Math Exchange

Today our math coach has set up an exchange between sixth grade teachers at the Middle School and fifth grade teachers from the three elementary schools. During the day we'll visit the current three different leveled math classes and then we'll have a chance to meet at the end to ask questions and exchange information and ideas.

At first, I wasn't going to attend this day because my sons have previously attended the Middle School so I have a parent perspective of the math program. Also the Middle School sends fifth grade teachers an update every year to let us know how our former students are doing. This information helps me to gauge the program I teach as well as how I coach individual students. Generally students have made a positive transition from the fifth grade program to the sixth grade math program.

Once the coach relayed the schedule, however, I asked to sign up because the schedule is not a visit alone, but instead an exchange which is an opportunity for all of us to talk deeply about the ways we teach students math. I know that the Middle School team is devoted to teaching mostly math all day and that they began a standards-based approach last year. I know that they are continually updating their program so I'm interested in the ways that they are employing current research to lift their program. I'll also look forward to seeing last year's students, and observing the many ways that the sixth grade teachers run their classrooms.

I really enjoy the ability to teach a subject with greater depth which is what the shared teaching model affords. It will be a profitable day.

Teach Math Well: Are We Asking the Right Questions?

Emails circulated about the value of using an online unit assessment versus the paper/pencil unit assessments of the past. It's a good question, and one that should be posed and discussed. Personally, I'm a fan of using multiple formal and informal formative and summative assessments, and I support the use of online assessments as part of that overall assessment approach.

I also believe that we have to be mindful to have a good assessment balance and not make teaching and learning all about the test--we have to make space for children to enjoy their learning. While it's important to discuss assessment types and the role of assessment when teaching math, there are also many more questions that beg our attention and discussion.

For example, one of the greatest math question that we face in our standards-based school communities, and how do we continually uplift and teach the students who are one or more years behind the expectations. Of course, I believe that math education should be progressive where every child is moving ahead from where he/she is and that the focus should be on that movement rather than if everyone is at the same level. For example if I have students at fifth grade who are testing at a second grade level and others who are testing at a seventh grade level, they all should be working to move up. I don't want those "seventh grade level" fifth graders to think they've achieved all there is to know in math and sail along without a good challenge, and I also don't want those "second grade level" fifth graders to get discouraged and always feel behind. So the question, How do we challenge all in positive, proactive ways resulting in good math growth, engagement, and knowledge?, is a great question to ask and discuss amongst peers.

Another good question to discuss in math is what are the best ways for specialists, assistants, coaches, and classroom educators to work together to maximize math teaching and learning for all. We have instituted Responsive to Intervention in creative ways that help in this regard. We also differentiate during core instructional times. The way we collaborate matters when it comes to uplifting children's skills, knowledge, and concept.

Further we can ask questions about content specific teaching and learning. For example, at a recent meeting, it was acknowledged that teaching the "behavior" of the base ten place value system is challenging. Students at fifth grade find it difficult to grasp that numbers increase by X10 as they move up each place in the place value system and decrease by 1/10 as they move down in value place by place. Fluency with that concept takes time.

Time is an important consideration. Many on the outside would like teachers to work like soldiers and be at the same place in teaching at the same time. This, in many ways, negates the where students are at and what they need. It also disregards the need for educators to make the curriculum their own and teach it with the artistry, experience, and analysis needed. Good teaching is not a robotic function, and good teaching makes good use of time. Unlike a robotic response, good teaching analyzes deeply and maximizes the use of time to teach all well.

Too often we spend time talking about questions that don't matter that much in education. Instead we should dig a little deeper and spend time discussing what matters--the big, deep questions that truly impact what we can do to better teach all children.

What Do You Do When a Child Arrives at a Grade Level "Behind" the Others with Regard to the Standards?

A great resource for math teaching and learning.

After reviewing a host of student data, I'm left with the question, What is the best way to teach students who are one or more years "behind" with regard to the math curriculum? I used quotation marks for the word, behind, as it suggests a negative label. We all learn in different ways and time frames, so I want to be careful with that term, yet I also know that when students come in far from the grade-level knowledge expectations, the learning community often thinks of those children as "behind" the others.

To answer my own question, I will create Boaler's "floor to ceiling" learning experiences that have what I've always called the 1-2-3 approach where 1 is review, 2 is grade level, and 3 is enrichment. I always open all levels to all students. Willingham in his book, Why Don't Students Like School, affirms the opportunity that exists when students review material that they "know" since there's always more depth to be gained by that review. I know that to be true because I've taught similar standards for years and each time I teach the standards anew I make more connections and learn more.

So with this 1-2-3 or "floor-to-ceiling" approach what's important and how does it work?

It works like this. Students enter the experience at level 1 with a review. For some the review will be quick and pointed, and for others the review stage will represent new learning. Level two is the grade-level norm or standard, and the place that we hope most students will master with the support of educators, classmates, and family members. The third level is enrichment and it's open to all. I find that when I open the enrichment level to all, it's amazing to see who reaches since it's never just those students you'd expect to reach. Often a child who struggles in one area of math may reach in another. That's why I'm not a fan of permanent grouping especially in the early years. I like the flexible grouping we use during RTI related to specific skills, knowledge, and concept goals.

Another great book when it comes
to matching learning with how the
brain works.

With the "floor-to-ceiling" or 1-2-3 approach, what's important are the following notes (and probably more):

• Introduce everyone to the big idea in an intriguing way. 
• Scaffold the experience so there are levels 1-2-3 and all levels are open to all.
• Leave the experience "loose-tight" with plenty of room for student choice and voice.
• Make time and space for discussion, share, and response.
• Use teamwork when possible and be strategic about how you create groups. Use a variety of group types so that students are working with like-partners, unlike-partners, mixed-ability groups, like-ability groups, interest-based groups, and more. As you employ various types of grouping, observe which groups inspire, engage, motivate, and forward student learning. 
• Use strengths/interest-based content and approaches as much as possibly and introduce many ways to learn and let students try out all the various ways to learn too. 

We can't predict how a child one or more years away from the curriculum grade-level standards will learn and grow. Sometimes when a learning experience is truly engaging, a child will leap ahead and demonstrate significant growth. Sometimes students will do this even if the experience isn't engaging as they reach a point of cognitive shift that helps them to merge and consolidate ideas with greater ease and strength. 

There are also times when a student remains stuck with a concept, knowledge, or skill. Give it the good try in multiple ways, and then take a break and return to that learning point later. 

Learning is not linear.

When teaching students who are behind when it comes to standards, think broadly and not narrowly. Make engagement the number one goal. Challenge yourself to work with that child in ways that helps him/her LOVE learning math. Next talk with the child and find out how he/she likes to learn. Work as the child's "servant" in learning. Tell them you are there to help them learn and you need their help in that regard. Assess regularly with the child and reflect too. Ask with the child, "What's working? and What's not working?" Work together to make optimal change. Teach the child how to be their own best advocate and learning manager. Explicitly let all children know that we're all on our own learning paths and those paths wiggle and waver as we learn more. 

How do you teach students who are behind when it comes to standards learning? Please share as I want to broaden my understanding of this as much as possible as I now we can grow our expertise in this area.

Merge Learning Mindsets/Behavior Lessons with Content Focus

Particularly at the beginning of the school year, it's essential to merge learning-to-learn mindset and behavior lessons with content focus. This integration helps students to gain confidence and skill as a learner as well as acquire the math content knowledge, concept, and skill.

The best way to do this is to have a ready list of learning-to-learn behavior/mindset lessons and match those lessons to the daily focus. For example I'll match a focus on collaboration with an initial number review and assessment during the Math Team T-Shirt lesson and the Global Cardboard Challenge project.

I'll weave more of the lessons from my Learning Mindsets and Behaviors website into other math lessons as well. Last year I did this regularly, and every time I focused on a learning to learn mindset and/or behavior lesson, I saw students sit up straighter with bright eyes as these lessons served to empower them and let them know that I knew everyone in the class was capable of success.

In a sense, the learning mindset and behavior lessons are catchy introductions that motivate the best of what students can do. In many cases, these lessons dispel long held myths about learning that students have learned at home and in the broader culture, myths such as some people can learn and others cannot.

To build this empowerment out event more, after I've exhausted my learning behavior and mindset lessons, I'll weave in current events, notable experts from all cultures, races, lifestyles, and religions, and new content and discovery. These kinds of introductions also serve to empower and engage students while making math meaningful. Valuable learning experiences always include a strong rationale as well as ways to make the learning brain-friendly and successful.

Please feel free to use the lessons I've created on my Learning Mindsets and Behaviors website--blended lessons that invite students into the learning. Also if you have other great empowering learning experience additions, please let me know. Motivating, engaging, and welcoming students to learning is as important as the content, concept, and skill learning--it takes both areas of focus to reach successful teaching and long term investment and learning success.

This little film is one example of an introduction I share at the start of the year--it's amazing to see how many students view this as new knowledge when they watch it and we discuss what it means.

Successful Math Community: Explicit Routines

It's important to visualize the math classroom and determine the routines that matter. Then it's important to explicitly teach and practice those routines.

Many elementary school teachers are masters at routine--they establish good routines at the start of the year and stick to those routines all year long. Others find this more of a challenge. A routine-oriented teacher is not better than the other, but the truth is that good routines create greater freedom and time for deep, meaningful, and joyful learning.

What routines matter with regard to your math classroom?

Transitions
Since our students move from classroom to classroom, making the time to teach transitions is integral to using time well. My colleagues did a great job with this last year, and I want to listen to their strategies so I can follow their lead. Good transitions save time and prepare everyone for quality learning.

Respectful, Targeted Use of Supplies
Since students move from place to place, they each have a drawer in the math classroom for their math notebooks and baggy full of supplies. It's important to make sure that everyone has the needed supplies including a grid notebook, pencil sharpener, colored pencils, and fine line marker at the start of the year. It's also important that shared supplies such as scissors, rulers, protractors, and manipulatives are easy to access, use, and put away. Early year introduction to supply locations, care, use, and clean-up sets the stage for a successful year.

Learning Experience Routines
Generally the learning experiences will follow a basic routine each day. In my class, students generally have an introduction, time to study, learn, make, or practice, and a closing comment or share. It's important to explicitly teach the routine so students know what to expect. You can ask students to monitor the routine too so that most of the time is their time to learn, create, share, and practice.

Speaking and Listening
One of the greatest challenges of classroom life is that you're typically working with large numbers of students at a time, that's why it's important to set speaking and listening rules and rationale up front. Typically, these rules lead speaking and listening:

• Raise your hand if you'd like to speak.
• Keep your hand down if someone else is speaking and then raise your hand when they are done if you'd like to say something.
• Speak with a strong voice so everyone can hear. It's advantageous to have a microphone available for the soft spoken students.
• Don't side talk when someone else is speaking.
• Listen carefully to what someone is saying, and if you want to add, but afraid you'll forget, write down your thoughts in your notebook so you're ready to share when the time comes.

Clean-Up

It's good to explicitly talk about and practice clean-up routines and expectations. Large numbers of students can make a big mess and it's important that they know how to clean it up.

Ask Questions, Seek Help

Students need to advocate for themselves, and it's important that we teach students how to do this. Generally I let students know that they can write me a note, seek me out when available, or email me if they have questions or need help. If it's an emergency, I tell them to interrupt me right away, and for leaving the room for the restroom or other reasons, we have a hand signal so it doesn't take too much time from the learning.

Organization

Teach students how to organize their supplies in varying work spaces and for a diversity of projects. For many students, organization is not natural and to provide students with organization tips can really help them succeed. 

Rules, Policies, and Protocols

It's important to review the "Never Go There" rules--rules that have to do with safety, rules such as how to use scissors, never throw things, don't use bad words, no name calling, and safe use of appropriate tools on the computer. You can ask students to add to this list. I tell students that it's always good to have a "Never Do That or Go There" list so that they don't do the things in life they can't reverse--actions that truly disrupt and hurt others.

Then we talk about general policies and protocols--what to do. Students will readily come up with this list. With the upcoming election in the news, this can be matched with the creation of a class constitution which is an effective way to learn about our government and govern the class too. 

These are some important routines to explicitly teach during the first six weeks of classroom life. Ruth Charney's book, Teaching Children to Care, further outlines important attributes of school life--elements that invite all children to a year of successful learning. 

I'm sure I'll add to this list in days to come, and in the meantime, if you have anything you would add, please let me know. 

Teamwork Builds Math Mastery

At the start of the math year, build teamwork by employing the Global Cardboard challenge. Also emphasize team in explicit ways through the Global Cardboard Challenge efforts and via the strategies and information included in the presentation below. It's worth the time to build a dynamic, purposeful sense of team at the start of the school year.

Teamwork Matters: Making Math T-Shirts

Start the year by focusing on the fact that students learn better when they work together. Emphasize that your math class is a math team, and as a team the way you work together matters. 

Ask students if they belong to any teams. Then ask them to tell you what's important when it comes to successful teamwork. After that, you may want to show one of my all time favorite teamwork videos, and ask students to look for the attributes of successful teamwork as they watch the video:

After the film, acknowledge that like the Panyee soccer team, most teams have T-shirts. Say that the class will have some fun with numbers as they make paper T-shirts and a class bulletin board that celebrates your dynamic math team.

To make the T-shirts, do the following:

1. Set up a computer and printer in the classroom. Have students take a good picture of their face and print it. I use PhotoBooth for this. Students go to the picture stand, take their photo, and print it one after another.
2. Hand out the number activity guide which includes a T-shirt template.
3. Allow students to work with calculators to complete and check their work. 
4. As students work, observe their efforts and listen to their conversation. This observation will serve as a good initial assessment of student effort and need--an assessment that will inform future lessons.
5. Have students complete the task in pencil, check the work with a friend, and then check with you. Coach students with regard to correct completion of the work. When complete, have students write over the numbers and words with a fine line pen, write their number on their t-shirt and add the fact data to the front of the T-shirt or just below, tape their picture on top and hand it in for a class bulletin board that will display all the students pictures with a title such as "Teamwork Matters: Marvelous Mathematicians."
6. When students are done, they can work together on the enrichment activities included on the number activity guide. 

This project is a great start-of-year activity, one that provides assessment, fun with numbers, vocabulary/fact review, and an emphasis on teamwork. I recommend. 

TEAM Matters: Global Cardboard Challenge

We've named our grade-level TeamFive and we'll use this graphic to lead their TEAM studies and collaboration.

Jo Boaler's book, Mathematical Mindsets, Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching, is a terrific well-researched book to read and use as you teach math in 2016-2017.

One study in the book that most caught my attention was a study that demonstrates the wonderful impact collaboration had on the success of all students. That's why it's important to start the school year with an emphasis on TEAM: Together Everyone Achieves More.

A good way to do that is to promoted the Global Cardboard Challenge as an initial team building activity. I've designed a number of activities leading up to the project to promote understanding of TEAM and one's place and responsibility on a team.

In years past students have remarked that this project was one of their favorite events of the year, and I believe that the project created a strong sense of TEAM across the grade-level too. Try it out. Let me know what you think. Year after year, I update and grow this project to best meet student's needs and interests.

Use Amazing Numbers in Math Class

Math class becomes a lot more interesting when you use amazing numbers.

You may easily teach math concept, knowledge, and skill by analyzing the math in current events articles and situations. Today's amazing space article is an article that will be understood much more with mathematical reasoning.

Below I'm going to collect a number of articles that provide a good stage for mathwork--articles that will lead students to use math well to understand the world around them.

Space Articles
New Planet with Three Suns

Fifteen: Building Positive Math Teams and Mindsets

Jo Boaler's book, Mathematical Mindsets, is a great resource for teaching math well. In her book, Boaler discusses the value of explicit efforts to teach and coach teamwork. I will follow her lead in this regard by teaching students the attributes of optimal teamwork as well as instituting team roles with regard to some of our math projects, particularly projects that teach math with a STEAM (science, tech, engineering, art, and math) focus.

To spur a conversation about team and what matters, I'll show one of my favorite teamwork videos:

I'll also use other resources that I've collected to inspire positive teamwork.

I'll likely include the attributes Boaler uses to describe mathematicians, mathematical thinking, and math study, attributes included in the presentation below. It's possible that students and I will create online or real-time signage as teams to post and refer to throughout the year to remind us of these attributes as we study and learn math. An emphasis on collaboration and mathematical mindsets at the start of the year will set the stage for a positive, collaborative, and open-minded math teaching/learning community.

Fourteen: Creating Class Community and Introduction to Line Plots

There's always the quandary with regard to starting the school year math program. There's a temptation to jump right into the curriculum in traditional math teaching/learning ways, yet when you do that you don't build community and get to know one another well. You also don't create an invitation to math learning and teaching--a curiosity and relevance for the subject.

Therefore, I prefer to begin the year by introducing students to the main vocabulary, tools, and concepts we'll study all year long in student-friendly, engaging ways. I don't detour too much from the standards as if I do that, I don't have the time to reach the expectations set by system and state standards.

One early review and community building lesson at the start of the year is the introduction to line plots. Introducing line plots with student- and family-friendly data points leads to community building and also allows students to review/learn a math concept/skill that they can apply throughout the year as they study multiple concepts in math.

To begin this study, students and I will create a data chart that includes data about the following student information:

• letters in first name
• birthday month number
• birthday number
• favorite numbers between 0-12

Note that the information items I use at the start of the year do not include information that could create worrisome comparisons or share. Then we'll create line plots for the data. We'll display the line plots for review and discussion.

For homework students will create similar line plots to describe family members. The following day we'll likely review, share, and write about those family line plots as I introduce math writing and math talk routines and protocols.

Throughout the year, we'll revisit our line plot work as we create more and more sophisticated line plots related to measurement and fraction understanding and problem solving. 

We'll use videos like the one below to develop knowledge and also to teach students how they might access videos online via our class website and elsewhere to aid their math learning and study.