the hospital but still coming to work with a smile on my face is a good mark I would like to leave.  Effectively using technology within the math classroom is another mark I would like to leave.  So I'm working diligently to develop ideas for using it effectively. I've posted many things on my school site so far. Feedback is useful to those fighting the good fight within the classrooms. 
http://schoolwires.henry.k12.ga.us/Page/59792