Teaching Walls: App-Friendly?

Many educators face challenges when it comes to technology since they are unable to easily access apps and programs that they learn of. This lack of ready access prevents the good teaching possible. For example if an educator has access to technology in fluid, workable ways, he/she can test apps and other programs with regularity and student input. However, if the systems for tech access are cumbersome, lengthy, and inaccessible, then educators will quickly lose interest and the needed timeliness to try out new apps and programs and employ them for best student learning.

For teachers to do their work well they need ready, regular access to the best tools, supports, and programs. Teachers do their best work also when they have voice and choice with regard to what they use and how they use it to teach well. When others, distanced from the learning, hold the reigns of teacher tools and programs, voice and choice is diminished and children don't get the deep and dynamic programming possible.

In light of this, systems need to think carefully about the following questions:

• How are curriculum decisions made? Do teachers have voice and choice?
• Are the people choosing the technology distanced from the daily classroom efforts and work?
• Are teachers and administrators asking the right questions when it comes to quality teaching and learning?
• Is there a good synergy between and amongst administration and educators when it comes to curriculum design and implementation?
• How is the entire learning community including students and parents involved in this decision making?
• Do we make decisions based on good informal and formal data analysis, discussion, and debate?

Khan Academy Fan

I continue to be a Khan Academy fan. His well supported learning/teaching platform provides students with helpful videos and practice exercises. Students may practice a skill again and again, and teachers and parents can use the platform to help support children.

As you can see from the chart above, my students have just started using Khan Academy to practice fifth grade math standards. Most students have completed less than 10% of the practice exercises so far this year. One chid has almost finished fifth grade so he'll likely move ahead to sixth grade.

In addition, Khan provides students with coding exercises and learning. Yesterday I introduced several students to those exercises. They were very excited. 

We're fortunate to have free access to the incredible learning tools that Khan Academy provides. The key is to coach and teach students how to use these tools as one way to support their learning.  Tools like Khan Academy support the fact that "the sky's the limit" when it comes to what's possible in teaching and learning today. 

Fifth Grade Standards Survey: Using Data to Teach Math Well

This is a snapshot of what some of the survey data looks like. 

I created a fifth grade math standards survey with one question that encompassed the main idea of each fifth grade standard. Students took the survey this week, and this morning I spent time analyzing the data. As usual, the data demonstrates a range from students who have little knowledge of the fifth grade standards to students who are very familiar with the standards' content.  The data also revealed that there are areas of the fifth grade standards that most of the class is very familiar with and areas that only a few have experience with.

I will use this data, in part, as I plan the program for the year ahead. I hope to employ Boaler's "floor to ceiling" approach by creating a number of learning experiences that begin at the review level and extend far beyond fifth grade if students want to take it there.

I have shared the data with the entire teaching team including paraeducators who will be providing a lot of one-to-one support, grade-level teachers who will lead "Response to Intervention" sessions, the math coach who will work with us, the math curriculum director, and the building principal. We all spend time at Professional Learning Community (PLC) meetings looking at data, both informal, formal, and observational, to discuss ways that we can teach each child well.

I will also share this data with family members at the fall conference as one way to demonstrate to family members the standards students are learning and where their child currently falls with regard to those standards. The data will provide a good discussion point about how we can work together to support each child's continued math development throughout fifth grade. I will also use this assessment at the end of the year as well for some or all to assess student growth. I may not use it with students who have already demonstrated precision with most or all of the questions as I will use other assessments for those students.

This process of giving the survey copied below is one way to know who my class is and what they need with regard to developing a strong math foundation. Feel free to take the survey below if you'd like and don't hesitate to provide me with feedback. I will continue to develop this approach.

Analyzing Students' Work Habits, Attitude, and Social Skills Survey

I took all of the work habits and social skill standards from our report card and a few more standards that I include in my teaching and added them to a Google form student survey. Students took the survey. Just taking the survey gave students a chance to think about the language and standards with regard to expectations and attitudes and behaviors for learning success.

Now I'll take the results that represent about 2/3 of the student response (there's still more students to take the survey and I'll update the response accordingly), and give students a chance to analyze the data.

With their math teams, I'll have students study the data chart below. Similar to the way our teaching team analyses data, I'll ask students to first share what they notice. Then we'll share questions that arise about the data. After that we'll discuss how this data set might affect individual's and the class's learning and teaching this year.

As I look at the data, my next steps include the following:

• Recognize that most students have great attitudes and work skills.
• Look for the individual students who answered "rarely" or "never" to see if there are any patterns there. If it's the same student, I want to sit down and talk to that student. If it's a few students, I may have a small group devoted to this.
• Look at the "other" comments and those that made those comments. I want to take their words seriously and see how that might affect my teaching and learning.
• Look closely at the areas where there was more scatter, and talk to students about how we might help the whole class to achieve in those areas.
• Think about categories that are not included in this survey--categories that are integral to learning well today. What would you add?

There were also a few errors in the survey that I need to correct. Students will take this survey including the new questions added again in January before we mark the progress reports. I'll be interested to see how the explicit teaching and learning we'll do together now will affect the results then. 

1. Learning Math Begins with a Good Attitude

This With Math I Can website has many helpful links
for teaching and learning math. 

Today officially begins the math year. After spending the first few school days on team projects, today we'll begin our math focus.

Today's theme is that our attitudes affect math learning engagement and success.

We'll start with the the With Math I Can video listed on this page.

We'll then talk a bit about the video and a few organizational matters.

After that students will review the day's online learning menu and then follow the menu which includes completing an attitudinal/behavioral self assessment and math warm-up games.

How Do You Keep Up with the Research?

Boaler's research points to the advantage of collaboration for students, and
it can be inferred that this collaboration works for educator development too. 

I received an invitation to sponsor a learning event within my school system. It was a clearly outlined invitation, the kind of invite I support when it comes to creating dynamic learning organizations. Hence, I had no choice, but to respond positively by submitting a presentation topic.

I thought a lot about what I wanted to present and lead. I knew I wanted it to connect to my "word," the acronym that will lead my work this year: TOME - Teamwork, Observation/Reflection, Math w/STEAM, and Everyday Learning, and I knew that I wanted to choose a topic that would contribute towards creating a useful, valuable math learning community.

I decided to propose a 15-hour learning event that would help colleagues and I to keep up on the latest research and literature related to math teaching. In addition, I chose to include creating websites and "hosting conversations" information and practice within the learning event. Hence educators who choose to sign up will engage in the following activities:

• create a learning/teaching website, 
• read, study, and reflect on new research related to math education, 
• engage in collaborative conversation that leads to wise action ("hosting conversations")
• readily apply the research to their current math teaching
• reflect and share the application of research to their teaching and its results

I believe this learning process will help the teachers who sign up and me when it comes to updating and deepening our mathematics teaching in many positive ways.

I've come to realize that the best presentations I offer are presentations I'm curious about and invested in--presentations that serve to create conversation, encourage collaboration, and result in positive student learning.

How does your system support collegial share and professional learning? How do you contribute to these efforts? When do these efforts result in meaningful learning and share?

I wonder if any or many will sign up for my class? One obstacle to this is that teachers' schedules are very tight leaving little room for extra study. Yet, one strength is that teachers can earn a salary increment credit and Professional Development Points (PDPs). Also, it will provide educators with evidence for their evaluation goals and provide them with a collegial team with whom to develop their math teaching and learning.

Let's see what happens.

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. 

Maker Math: Volume Exploration - The Candy Box

There's been many iterations of the volume related candy box exploration, and this is one I'll use with students in the days ahead to teach and practice finding the volume of three-dimensional figures. Prior to teaching this lesson, students will study and learn to use rulers.

Story

Bon Bon Recipe and Picture Site

Angela liked to make candy. She especially enjoyed making bon bons the old fashioned way. Her candy bon bons became so popular that people started asking if they could buy them from her to sell at their shops. Angela decided to put each bon bon in an individual box, and then put 24 individual bon bons boxes in each big box. That way people could display the big box while selling each individual bon bon.

First, she designed an individual box for each bon bon. She created a net made up of squares that measured one inch on each side. That was the perfect shape for her bon bons as they fit tightly, but did not squish the candy. Angela worked with a local packaging company to find the just right paper--a kind of paper that wouldn't melt the candy and keep its shape too.

Next she wanted to make a good strong and beautiful box to fit all 24 bon bon boxes. That's where she needs your help. Follow the directions below to help Angela.

Net Maker

Math Investigation

1. Take a look at the bon bon (real or pretend (a clay version)).
2. Create the one-inch box. One-inch box net available via this website. 
3. Go to the Maker Station and choose the kinds of paper(s) and other supplies you'll use to make a box that can easily fit 24 bon bon boxes. The Maker Station for this project includes a variety of paper weights, cardboard, tape, and decorative materials. 
4. Design your box net and create the box.
5. Complete the box data sheet and try out the enrichment options listed on that sheet.

Follow-Up

• Have students bring in a number of recycled boxes. Measure and figure out the volume of those boxes.
• Make a collection of nets available for students to make, measure, and describe. 
• Practice figuring out the volume of a variety of three dimensional prisms: simple sheets,  more complex Common Core practice. and word problems.
• Show this Khan Academy volume video:

Real World Connections
Tell students that there are companies that's goal is to make just right packaging for products. There's even a packaging magazines and websites. Happi is one example. Ask students what skills they think a packaging expert would need, and how a business like that would be important. Show the videos below that tell how cardboard boxes are made:

More about Packaging and its effect on the environment. 

Packaging Design

Math Homework Study and Routines

“I know you've heard it a thousand times before. But it's true - hard work pays off. If you want to be good, you have to practice, practice, practice.” -  Ray Bradbury

Many studies report that there is little gain from homework, yet I'm not ready to give up on math homework altogether as I believe homework still has value with regard to building good study habits, practice, and independent or family time to think deeply about math ideas.

I do want to heed the homework research and results though by treating homework routines with greater care, differentiation, and simplicity. I don't want homework to turn into added struggle for students or families. Therefore I will establish a positive homework routine beginning on the first day of school.

The routine I'll foster includes the following actions and goals:

• Students will receive a back-to-back weekly assignment sheet (see below) each Wednesday.
• A math practice challenge problem or activity will be assigned for three school day nights: Wednesday, Thursday, Monday, and Tuesday. The time to complete the practice problem will be a 5-10 minutes.
• There will be a 5-10 minute online math tech activity suggested for each day.
• Enrichment activities will be shared as well and those options will be optional.
• Parents or guardians will be asked to sign the sheet each week on Tuesday night to be returned on Wednesday. 
• The assignment sheet will be due each Wednesday and I will review and respond to the students' efforts as well as their weekly class efforts on the weekly sheet and return sheets by the following Monday. 

There are many reasons why I want to establish and embed this routine into the math program.

First, I want a way to think carefully about, and respond to, each child's efforts each week. This simple sheet will give me a chance to do that. Children thrive when they get regular, positive and helpful response.

Next, I want family members to regularly know about the math concept, knowledge, and skill we are focusing on. Although I do explain that in the newsletter, parents are more likely to look closely and engage in a conversation with their child when they have to sign off on a child's paper.

And, I'll use this review, in part, to inform the program as I'll gather important data about student effort, mathematical thinking, and need. I'll be able to use that information for program design and coaching meetings as I work to teach all children well. 

Establishing weekly study and practice routines helps students to learn math well and see the connection between good routines, practice, and learning well. 

What routines do you establish at the start of each school year to promote student success and regular, positive teacher/parent response? How do you coach students in ways that support these routines with success?

Mathematics in Massachusetts: Preparing for Next Generation MCAS

Membership in The Association of Teachers of Mathematics in Massachusetts is one avenue to keeping up with
expectations and changes related to Next Generation MCAS and other state-wide math initiatives.

I like to stay on top of new initiatives. I don't have to backtrack and re-step to meet new policies and protocol. Hence I've signed on to a number of good resources that inform me about upcoming changes and expectations. Massachusetts' Department of Elementary and Secondary Education does a good job with communication. The Commissioner, Mitchell Chester, writes a weekly newsletter that keeps all educators in the state abreast of what's happening with lots of links, details, and opportunities for learning and leading.

Similarly there are many agencies in the state that help to inform and prepare educators as well. Recently I joined one of those associations, Association of Teachers of Mathematics in Massachusetts (ATMIM). ATMIM just sent out an update so that educators can prepare for our upcoming assessment changes for 2016-2017 school year. I respond to the update notes below:

• ". . .all schools will administer the computer-based versions of the ELA and math tests in grades 4 and 8. Fo grades 3, 5, 6, and 7, schools may elect wither the computer-based or the paper-based tests next spring." The note goes on to say that the state encourages schools to use computer-based testing at as many grades as possible. Fortunately, our schools are well equipped to give the computer-based tests. Khan Academy is free and provides student with good practice for these online tests. TenMarks is another program that provides students with good practice for these kinds of tests. Schools may want to look closely at their computer-use schedules so that students have adequate use of computers for this practice and learning. Also, I recommend that schools invite families in early in the year to learn how to use Khan Academy so that they can support their children in this study. This computer time should be in addition to the core program as I don't believe computer practice/learning programs should replace the creative, collaborative, and critical thinking skills-oriented math programs that make up the core program. 
• The state offers support with regard to preparation for these tests. It's my guess that it's best to reach out for this support, if possible, during the lazy days of summer when they're likely to be less busy. "Department staff in our Office of Digital Learning (odl@doe.mass.edu) and in Student Assessment Services (assessment@doe.mass.edu) are available to answer questions from districts and provide additional assistance."

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Teaching and Learning: Numerical Expression

It's great to start the school year with a challenging, engaging math lesson. Children love to come to school at the start of the year and learn something new. This sets the stage for a vigorous, engaging year ahead.

Teaching numerical expression lends itself to engagement and provides students with a terrific skill to use as they learn, practice, and apply mathematical operations with numbers simple and complex.

Introduction: What Do These Expressions Equal?
Evaluate one or more of the expressions below in any order by hand or with a calculator. Giving students the chance to use a calculator takes away the pressure to remember facts and to calculate correctly. This frees up all students to reach for higher level learning in this lesson. 

8 + 6 X 5 - 1/2 + (8-3)

99 - 1 + 2 X 3

Let students play with it. Some will finish quickly, others will take a bit of time, and some may not know where to begin. Give the students about 10 minutes, then ask for children to come up to the board to explain their thinking about each expression.

Teach Order of Operations

Show Flocabulary's PEMDAS movie. While some mathematicians are not in favor of PEMDAS, I still think it's a good tool for early learning with regard to Order of Operations. As students work becomes more advanced, they quickly understand where PEMDAS doesn't exactly fit, hence I still believe it's a good starting point. 

Also introduce this graphic shared by a former student:

Study and Practice
Net talk with students about what they can do to remember, study, and apply the Order of Operations. List their ideas. Then let them work with classmates to do all or some of the following activities plus any good ideas they've come up with that you want to add to the list:

• Create a mnemonic, poem, picture, or mini poster that will help you remember the Order of Operations.
• Watch the PEMDAS rap over again, then make up one of your own.
• Make up your own expressions and evaluate them. Check with the teacher.
• Write 5 different expressions and 5 different equations that equal 50 (remember expressions do not have equal signs while equations do). Use at least two different operations in each expression. Make sure you use every operation at least once. Use parentheses, brackets, and/or braces in at least two expressions.
• Use exponents in at least two expressions. 

More Practice

Study the chart below. Then determine where you might add parentheses, brackets, and/or braces to simplify the challenging expression and puzzle below. Then solve the puzzle and expression.

ASSESS

After a day or two of practice and some Khan Academy review and study related to the topic too, it's a good time to assess students' skills. This is one assessment that provides the teacher with a good understanding of what students learned and still need to know.

Related Grade Five Standards

Seven: Know the Math Content

You will be able to teach math well if you know the content well.

Too often elementary school teachers don't have a solid foundation of math concept, knowledge, and skill, and realistically, for many educators, it's been some time since they studied math with depth and it's also likely that when you learned math you may have learned it mainly by memorization rather than deep, conceptual study, the kind of study we utilize with students today.

There are many paths to learning the content well in preparation for the school year.

One of my favorite teaching/learning vehicles is Khan Academy. I recommend that you get to know this platform well and do all the exercises associated with the grade level that you will teach in the year ahead. Khan Academy utilizes the latest research with regard to teaching and learning math and develops student understanding in a blended way using mathematical language, models, real-world problems, and many exercises. You may complete the whole grade level section during the summer or plan to complete each unit section prior to teaching that unit. Khan Academy is a terrific resource for teachers and students everywhere when it comes to deep understanding of math concept, knowledge, and skill. Even better, Khan Academy is free and accessible anywhere that you have a computer and WIFI.

Another way to learn the standards and content is to take a course at a local university. When the new standards were announced a few years ago, I signed up for a course right away and it was an awesome, collaborative way to gain expertise with regard to the standards.

Further there are multiple standards-based platforms online that help you to gain a firm understanding of all the standards and how to teach those standards, and system resources offer support too.

To know the content well prepares you well for the teaching and learning ahead. Summer is a great time to shore up content knowledge and skill. Once you gain expertise in the grade-level standards, its important to grow your knowledge of the foundation skills, concept, and knowledge leading up to your grade level and the mathematical content that your grade-level knowledge leads to--the multiple grade-level standards beyond the grade you teach.

Six: Math Manipulatives, Tools, and Proceses

As you prepare for a terrific math teaching year ahead, affiliate with supportive organizations, establish a positive math teaching mindset, make time for a dynamic room set-up, create a website, build knowledge of expectations, and make plans to introduce math manipulatives and tools as well as the protocols for strategic use and practice.

Utilizing manipulatives help students to learn and apply math knowledge, concept, and skill.

To use math manipulatives, process, and tools well students need to know what they are and where they are located. They also need to understand the protocols associated with good use so that the tools, processes, and manipulatives are available when and where they need them.  You may couple the introduction of specific manipulatives with early year lessons, practice, and vocabulary review. Essentially beginning the year with these kinds of lessons lets students understand the playful, hands-on, and accessible discipline math is and provides them with engaging avenues for mathematical thinking, exploration, and study.

I've listed some of the tools, processes, and manipulatives I plan to use at the start of the year below. It's a list I'll continue to add to, and if you have suggestions for me, please let me know.

Grid White Boards and Pens

Students really enjoy learning math with grid white boards and pens. A great early year lesson is using the white boards to set up a coordinate grid, plot points, and create a picture. After that students can create another picture and set of coordinates to share with a friend. The most important protocol with regard to white boards is where to store them, how to clean them, and organization of the pens (and caps).

Rulers
A great way to learn about rulers is to make your own rulers. An early year lesson on using a ruler to make a ruler introduces students to the language of measurement as well as benchmark fractions and the fact that the ruler is a number line. Later students can practice drawing lines of specific lengths, making margins, learning to start at the 0 point, and later practice using the rulers to draw designs. Early learning about how to use the rulers and where to store them allows students to access rulers whenever needed during the year as they complete projects, make math models, and study numbers.

Tiles

Tiles are a great resource for all kinds of math teaching/learning, and at the start of the fifth grade year using tiles to review facts and arrays is a great exercise. Beginning with 24 tiles and asking students to make as many different arrays as possible is a great exercise for initial tile use and review of arrays, facts, area, and perimeter concept, knowledge, and skill.

Legos and K'nex
Building and creativity toys like Legos and K'nex offer positive math model making materials and free time play too that supports math teaching and learning.

Google Apps
Google Apps are terrific for math teaching/learning. Beginning the year with teaching students how to use Google table and draw to create math models is very helpful. Students in fifth grade will use Google apps to make number posters for numbers 0-100. The posters will include meaningful illustrations of the number, the numbers' factors and some multiples, number facts, expressions equivalent to the number and equations too. There's more information about this activity on this post.

Pattern Blocks
Early year introduction to the definition of a pattern and the properties/attributes of pattern blocks enables students to use these blocks all year to inform math study and project work as well as to have the lens of "pattern seeker" and "property/attribute identifier."

Tangrams
Tangrams are lots of fun to use and provide a great way for students to develop mathematical thinking and understanding of two-dimensional shapes and their properties. There are great online tangram exercises as well.

Origami Paper
Having a collection of origami paper, origami books, and online origami sites also supports math teaching and learning. In the past few years, we've had an origami expert come in to teach math with origami. Starting the year with a simple math origami activity introduces students to this wonderful math activity--an activity they can explore more at home and during their free time.

Math Books
Having a basket or book case filled with math related books is a great way to demonstrate to children that reading about math is a great way to learn math. There are lots and lots of great math books out there, so many that you could actually begin math class every day by reading a short excerpt from or entire math picture book. These books have been well organized and researched, so it's a great way to teach.

Online Math Games, Songs, and Videos
Introducing students to online math games, songs, and videos, and making those sites easily accessible via your math website provides another enjoyable avenue for math learning and teaching.

Scissors
It may seem silly, but many students don't know how to use scissors well. An early year activity with paper folding and cutting can help students to study symmetry, right angles, and the properties of two-dimensional shapes. You can use this lesson to review scissor safety and protocols too.

Colored Pencils and Markers
Since the fifth grade year includes lots of math model making, students can practice making arrays using graph paper, colored pencils, and markers early in the year. This can be coupled with the tile lesson and will support students' model making all year. Students can learn how to use fine line markers to border edges, while using colored pencils to shared different model parts. Research has demonstrated that using color helps students to delineate concepts, parts, and ideas in math. An early year explicit lesson in this regard helps students to make precise models all year long.

Cubes
Learning to use cubes provides a great opportunity for students to learn volume. Our cubes became difficult to connect last year, so this year I'll likely use sugar cubes. Or I may use this as an opportunity to teach students how to create nets and then use those nets to make three-dimensional figures, and later use those three-dimensional cubes to learn and study volume. The more we can deconstruct concepts with manipulatives and project work, the better able we are to help students develop deep understanding of mathematical concepts, knowledge, and skill.

Base Ten Blocks and 3D Models
At fifth grade I prefer using online base ten blocks to review the base-ten system, but it's also good to have some base-ten blocks available for trading games to build understanding. Last year I used the 3D printer to create a 3D base ten model which was a terrific exercise, one that would be great for students if you have access to 3D printers.

Coding
Teaching students to code early in the year will support students' creation of animated math models. In the past, I've used Khan Academy coding and Scratch in this regard. Prior to the Base Ten Number System unit, I'll make some time to review coding with students so they can animate models that demonstrate the "behavior" of the base ten number system.

Paper
I have many types of paper in my classroom. Organizing the paper well and introducing the paper to students will help them to choose the right paper for the right task. I'll discuss paper types and we'll use lots of different kinds of paper at the start of the year so students know what to choose and how to use.

Pencils, Sharpeners, and Erasers
So often students' hands get tired because their pencils are dull. We'll talk about sharpening pencils regularly so you have a good point. We'll discuss when to use an eraser and when crossing out is just fine. The goal here is to know how to use the tools well so that most of the focus is on developing a strong mathematical skill, concept, and knowledge foundation.