Math Talk

"Mathematics is a Language" - Josiah Willard Gibbs

Today I introduced the idea of "Math Talk" to my students.  I've read, discussed and heard about many initiatives related to giving students the opportunity to talk about and share math concepts.  Like every teaching venue, it's important to personalize the approach for your students and your overall classroom goals and style.

We started by transitioning to math by listening to a YouTube math song.  Then, using the strategies I'm employing with the daily 5, I started by engaging students in a discussion about the purpose of Math Talk.  Together we came up with many ideas including the following:

• to understand.
• to learn.
• to "know how to do it."
• to come up with strategies.
• to feel more comfortable
• to teach others
• to practice math language.

Then we discussed "Math Talk" protocols:

• Time: we agreed on 18 minutes and had a time keeper.
• Sharing Ideas:
• respect all ideas - no "making fun" of ideas.
• don't think anyone's idea is "stupid."
• be open minded to ideas.
• raise hand when you have an idea as we can't all talk at once.
• Pay Attention
• no side talk--write it down if you think you're going to forget.
• look at speaker (now and then, sometimes you may need to look elsewhere).
• try to stay focused; don't do other things.

After that, we tried our first "Math Talk."  Ms. Phipps, the student teacher was our time keeper.  I sat in the front of the room and scribed the notes related to our "Patterns for Counting to 1,000" discussion on a Google doc which students could view on the big screen.  At the end of the discussion, I published the notes and put the link on our closed NING network for students and parents to revisit at home.  

I'm excited to think about the journey ahead related to "Math Talk."  I'm also open to your thoughts, suggestions and ideas as we travel this road to deeper math understanding.  Thanks for listening.

The Math Year: First Lessons

Throughout the year I'll emphasize the elements of successful math teaching/learning as
described by Jo Boaler in her book, Mathematical Mindsets

As I think about the math year ahead for 2017-2018, I want to have the year's first lessons ready. Note that we have a system plan that I have to follow, and within that plan I have the ability to teach in ways that I have found to be successful.

The core program will begin with the lessons below, and the Response-to-Intervention (RTI) periods and math technology will serve to build on and enrich these lessons/goals.

Day One: 

• What is Math? 
• Why do we learn math in school? 
• What are the best ways to learn math? 

I'll begin by reviewing student names and supplies. 

Then I'll have students open up their Chromebooks and go to a Google classroom page that lists the questions above. I'll tell them to take a few minutes to add answers to the doc with their initials. The answers will stream in on the big screen as they write. 

After a few moments, we'll talk about each answer. For the question, What is Math?, I'll note that the definition of math is not a simple (as illustrated in this blog post and web page), however I like Keith Devlin's description that math is the science of patterns. 

Next we'll discuss the many reasons that we learn math and I'll emphasize that we learn math to become good thinkers and problem solvers--math provides us with many systematic ways to understand, discuss, and create. 

Then as I listen to children tell me about the best ways to learn math, I'll note that we all learn a bit differently from one another, and it's my job to understand how each student learns best so I can help them learn math successfully. Further it's important for every child to understand how they learn best to help themselves learn math and other subjects well. After all the student is his/her first and most important teacher. 

For homework, I'll ask students to write me a letter telling me how to teach them math--I'll ask them to be as specific as possible and tell them that their letters can be handwritten or typed and that they can put it in traditional letter form or make a mini poster, diagram, list or other format that will help me to understand what they want me to know. 

Finally if we have time, we'll watch a couple of introductory films about learning math, and then discuss how we might change or add to the list they've created. 

Day Two/Three: Building Community Birthday Math and What's Your Number

Note that the next five lessons will be interchangeable since they rely on the supports of the technology and math department so they may not be taught exactly in this order. 

Day Four: Intelligent Assistants for Math Teaching/Learning

I'll tell students that I read a great book about the future this summer and that the book was named, Thank You for Being Late by Thomas L. Friedman. Then I'll tell them that Friedman notes that we will all continue to use lots of "intelligent assistants" in our lives to learn. I'll ask them what they think that means. Then I'll introduce them to one intelligent assistant we'll use which is Symphony Math, a math online learning program that helps students to learn math through good interactive use of language, numbers and models. Since many students have experience with this, we'll talk about successful ways to learn with Symphony Math and make a list of those strategies for the classroom. Then students will sign in and get started. I'll do a lot of assessment with regard to how students sign on, access the technology, focus and more .

For home study I'll have students complete a short math facts assignment to warm them up for the next days work. 

Day Five: Assessment Helps Us Learn and Teach

On day three, I'll talk to students about assessment. First, I'll ask them what it is and what their experience with assessment has been like. We'll talk about what it means to assess our own work, and how we can use assessment to develop our performance and learning in any subject. Then I'll introduce the That Quiz facts assessment. I use That Quiz as a tool for lots of simple assessments and practice throughout the year. I'll show students how the assessments are accessed and displayed on the class learning menu, and then I'll have students get started with the assessments. When done, they'll work on their Symphony Math. 

For homework I'll assign a number of short That Quiz assignments which will be listed on the learning menu for students to use for practice and enrichment. 

Day Six: Using Assessments to Drive/Inform Your Learning

On day four, I'll have students analyze their That Quiz results with regard to the assessment. Then, I'll have a host of learning options available to help them reach for the next steps with regard to math fact accuracy and fluency. This will give them a chance to see how they can lead their own learning.

For homework students will be asked to access the same learning choices available in class and practice and develop their fact knowledge more. 

Day Seven and Eight: What's Your Number?

To build community and help students to get to know one another as well as review math vocabulary, we'll complete the "What's Your Number" activity. 

For homework students will begin working on a number fact array packet that focuses on specific facts and landmark numbers. 

Day Nine, Ten, Eleven

Additional systemwide assessments and completion of activities listed above. 

Day Twelve: Providing Context: Math Has a History

I will tell students that math is manmade--it's not natural though a purpose of math is to understand and describe the natural world. I will ask them what they know about math's history and then we'll watch a number of short videos that describe the history of numbers. 

For homework: students will continue their array packet.

Day Thirteen: What is a System? What is the Place Value System?

We'll begin by talking about what is a system and what makes up a system. We'll talk about the many systems they belong to and learn about. Then we'll specifically discuss the place value system, a system that we learned is a human-made system. We'll begin to create a big model of the place value system.

Following Days:

Then we'll begin to study the place value system with depth to master the following standards:

This unit roll-out will include the following lessons and activities:

• Formal/informal pre-assessments to see what students already know
• Explicit introductions to standards/learning goals
• Floor-to-ceiling exploration related to the standards
• Practice
• Problem solving
• Writing
• Math talk, debate and presentation
• Assessment, reflection

Note that I will assess the unit roll-out plan to make sure that I'm teaching w/future-readiness skills as noted in the mini posters at the bottom of the page. 

After that we'll continue unit-by-unit with the systemwide roll-out using similar elements to teach and enrich all standards.

Also, as I plan and lead the unit roll-out, I want to be mindful of future-ready teaching/learning that I culled from recent reading and noted in the posters linked on this post.

Today's Blended Math Program

The Math MCAS test is right around the corner in Massachusetts, hence we're in heavy math mode. As I've mentioned before, I really enjoy teaching math. It's amazing to relay concepts in pictures, numbers, words and problems, and then see students strive to understand and apply the concepts in meaningful ways. When students err, I point out that we've found an area for growth and understanding, and using a math workshop model I conference with students to tease out the errors to help students make meaning.

As I planned this year's review, I was once again amazed at the multiple resources available online and off.  It certainly is a "brave new world" of math education given the tremendous resources at our finger tips.

The key for the teacher is to blend those resources in ways that emphasize math practice, standards and mastery.  One book or text is insufficient today when it comes to math education as we now have the ability to craft a much more personalized approach to math learning for every child and family using the multiple resources available. Yet a streamlined online or offline text can offer teachers a solid guide.

This year I've been able to blend the following tools for math growth and strength. Typically I introduce a standard, assess, and then plan for the differentiated roll-out of the standard employing past concepts for review and new concepts for learning through the use of multiple tools.  I assess as I move along the standard path, adjusting instruction and materials as I go to best teach the students.

These are some of the wonderful math education tools and processes I used this year. I look forward to updating my class math website this summer to emphasize the best of tools and links as I move forward with math education and understanding.

Tools and Processes:

That Quiz: Free online program where students and teachers can easily make short (or long) concept/skill tests for student practice and assessment.  There is quick feedback and score reports for the teacher.

Symphony Math: An online math model approach to math education that places students at their current level and uses many personalized activities to move students up the ladder of math understanding.  What I like best about this tool is that it forces students to see numbers as models.

SumDog: An engaging online math game that meets students at their current skill level and provides many enjoyable, interactive games and contests for practice

YouTube: YouTube has countless math videos that explain concepts and provide wonderful ways to practice concept knowledge such as songs and dances.

The Internet: There are countless sites to find and print math worksheets such as mathdrill.com. There are also multiple creation sites that help one create tailored math practice materials such as crossword puzzles, comics and more for math practice and review.

Google apps: Google table provides a wonderful vehicle for quickly creating and sharing personalized, responsive math assignments, projects, sites and templates.

Paper/Pencil: Students continually draw, create and make math models to learn and explain concepts. Often they do this in their hard copy math journals.

Manipulatives: We have a solid supply of manipulatives that help students identify and depict mathematical concepts.

Xtra Math: This is a great site for fact practice which can be used at home or in school for free.  The site tracks students' progress and need.

State MCAS Materials: Problems and tools available online through the Massachusetts' Department of Elementary and Secondary Education.

RTI: This year we started using the RTI approach in math.  This has given us more time and staff to target specific math learning needs for students.

Quick Time/iMovie: These two resources have been terrific for student and teacher content creation which emphasize "math talk" and explanation.

Math Workshop: A differentiated approach that includes a focus lesson, small group and independent math exploration and work, math conferences and share.

Math Project Base Learning: Engaging, meaningful math projects that provide multiple, relevant opportunities for students' math exploration, learning and share.

Math Tech Time: At this time a menu of differentiated, targeted math links are placed online.  Students work on computers and follow those links to strengthen their skill.  The teacher is able to conference one-to-one and monitor the class's work/efforts with a steady stream of online reports.

This short list demonstrates only a fraction of the wonderful math tools and processes available for student learning today. The key is to find the best tools; tools that are both streamlined and engaging hence leaving most of the time for mathematical thought, practice, share and presentation.

How do you create an engaging, standards-based, blended math program for your students?  How do you work collaboratively with your peers to create, develop and strengthen your program?  What tools, strategies and practice do you find most useful?  What challenges still exist?

I'm anxious to give Kahn coaching, Manga High and Tynker greater attention as I incorporate further tools. I'm also looking forward to building my students' ability and efforts with regard to brain-friendly lessons, math talk and problem solving. Math education today is one terrific area for learning investigation and growth--one that I look forward to developing more.  I look forward to your thoughts and ideas in this regard.


Related Information
Blended Learning Article

Supporting Math Talk

How do you foster a great math talk in your classroom? In what ways do you develop the Standards of Mathematical Practice (SMPs) with your students?  I've been thinking a lot about that, and today I found myself one step closer to achieving a wonderful math talk.

Here's what happened.

First, I was strategic about seating. We gathered in the classroom digital share area, and I made sure that everyone had a comfortable place to see the big white board and participate in the conversation.

Next, I created a packet to foster discussion. I placed one of my tech savvy students at the computer to move the doc as we talked.

I told students how Math Talk is essential to building great math skills, and how some engineers I've spoken to recently discussed the way that many of their employees are good at calculations, but struggle with mathematical discussions that focus on number estimation and relationships. This introduction fostered investment.

We worked through the packet with lots of discussion as we looked for ways to describe patterns and relationships.  There were a couple of errors (now corrected) that actually created some great discussion. What I liked most is that students came up with many answers that I had not thought about. "I love learning from my students," I commented each time that happened.

Setting the stage for a great Math Talk matters--a stage with apt seating, a good discussion guide/packet, and a sense of importance.

How do you foster Math Talk in your classroom?  What strategies work best?  I look forward to growing this initiative in the weeks to come.

Math Smart?

How do we help students forge math smart brain paths so that they can think and problem solve with mathematical process and problem solving?

I suggest the following activities.

Positive Attitude Towards Math
Eliminate all negative math talk and replace it with math interest, talk, and activity.

Early Learning in Math
Read math children's books, play math games, and include math in early learning talk and play.

Computation Ease
While modern day math education leaders are prompting us to use technology to do most of the calculations, it's still important for young children to count, establish one-to-one correspondence, understand the basic operations, and know how to calculate and estimate simple computation mentally and on paper.

Rationale and Real World
As much as possible tie every math activity to a real world context or problem.

Progressive Programs
Teach math by building one skill on top of another. Look for ways to boost progressive math programs rather than grade-level approaches to math learning. Like reading, math takes on a step-by-step process for most concepts, knowledge, and skill.

Collaboration and Engagement
Allow students to regularly work together with engaging math activities.

Technology Integration
Identify and use the best online math tech tools regularly to develop students' math ability. Teach students how to learn with online tools and activities.

Professional Learning
Create teams of math professionals who study, learn, and develop programs together. This professional collaboration will help to develop all math programming.

Vital Math Learning Environments
Make sure that math is visible in thought provoking, engaging ways in the hallways, classrooms, and meeting spaces throughout your school.

History of Math
Tell the story of math.

Vocabulary
Make sure that students understand that math is a language that has its own vocabulary. Be explicit about teaching that vocabulary.

Math Play and Playgrounds
Create play spaces that allow students to experience math as they play.

These are a few starters as I think about how to increase math learning and engagement for my many students. What would you add to the list?

School Year Warm-Ups: Math Smart

Dear family members, camp counselors, and child care workers,

Many helpful links are available on this website.

Now that the school year has started or is right around the corner, what can you do to prepare your children for the math year ahead?

• First, do an attitude assessment--have you told your child you can't learn math. If so, change that attitude right now. Studies show we can all learn math, and there's no truth in those old myths about some being able to learn math and others not able to learn math.  Yes, some will have to work harder to reach success, but learning math is within everyone's grasp. So dispel the old myths about math, embrace the beauty that math holds, and give your child a positive attitude towards math learning.

• Next, access technology. Computers are inexpensive, and are probably one of the most important long-term investments you'll make for your child's education. Go out and buy a computer that has Internet access. If you can't afford a computer, talk to school personnel as perhaps there's a way to finance one. There are also computers available in most libraries, and often schools are willing to let students stay afterschool with parental support to use computers.

• After that, make sure you have WIFI.  The federal government has waged a deal with WIFI providers for affordable WIFI. Watch this video to learn more:  http://vimeo.com/96726329

• Then, try out these games and programs to boost your math ability. Sit down with your child and explore the games together. Decide which ones you like, then make a menu for math practice game playing.

• Math Game Page
• SumDog
• SCRATCH: Watch the videos, learn how to program as this builds great mathematical thinking.
• Khan Academy
• Xtra Math

• And, build your child's fluency with facts.  Get those facts as solid as you can with games, flash cards, making posters, and more. The better your child's basic facts knowledge is the more able he/she will be able to move ahead with higher level math concepts.

• Also, notice math in nature and the world you live in. Talk about math by wondering how many, what size, comparing/contrasting, and looking for shapes and angles.

• Read math books--there's lots of fun picture books in the library that include math concepts. Just ask the librarian for help.

• Cook with your child. Let your child read the recipes and measure the ingredients. 

• Sing math songs--YouTube has hundreds of math songs. Here's one of my math song playlists. 

• Play math board games. Yahtzee was the reason I was so facile with math facts. My cousin Judy and I played this game endlessly every summer.

• Work with money. Open a bank account. Find all the lose change in the house and bring it to a machine. Have a lemonade stand (in a safe place). Cut and use coupons. Make a money plan for the year ahead with respect to allowance, savings, and little jobs.

Most of all make it fun!  Math can be lots of fun, and if teachers and family members work together to dispel the old negative notions about math, we'll better prepare all students to succeed in this area with skill and engagement. 

We now live in a world that's dependent on mathematical thinking in almost every profession and discipline. Deep understanding and ability in math will help all children succeed.

What other ideas do you have for building competent, successful math students?  I'm open to your ideas, and thanks for your help!

What do you notice? Prepping for Math Talk

I've started using Google conversation/writing threads to foster community, develop writing skill, and share ideas. I post a thread or presentation and invite all the students in.  Each child adds to the thread with a post. I offer a comment or place a "sticker" on the page to respond to the child's work.  Children who are uncomfortable with the share may write their own document.

This week I'll post the math chart below and ask students to share what they notice.  This thread will help students to prepare for Friday's Math Talk, an introduction to multiplication facts, multiples, and factors.  I know that I don't like to attend a talk cold, instead I like to warm up to the idea with pre-reading, writing, and thought.  This thread will give students the same opportunity.  I'm excited to see what happens.

Students will comment on a thread similar to the chart below to prepare for Friday's Math Talk.

Students will add to the Google doc during homework time and class tech time.  I will print and hand out copies of this document to support our Friday morning Math Talk. 

Math Debate:Teaching Students Who Struggle in Math

Debate arose as to how to teach students who struggle with grade-level expectations in math.

I have read about this and discussed this often with colleagues over the years.

First, why do students struggle with math?  There are many possible reasons including the following:

• learning disposition
• foundation of math concepts, knowledge, and skill
• language barriers
• teaching strategies, programs, and efforts
• access and opportunity 
• health
• behavioral issues
• environmental issues
• neurodiversity and the way it is handled in schools/classrooms

When a child struggles in math, there's lots to consider with regard to how to help that child. In this regard, I think about the following questions:

• What was the child's math learning history like? Has he/she had access to fluid learning with regard to math concepts, knowledge, and skill? Generally children who have the opportunity to build with blocks and legos, play Minecraft and similar math-friendly platforms, participate in number games, and learn in a steady fashion come to the grade level with good math skills, concept, and knowledge. If a child has had little access to good math learning, then I'll look for ways to fill in the gaps.
• What is a child's attitude towards math learning and teaching like? If a child comes to class with poor self esteem and an unwillingness to learn, I'll think about that. I'll wonder why is he/she unwilling to participate in the class, and how can I make the teaching more accessible and user-friendly for that child.
• Does the child have access to the tools, programs, and events that foster terrific math learning and engagement? If a child doesn't have access to the supports, tools, programs, and events that other children enjoy, I will look to provide that child with access. For example most of the children in our school have access to technology at home, but some do not. Our school is working to provide 100% access to technology for students as one way to lift math performance and engagement. 
• Does the teaching/learning program invite the child into the learning? Is the program engaging and welcoming? My colleagues and I continually think about this question and redesign our program content and pedagogy to better welcome all children to the learning table. This work profits from our collective efforts, research, and creativity.
• What supports does this child get and how can these supports assist the child with math learning? Many children who struggle with math get a lot of other supports such as English Language Learning support, Special Education, Occupational, Speech, or Physical Therapy Counseling and more. Often a child who struggles with math has a complex learning profile that includes many sensitive and important issues to consider.
• Where is the child with regard to progressive concepts, math concepts that build on one another? I am in favor of a progressive approach to math learning and teaching rather than a grade-level standards approach. An approach like this helps all children to continue to build their math proficiency no matter where they fall on the progression from early learning to more sophisticated learning. Thankfully platforms like Khan Academy provide one avenue, an avenue that children who are ahead of grade level standards typically embrace. Saul Khan's recent Ted Talk also supports this approach. I believe schools can successfully apply this approach with creative collaboration and programming amongst all department members including regular education, special education, specialists, therapists, and more. The first step is to embrace a movement towards progressive math education rather than grade-by-grade education. I want to learn more about this and would love to see models of this in action. Of course, I'd also like to see Jo Boaler's research embedded into this progressive approach with the use of meaningful, rich, hands-on project/problem based learning that have the "floor-to-ceiling" scaffolding she promotes--scaffolding I've had the opportunity to witness and be inspired by. 

After considering these questions, I'll generally do the following:

• Work with family members, colleagues, and educational support professionals to pool our resources to support a child well?
• Analyze the supports in place to see if we can make the supports more engaging, targeted, and successful?
• Talk to the child and let him/her participate in his/her math program planning and efforts? What does he/she thinks need to happen to help him/her learn math more and better.
• Advocate for the child so he/she has access to similar supports, programs, and tools and his/her peers. The computer access mentioned above is one area of advocacy. Another could be the kind of homework/extra support a child receives to support his/her progression in this regard.
• Look for ways to better engage a child so that he/she generally wants to continue the learning at home. When the way we learn is engaging, children naturally want to continue the learning. For example there are computer programs that are dry and dull and others that are exciting and inviting--the more we can offer students math learning programs that are exciting and inviting, the more they will want to play and the more they will learn. It's been difficult to convince some in the school environment of this notion.
• Work to dispel the myths that some can learn math and others cannot.
• Look for ways to provide the academic support needed to help a child succeed in math.
• Work with colleagues to creatively design research-based programs to promote greater math learning and success. 
• Design and implement teaching content, strategies, and tools that help children learn well.

Going forward as the debate continues, I'll listen carefully to all sides and consider what I can do on my own and with the greater teaching/learning team of students, families, educators, administrators, and citizens to make math learning and teaching accessible and successful for all children.

In the meantime, I welcome your ideas. Tell me what has worked in your learning/teaching sphere to uplift students who struggle in math and help them to master math knowledge, concept, and skill with success, meaning, and engagement. I want to know. Thank you!

Developing a Blended Math Program

In the past few years I have written a lot about developing a blended math program.  At this point, potential tools and materials are abundant, and the pressing questions lie in the areas of strengthening the program so we are using the best materials, tools, routines, activities, and projects to effect engaging, empowering math learning.

As a classroom teacher, how do I blend all of these components into a solid, effective program?

Curation
First, I have to think about curation.  There's been a lot of talk and debate about what math materials are the best and how we identify effective math tools and practice? Currently, my best answer to this is that I look for tools that have many of the following criteria. Note I am using the word "tool" in the broadest sense to mean any material (online or off) that supports students' math learning.

• Engages Students: children want to use the tool, and are motivated to use often.
• Provides Meaning: the tool brings meaning to students' mathematical work.
• Accurate and Precise: the tool uses accurate mathematical language and information.
• Fosters Differentiation and Personalization: tool provides multiple paths to math learning.
• Just Right Challenge: the tool is not dull, but instead challenging 
• Blends models, equations/expressions, and words: to build meaning
• Collaborative: the tool works to foster and contribute to apt student collaboration.
• Provides Effective Feedback: feedback that inspires, motivates, targets, and teaches.
• 24-7: Tools which can be used in and out of the classroom.
• Efficient: Tools that are quick, and easy to access. 
• Results in Effective Learning
• Promotes Systematic Thinking and Problem Solving: : the tool engages children in mathematical thought and problem solving.

I want to reach out even more to colleagues to learn about the great tools they're using to effect math success in their classrooms. The more we share our best tools and practices, the better service we'll be able to offer to all students. 

Expectations

Next, I have to think about expectations. What are the system, state, and national expectations for math education. What are student and family expectations for math learning? What do I expect? The expectations as I understand them include the following:

• the development of a comprehensive foundation of math skill, concept, and knowledge for every student 
• engaging activities that include substantial teacher guidance and feedback.
• teach all standards with depth
• provide personalization and differentiation so that every child is coached to his/her best potential and math development during the year 
• know and understand the standards, content, and process well
• create a math classroom with multiple, well organized, accessible tools and spaces for math learning

Teacher Preparation

After that, there's the preparation including a complete understanding of the standards which includes:

• review all math standards with Khan Academy and related books and conferences.  
• regular review of current math information via blogs, threads, math periodicals, and researched articles. 
• review all information related to the common core standards, the PARCC testing requirements, and other state standards. 

Program Assessment and Scope and Sequence

• review current scope and sequence related to math.  
• review students' final assessments, and determine next steps. 
• determine more ways to provide students with the independent support and targeted learning opportunities they need via multiple learning paths including paper/pencil, games, explicit teaching, problem solving, online work, and more.

Classroom and Student Preparation

• rework my class math resource area by organizing and labeling all math tools
• create an environment that has multiple go-to reference posters to inspire and inform
• review and update all online math resources such as the class math resource website, math learning lists, passwords and more. 
• create summer math study cards for students that include online passwords for math practice games and sites, and offline math learning suggestions.

Program Components

Create a math learning routine and schedule with collaborating teachers that includes the following:

Math Dispositions and Learning to Learn

Start the year with a "learning to learn" unit where students learn that they truly have the capacity to learn any topic or subject they desire to learn, and all it takes is an "I can do it" attitude, advocacy, practice, thought, and perseverance. Also dispel the untruths related to math learning that pervade our environment--attitudes such as "you're either math smart or you're not," "math is boring and dull," "I can't learn math," or "my family doesn't do well with math."

Response to Intervention

As much as possible advocate for a five-day a week, 30-45 minute numeracy pull-out program with skilled teachers to support our most at-risk, tier three math students, students who fall one to two grades below the expectations of the grade level.  Also seek to build in apt interventions for students at tier two, core, and enrichment students during the same 30-45 minute numeracy time. I'd like to build in more formative assessment in this regard so that the interventions continually meet the objectives set.

30 Minutes Numeracy Block

This year we typically gave math about 90 minutes a day.  I think this was perfect for fourth grade, and would like to continue the effort.  The numeracy time included lots of games and personalized, differentiated, grow-at-your-own rate numeracy practice, projects, and activities. 

Core Program Components

The core program is a sixty-minute a day program that follows a sequence of learning events for each math unit. A math unit roll-out usually includes the following components:

• Unit introduction, vocabulary building.
• Use of manipulatives, model making.
• Multiple teaching voices: videos, peers, visiting teachers. . .
• Explicit teaching: focus lessons
• Paper/pencil practice.
• Problem solving with a focus on the Standards of Mathematical Practice.
• Online/offline games and activities.
• Formative and summative assessments.
• Small group, partner, independent work.
• Lots of teacher coaching and feedback.
• Grow-at-your-own rate, quick feedback online learning programs such as Xtra Math, Symphony Math, and Khan Academy.
• Review of past concepts and skills. 

Home Study

As much as possible math homework allows students to follow an online menu of mostly quick-feeback math activities including Khan Academy, That Quiz, and Xtra Math.  Students also watch videos to prepare for upcoming lessons, review concepts, and study vocabulary.  Hands-on activities and projects are sometimes assigned too.  I'd like to grow the differentiated, personalized aspect of home study more, and I'll think about that over the summer.

Math Tutors and Boost Programs

Several students benefitted from Boost programs this year.  Next year I'd like to ask for a regular update from the Boost program so I can incorporate that information into my coaching and feedback related to specific children. I'm also wondering if a mid-year re-look at the Boost program participants and progress would be helpful as sometimes you notice dramatic learning shifts with regard to specific students during the year. I also want to know upfront which of my students receive help from math tutors and special programs so I can think about how I can use that information to better serve the students.

The Friday Test
With the knowledge of the fact that effective feedback is one of the top ten elements when it comes to teaching students well, I want to give a test each week to help students' build their attention to detail, independent work, and thinking skills.  I will correct the test each week and provide targeted feedback. I always say I am going to do this, and then when other parts of the curriculum dominate, I don't follow through.  Next year I hope to follow through with this as it is very important to students' success with math. 

Preparing for, delivering, assessing, revising, and developing strong math programs is a big job for all members of the learning community.  I'm wondering if I'm missing any components as I create this list--components which will help me to serve my students better. If you think of any, please let me know. 

Math Teaching/Learning Start: Details

We'll play How Close to 100 in the early days of the school year. 

Now with school starting a few days away, I'm planning the very specific details--the day by day lessons. While scope and sequences maintain an early start for standards-based study, it's important to spend time up front building a strong math teaching/learning community.

The weekly math routine will include the following:

Core Program:

• Monday: Teaching/learning activities - taught in math block. 
• Tuesday: Collect homework, review That Quiz practice, continue w/core program - taught in math block.
• Wednesday: Pass back homework, assign new homework, continue w/core program - taught in math block.
• Thursday: Teaching/Learning activities - taught in math block.
• Friday: Students begin with math tech menu, complete w/teacher check-in review with individuals and/or whole class. Taught by all fifth grade teachers.

RTI

• Year starts with a focus on jump starting Symphony Math Activities and Assessments
• Then the year follows the RTI protocol as determined by the math team

Homework/Classwork

• Homework packets assigned on Wednesdays
• Homework collected and passed back on Tuesdays

Kindergarten/First Grade Buddy Math

• Fifth graders engage buddies in hands-on math activities related to the a unit of study the fifth grade is studying at a kindergarten/first grade level. This gives fifth graders an opportunity to be math teachers.

The math lessons to come include the following starting on the first transition day:

• Thursday, September 6: Names, collecting summer homework, Create math class norms, math study spaces/groups and routines for the math classroom. 
• Friday, September 7: History of people: introduction to timelines. History of people, skin shade, timeline - "The past affects the future." video
• Monday, September 10: No school
• Tuesday, September 11: Review norms, introduce and begin Name Value activity
• Wednesday, September 12: Introduce Math Reflection Journal (in 3-prong folder). Complete part of the assignment together and assign the rest due Tuesday 9/17. Work on Name Value activity.
• Thursday, September 13: Complete What's Your Name name value activity. Students who are done work on Symphony Math. 
• Friday, September 14: Symphony Math practice, follow-up goal setting with Symphony Math.
• Monday, September 17: Systemwide Assessment if ready. Possible facts assessment.
• Tuesday, September 18: Collect Homework. Review That Quiz and let students practice.
• Wednesday, September 19th: No School
• Thursday, September 20th: Pattern exercise. Pass out next week's homework, pass back last week's homework.
• Friday, September 21st: Boaler "Everyone can learn math" Ted Talk. Making Mini posters about a positive math mindset. (Teacher professional day)
• Monday, September 24: warm-up on facts and arrays: playing a math game
• Tuesday, September 25: Review order of operations with "How Many Ways Can We Make 48?" Pick up/pass back homework.
• Wednesday, September 26: Introduce new homework. Introduce unit one: Place Value
• Thursday, Place Unit continues
• Friday, September 27th: Field Trip
• Follow Standards-Based Scope and Sequence in days ahead using systemwide scope and sequence, unit guides, Boaler's grade five book, and other resources.

Kindergarten-Buddy Math

• Sunflower Glyphs
• Time Line 1-11; interview and make 1-6 timelines with kindergartners
• Place value finger activity

Great Learning at ATMIM Conference

Today I attended and presented at the ATMIM Math Conference. It was very inspiring to be in the midst of math enthusiasts and educators.

I began the day with informal conversation with a couple of math educators about their current challenges, goals, and accomplishments. I was excited to learn about a practice used at some schools which is Teacher on Special Assignment (TOSA). The teacher I spoke to, Timothy Marum, has had a year to visit multiple schools, read, and research about how to elevate blended learning in math classes in the system. He was clearly excited about this opportunity, and later presented the tremendous learning he has done.

During the first session, I attended Jenifer Carline's presentation about blended learning at elementary school. With Jenifer's permission, I linked her presentation with my presentation so I could incorporate her many terrific ideas to my teaching program. Jenifer regularly uses IXL in her classroom, and I learned that's a platform our system is exploring as well.

I presented during the second session. My presentation which is linked above described many of the tech tools and efforts I use to teach math. At the start of the presentation, I asked the participants to share a few sentences about where they teach and what pedagogy they use that they are most excited about. I included their wonderful ideas and share in the at the end of my presentation so that I can dig deeper into that information later.

At the break out session during lunch, Jennifer Fairbanks discussed how to elevate relationships with students. She discussed saying hello, acknowledging birthdays by playing students' favorite songs during the walk-in time, making good luck rocks for students to put on their desks during tests and quizzes, and prior to tests she give students time without pencils to strategize, share, and think about the test or quiz ahead--this slowed students down and helped them to do a better job on tests. She made time for students to get to know one another too using Google slides. Students make their own slides as does the teacher to create a scrapbook about the class that helps students to get to know one another and create community.

ST Math was presented as well during the break out session. ST stands for spacial-temporal. It is a personalized learning platform that is looking for 75 new schools to add to their schools and are willing to provide the platform via grants for the next three years. Beverly just received this grant, and the well researched and regarded site is eager to attract schools and provide these grants.  This platform is particularly good for EL students since there it is primarily visual and there are few to no words. The program invites productive struggle which builds deep conceptual understanding of math as well as growth mindset and perseverance in math. Student data is also provided via this program.

Karen Campe discussed her use of "My Favorite Puzzles on Twitter" and invited us to follow her @karencampe and take a look at the many puzzles offered via the following Twitter addresses:

• @YohakuPuzzle or www.yohaku.ca
• @Cshearer41 for geometry puzzles
• @solvemymaths by Ed Southall

#MTBOS and #edchatri (8pm on Sundays) Twitter connections were recommended as well.

Many math teachers are using Google classroom and all the Google apps as well to streamline and improve instruction. We learned about a new math platform named Graspable Math and there is currently a research study related to this tool that involves a math game. I can't wait to look this over since I've been hungry to find good math resources for students in my class that love gaming. A strength in this program is to help students look at equations forward and backward rather than the typical left to right direction. Christine Heffernan from WPI, the individual who introduced my school system to Assistments introduced this too.

Timothy Marum @tmarum23, a tech integration specialist from Rhode Island, presented a thought provoking blended learning presentation that began with a great video about the future of work:

Tim is the individual I met earlier in the day who is a TOSA teacher so I was excited to hear about his research. Tim shared the popular quote, "If you always do what you've always done, you'll always get what you've always got." He noted that to change by 10% is a reasonable regular goal. He noted that the choices can be overwhelming, but begin with one, celebrate what you do, and then try more.

He spoke about the beliefs related to teaching mathematics beginning with how we use Google forms in math class. One teacher uses it once a week with the question, "I wish my teacher knew" and students complete that sentence which provides that teacher with great ways to respond to student needs in a quiet, personalized way. He also collected information about the room with Google forms and shared that data with us with Google Form metrics. Tim introduced the book Fish as well as productive and unproductive beliefs about teaching and learning mathematics:

He also reintroduced me to Dan Meyers' Table Talk work, work I would like to replicate more in my class. It was exciting to hear participants describe how they use this approach to engage students and deepen student learning. It was noted that it takes time to build that kind of culture with students. How we update tasks is important. We need to make the tasks more student-friendly while not reducing the rigor or deep learning available.

A big emphasis of the day was how we lead good learning with Mathematics Teaching Practices, which emphasized that we should let the students do the hard work. Let the students utilize the Standards of Mathematical Practice. Use student evidence, provoke their thinking, and make their work, ideas, strategies, and processes transparent and visible in the classroom.

Teachers should do this:

Students should do this:

So many great resources were shared such as The Right Question Institute, Kaplinski's work including the open middle, clothesline math,  My Favorite NO,  Go Formative, and edreports.com,  Accountable Talk posters to help students with their math talk, Quizlet Live and shutter folds for math notebooks.

In the end, the entire day was a productive day which made me realize once again how important it is to attend professional learning efforts regularly to update your practice, find out what's going on in the greater teaching/learning community, share with colleagues, and challenge yourself to try something new and/or better. ATMNE's next conference is in December and then there will be another ATMIM conference in April. I recommend that Math teachers in New England join ATMIM/ATMNE to connect with a preK-higher ed community of math teachers and learners as one way to develop your practice into the future.

Teach Math Well: Learning Update

I continue to find my Tuesday night math class to be both informative and inspiring.  The pace of the course is a perfect match for my busy school schedule, and the content continues to serve as both affirmation and challenge for my current teaching program.

After a thoughtful YouTube film related to the benefits and practice of formative assessment, our professor, Mary Corkery, presented highlights from a webinar that was presented by Dr. Paul Riccomini, President of The Division for Learning Disabilities (DLD), one of 17 special interest groups of the Council for Exceptional Children (CEC), the largest international professional organization dedicated to improving educational outcomes for individuals with exceptionalities, including both students with disabilities and the gifted.

The webinar discussion served to both affirm and challenge the math program I currently teach to my fourth grade students. As I expected, Riccomini emphasized the need for positive, math-friendly teaching environments where all professionals exhibit confidence, knowledge and positive language related to math teaching and students’ ability to learn. He supported the notion that more time should be spent on strengthening teachers’ understanding of math concepts and knowledge since many elementary school teachers lack a strong foundation in math.

As he listed the attributes of a successful math program, the one area he mentioned that I would like to increase is students’ time to think and talk aloud with regard to math problem solving.  Due to class sizes, students often don’t have time to talk out a problem or question aloud, especially students who may take more time to process or verbalize their thoughts. Since I have many volunteers, teaching assistants and specialist teachers working in my class, I hope to use our collective resources to give students more time, in small groups, to thoughtfully discuss and solve meaningful math problems related to the Massachusetts State Frameworks which include the Common Core Standards.

I was pleased that recent updates in our system-wide math program reflect the six pieces of a successful math system including the following:

• A Strong Belief System.
• Assessment and Data.
• Instructional Support.
• Refinement of Instructional Supports.
• High Quality Professional Development.

Our system has created greater opportunity for teachers to attend worthy math courses and conferences to boost their professional repertoire in this regard. This movement towards greater differentiation with regard to professional development in math is serving to boost teachers’ knowledge and strength in that area.

Riccomini emphasized a tiered program with a strong emphasis on the core program which aligns well with our school system’s current movement towards increased RTI (response to intervention).  I was pleased and affirmed by his call for standards-based classrooms that actively engage in purposeful learning experiences that stimulate curiosity, enjoyment and deep understanding of the mathematical concepts. Too often, math activities are mundane, and I would like to move towards greater engagement and purpose in this regard.

He offered his ideal for the math lesson breakdown which included this list:

• Fluency practice and homework review.
• Standards focus.
• Vocabulary (literacy is very important in mathematics).
• Mini lesson-whole class instruction.
• Work sessions - flexible grouping and small group intervention.
• Closure and sharing.

The current program at my school includes the features above.  Fluency practice is often completed during transition times and morning work. Homework is often given via quick-feedback Internet sites such as That Quiz, TutPup, SumDog or Xtra Math, all free, engaging math websites for young students. The standards are communicated via the classroom math website, social network and the unit/lesson introduction.  Vocabulary is practiced in a number of ways including the use of charts, crossword puzzles, the Frayer model and multimedia projects such as film.  I find that crossword puzzles elicit a lot of discussion when it comes to vocabulary thus enriching students use of mathematical language in a natural way.

The webinar supported my colleague Mike O’Connor’s notion that learning facts is “mental push-ups.”  He suggested that schools employ explicit, direct teaching to help all students attain fact mastery. Rather than “Mad Minutes,” he recommended that teachers carefully assess students' number sense and begin to build their fact fluency from early skills to later skills with targeted intervention. While listening to the webinar I created this assessment based on Riccomini’s research and other research I’ve done to begin a targeted program with my student who demonstrate little fact knowledge.  I’ll build a similar assessment and intervention for children who have mastered addition facts.

Not surprisingly, Ricomini relayed that fractions is the "biggest weakest area" in terms of math in the United States, and if students don't learn fractions well, they will have great difficulty grasping algebra. He stated that students don't realize that fractions are numbers, instead they think of a fraction as only "part of the whole." Rather than saying 1/3 is larger than 1/6, they should say that 1/3 is a greater amount of the whole than 1/6. He emphasized the use of a number line (with both negative and positive numbers) to build number sense in all areas including fractions because the number line explicitly shows quantities. He offered the article, "Developing Fractions Instruction for Kindergarten Through 8th Grade," as an excellent resource.  

Currently I am teaching measurement standards and the correct use of a ruler. I have noted to students that a ruler is a number line," but now, after the webinar, I'll explicitly use the ruler to guide students' efforts related to counting and marking specific fractions on the number line with this exercise. I also plan to take a recent measurement open response problem and revise it with a variety of rational numbers (not just integers) to give students the experience of using the ruler or number line to solve complex problems that involve fractions.

The Tuesday math class continues to invigorate my math instruction and knowledge, and I'll continue to share the highlights with those that read my blog. Please let me know if you have any links or thoughts related to the information above.

Math Program Design (revised 10/30/12)

What does your math program look like? Do you stick to one series or book, or do you use a myriad of materials?

I continue to think deeply about math education in my class.  Underlying my thought is the premise that math is a marvelous subject to learn and teach.  I want to make it meaningful, relevant and enticing to students.

I teach math in a multi-faceted way including the following components. The program is based on the Massachusetts State Standards.

• Weekly Computation Practice in-school and at-home.  Children are encouraged to “climb the computation ladder” by practicing their fact/skill level and taking That Quiz tests (about 4 or more a week) and using other online venues such as FastMath, TutPup, SumDog, XtraMath and BigIQ.  I review student print-outs and emailed copies regularly and have mini conferences with individuals and small groups regarding their math computation development at that time.

• Weekly Target Skill: Each week we’ll target one skill set.  Students will receive an introduction to that skill on Monday via a teacher lesson, videos and practice.  During the introductory lesson, our notes will be taken on a Google doc and/or anchor chart, then published on our class Math Website (new venue) for review, revision and addition. We will review the skill again on Wednesday and Thursday.  Then students will have a skill quiz (formative assessment) on Friday.  The page of practice links, notes and information will be posted on our class HomeStudy Google doc and NING, a closed social network, for student and teacher review.

• Explicit Teaching: Each day I will spend time on explicit teaching related to grade level math standards (note class doc is a work-in-progress).

• Practice Pages: I will assign a number of practice activities on Monday that will be due on Friday. The activities will come from many resources.

Link to Word Problem Strategy Video

• Problem Solving Workshop (similar to writing workshop): Once a week we’ll spend an hour or more on math problem solving using multi-step math problems similar to those on the MCAS test and new common core multi-step problems. We'll review problem solving strategy, complete problems with small groups and partners, edit/revise and share.

• Project Based Learning (PBL):  Students will engage in a number of collaborative math projects that integrate skill, concept, and knowledge to develop their math problem solving, communication and presentation skills. The Fraction Project is one example of this kind of project, and the "Khan" video project is another.

• Vocabulary:  We will continue to focus on math vocabulary as part of the overall program.  Vocabulary learning will take many different forms throughout the year. I will access a wonderful math vocab flash card website, math dictionaries, crossword puzzles, and other resources to build this skill.

• Differentiation: Friday formative assessments will dictate differentiation efforts. Differentiation will be based on individual student need and targeted through a number of practices including individual/small group efforts and multi-modal instruction. This year we will also employ RTI as a way of meeting all students' needs in math.

• Math Writing and Communication: Students will practice explaining their thinking and questioning with Math Blogs, project work and problem solving workshops. The focus will be concise language/numbers and clear explanations that even a "first grader" can understand and learn from.

• Math Talk: An opportunity to discuss and share our math thinking aloud.

The components above will be integrated as often as possible with other content areas. For example, this week I'm using relevant data to teach and practice place value skills. The components will also be integrated with each other as units evolve. Time and energy is always a challenge, so the pieces need to be well choreographed to sustain just right student response, motivation and optimal learning.

How is your math program different than mine? What critical points did I miss? What suggestions do you have for me? Thanks for listening.