With just over two months until the T^{3} International Conference in Chicago, we are excited to introduce the #T3Learns slow-chat book study on *Balancing the Equation: A Guide to School Mathematics for Educators and Parents*, by **Dr. Matt Larson and Dr. Tim Kanold**.* *All educators are invited to participate in this discussion.

Join Dr. Larson, president of NCTM and author of several key books on mathematics education, as he introduces *Balancing the Equation* during a T^{3} Professional Development Webinar on January 10th, 8 PM EST.

**Dr. Larson will be delivering a session at the T ^{3} International Conference based on the book with co-author Dr. Kanold, who is the conference keynote speaker and an award-winning educator and PLC expert.**

**Slow-Chat Book Study**

We will cover a chapter each week, ending shortly before the conference. We will use Twitter to share our thoughts with each other, using the hashtag **#T3Learns**.

With a slow chat book study, you are not required to be online at any set time. Instead, share and respond to others’ thoughts as you can. Great conversations will unfold – just at a slower pace.

When you have more to say than 140 characters, we encourage you to link to blog posts, pictures or other documents. There is no need to sign up for the study – just use your Twitter account and the hashtag **#T3Learns** when you post your comments.

Don’t forget to search for others’ comments using the hashtag **#T3Learns**.

Need to set up a Twitter account? Start here.

If you need help once we start, contact us (see below).

**Book Study Schedule**

We have established the following schedule and daily prompts to help with sharing and discussion. This will allow us to wrap up in late February.

Tuesday January 10, 2017 – 8 pm ET

Introductory Webinar with Dr. Matt Larson – T^{3} Professional Development Webinar

Week of January 16, 2017

Chapter 1 – Why Mathematics Education Needs to Improve

Week of January 23, 2017

Chapter 2 – A Brief History of Mathematics Education

Week of January 30, 2017

Chapter 3 – The Common Core Mathematics Debate

Week of February 6, 2017

Chapter 4 – The Equilibrium Position and Effective Mathematics Instruction

Week of February 13, 2017

Chapter 5 – How to Help Your Child Learn Mathematics

Week of February 20, 2017

Epilogue – Conclusion and Action Steps for Educators and Parents

**Daily Prompts**

We encourage you to post your responses to these prompts each day.

**Contact Information**

The moderator will be Kim Thomas.

Please contact kspry@ti.com if you have any questions.

-Kevin Spry

]]>

After the success of the slow-chat book study on ** Embedding Formative Assessment** we plan to engage in another slow chat book study.

A few years ago, as we embraced focusing our classrooms on the **Standards for Mathematical Practice**, a number of our community began reading and using the book by Margaret S. Smith and Mary Kay Stein, ** 5 Practices for Orchestrating Productive Mathematics Discussions**.

This book has been transformational to many educators, and there is also a companion book focused on the science classroom, ** 5 Practices for Orchestrating Task-Based Discussions in Science**, by Jennifer Cartier and Margaret S. Smith.

Both books are also available in pdf format and NCTM offers them together as a bundle.

**Simultaneous Study
**As our community works with both math and science educators, we are going to try something unique in reading the books simultaneously and sharing ideas using the same hashtag.

We know that reading these books, with the emphasis on classroom practices, will be worth our time. In addition to encouraging those who have not read them, we expect that those who have read them previously will find it beneficial to re-read and share with educators around the world.

**Slow Chat Book Study
**For those new to this idea of a “slow chat book study”, we will use Twitter to share our thoughts with each other, using the hashtag

With a slow chat book study you are not required to be online at any set time. Instead, share and respond to others’ thoughts as you can. Great conversations will unfold – just at a slower pace.

When you have more to say than 140 characters, we encourage you to link to blog posts, pictures, or other documents. There is no need to sign up for the study – just use your Twitter account and the hashtag **#T3Learns** when you post your comments.

Don’t forget to search for others’ comments using the hashtag **#T3Learns**.

Need to set up a Twitter account? Start **here**.

If you need help once we start, contact us (see below).

**Book Study Schedule
**We have established the following schedule and daily prompts to help with sharing and discussion. This will allow us to wrap up in early June.

The content of the Math and Science versions line up fairly well, with the exception of the chapters being off by one.

**Daily Prompts**

**Contact Information**

Moderators will be **Jill Gough**, **Kim Thomas**, and **Jennifer Wilson**.

Please contact kspry@ti.com if you have any questions.

-Kevin Spry

]]>But if it ** is** the question, you need an answer that reflects putting students’ success at the forefront. This is a question I have been asked all too often recently by both administrators and educators at all levels. Of course, the technology they are usually referring to is … the calculator. With the release of the Calculator Policy statements by PARCC and SBAC as well as state assessments such as the TN Ready in my own state of Tennessee, many teachers, principals, and district level personnel have often made the decision to simply eliminate calculator use from the classroom. “If they can’t use it on the test why should we let them use it in the classroom?” That is the rationale for many of the decisions that have been made.

As with any educational strategy or tool, in this case – technology, more specifically calculators or handhelds – the implementation has to be effective. Effective technology integration supports curricular goals. To effect change with the learner, the use of technology must employ the active engagement of the learner through participation alone as well as in cooperative groups. Frequent interaction and feedback from the teacher as well as peers that moves the learning and the learner forward is also needed. The teacher becomes the conductor as he/she orchestrates rich mathematical discourse around the investigation.

Students need to “use appropriate tools strategically” (CCSSM.SMP.5). They need to understand what the calculator does for them, what it does not do for them, and when and how it can help them develop a deeper understanding of the mathematical concepts they are investigating. And this is true from the elementary grades through the secondary course. Take a look at two examples: one from the elementary strand and one from the secondary strand.

The TI-15 is a powerful, pedagogically correct tool of investigation. This tool, when coupled with a rich activity such as “100 or Bust” from Texas Instruments, supports the development of deeper understandings of the foundational concepts of place value. Effective facilitation of this task includes reading a trade book, thus providing a literacy connection as well as guiding mathematical discourse through effective questioning. Students develop an appreciation for each of the three types of “tools of investigation” that are employed. And the activity can be easily adapted for use in kindergarten to the middle grades.

Being able to ** communicate** important foundational mathematical concepts,

Secondary students are now encountering mathematics that for many can be quite challenging, especially when they may have gaps in their mathematical experiences. *Walk This Way* (Texas & Jones, *Strategies for Common Core Mathematics: Implementing the SMPs*, Eye On Education, Routledge) is an activity that allows participants to use repeated reasoning to investigate mathematical concepts in a variety of graphing situations by physically representing mathematics on a life-size graph first. A variety of mathematical topics can be modeled – integers, basic linear and quadratic functions, complex numbers, and polar graphs – to cover the secondary bands. Investigating graphing kinesthetically at any level supports the development of deeper understanding and increased retention.

Students physically analyze how various graphs are transformed both on a number line and a variety of coordinate grids. By asking probing questions rather than just repeating formulas and telling how each of the components of an equation affects the graph, students are better able to develop meaning on their own and understand how functions behave. Students are able to understand and convey why certain changes to equations transform a graph as they work both on table top grids & number lines, floor grids and number lines, and on a graphing calculator/handheld. Technology is employed both as a tool of investigation and as a way to check and to make connections to other representations of equations and functions. Literature again can used to support developing mathematical concepts. Extending these basic concepts students can engage with the TI-Nspire iPad APP and create graphs to model real life contexts, such as this art exhibit found in an airport. Students again are engaging kinesthetically by “touching their math” on their iPad! This is truly a powerful experience for students to have.

So do we use technology or not? Technology, used in collaboration with rich tasks, other tools such as manipulatives, literature, etc., effective facilitation, and meaningful discourse can level the playing field for students by supporting making mathematics accessible to all learners, no matter what their grade or level. So what if calculators cannot be used on all the test? The true power of the calculator or handheld comes in to play as it is used as a tool of investigation – not just a number cruncher. Teachers can and should frame assessment experiences that model the next generation of assessments their students will be taking. But in preparation for those assessments and in preparation for the next mathematical experiences students will encounter on their mathematical journey, the calculator/handheld is a powerful tool that all students should have available in their mathematics toolkit.

]]>

We are excited that Dylan Wiliam is delivering the opening keynote and a number of sessions at the T³ International Conference in Orlando, Florida, on February 26, 2016.

Dylan is a leading educator on formative assessment (see his website here). His recent book *Embedding Formative Assessment* is a thought-provoking read for all educators wanting to better understand and implement formative assessment.

In preparation for hearing Dylan, we are going to embark on a “slow chat book study” of *Embedding Formative Assessment*. We invite all educators to join with us in this discussion.

Beginning in January, we will cover a chapter each week, ending just prior to the International Conference. We will use Twitter to share our thoughts with each other, using the hashtag **#T3Learns**.

With a slow chat book study you are not required to be online at any set time. Instead, share and respond to others’ thoughts as you can. This allows for great conversations to unfold at a slower pace.

When you have more to say than 140 characters allow, we encourage you to link to blog posts or other documents to share more.

There is no need to sign up for the study – just have a Twitter account and use the hashtag **#T3Learns** when you post your comment. And search for others’ comments using the hashtag **#T3Learns**.

Need to set up a Twitter account? Start here. If you need help once we start, contact us (see below).

We have established the following schedule and daily prompts to help with sharing and discussion.

Date | Ch | Topic |

Jan 2 | 1 | Why Formative Assessment Should Be a Priority for Every Teacher |

Jan 9 | 2 | Your Professional Learning |

Jan 16 | 3 | Strategy 1: Clarifying, Sharing, and Understanding Learning Intentions and Success Criterial |

Jan 23 | 4 | Strategy 2: Engineering Effective Discussion, Tasks, and Activities That Elicit Evidence of Learning |

Jan 30 | 5 | Strategy 3: Providing Feedback That Moves Learning Forward |

Feb 6 | 6 | Strategy 4: Activating Students as Learning Resources for One Another |

Feb 13 | 7 | Strategy 5: Activating Students as Owners of Their Own Learning |

Feb 20 | Conclusion |

Moderators will be Jill Gough, Kim Thomas, and Jennifer Wilson.

Please contact kspry@ti.com if you have any questions.

-Kevin Spry

@kspry

Re-posted by permission of Lucas Allen, Tech Powered Math @techpoweredmath http://www.techpoweredmath.com/

Originally posted on October 6, 2015

My wife was good enough to pick up extra bed time duty with our kids tonight so I could take in the latest Texas Instruments T³™ webinar, STEM Behind Health with TI Technology. As is always the case with these webinars, the content was excellent, incorporating interdisciplinary content from science and statistics. This particular webinar focused on TI’s Stem Behind Health, which I talked about more in a previous post. The content in their latest module focuses on breast cancer. I was quite taken with how they were able to both address mathematical and scientific issues while at the same time addressing a very serious health issue in a thought provoking way. At the webinar, it was announced this newest activity goes live on the Stem Behind Health website on Monday, October 12.

Attending the webinar got me thinking that there are probably readers of this blog who aren’t aware of the T³™ webinars, or have never attended one. I know how busy teachers are, but if you are looking for good ways to engage your students in a math or science context, give me the next couple of minutes to make the pitch for attending one this school year.

T³™ Webinars are taught by engaging instructors, who are either experienced educators or experts in a specific field. In the case of the tonight’s webinar, the instructors were Liz McMillan, Director of Education and Outreach at Sanford Research, and Jeff Lukens, a T³™ National Instructor with 34 years of experience in the classroom and 2002 South Dakota teacher of the year. The type of lesson that webinar instructors put together always involves a Texas Instruments technology such as the TI-Nspire™ handheld or TI-84 plus graphing calculator, but I have found that these webinars are more focused on engaging students on a particular set of concepts than they are focused on the technology itself. That said, the instructors do a good job of implementing the TI technology for teachers wherever they are, be it as a beginner or more advanced user. I have attended the T³™ International Conference on several occasions (which I would recommend to anyone as it is fantastic), and these webinars would fit right in if presented as sessions at the T³™ International Conference.

The webinars are presented live, and you have the opportunity to interact by asking questions via chat. The webinar I attended tonight had 101 participants; a reasonably small enough number that I believe just about everyone who asked a question got it addressed. The list of upcoming webinars is posted on the TI website. If you are unable to attend live, you can always catch the recording of a webinar on demand when it is posted in the large webinar archive shortly after the live session.

In addition to the new ideas you’ll leave a T³™ webinar with, you’ll also leave with some tangible benefits. First, Texas Instruments provides those that attend a live session with a Certificate of Attendance. Depending on your state’s rules, you may be able to use that as continuing education hours towards renewing your teacher’s certificate. Additionally, Texas Instruments creates very polished lesson plans and other materials necessary to accompany the lessons suggested in their webinars such as handouts for students and document files for the TI-Nspire™ handheld. Considering the cost (free), it’s especially hard to overlook this great source of professional development in a time of shrinking school budgets and busy schedules.

Link to original article: http://www.techpoweredmath.com/texas-instruments-webinars/

]]>The Computer Algebra System (CAS) enables students to investigate unit rates, opening up a world of options because the device recognizes words as variables. Teachers can actually enter “one cup of sugar makes two cookies” in fraction form on a TI-Nspire™ CX CAS and get the results shown here.

To promote deep thinking about the topic and engage students in a discussion, ask questions like:

- Why are these equations true?
- What stays the same?
- What changes?
- What other ratios would work?
- What other ratios would
**not**work?

Asking the right questions is key to starting effective discussions, but what then? Multiple representations help students visually see what the math is doing, which in turn leads to better understanding and skill mastery. Look at the following situation:

Joe can mow seven lawns in four hours. How many lawns can he mow in three days?

Now look how the CAS can investigate this problem using numerical forms, a table and a graph.

This allows students to see relationships between “doing the math” and “using the math.” See how long it takes for students to realize that the data is in hours, but the problem is in days. The number of days (three) appears nowhere in the data, which will generate questions from students. This opens up a broad range of “teachable moments,” which is what teachers love to see. The students want teachers to explain instead of begging them to listen.

Now let’s throw in some measurement geometry.

This introduces the concept of using unit rates for unit conversion. Although unit rates are a sixth grade skill, students can see how solving equations will play a part, even though they haven’t mastered that particular skill. Ask the students to investigate how the device reached that answer!

Michelle Bonds

@mibonds

https://usemorecas.wordpress.com/

]]>

**Leverage tools. See. Question. Think. Show what you know. Learn.**

We want every learner in our care to be able to say *I can attend to precision*. But, what if they can’t? How are we practicing, teaching, and growing as we attend to precision? What is your precise answer to the question:

*What is a fraction?*

Is your answer descriptive, clear, and precise for a 5th grader? a 6th grader? a 7th grader? You see where I’m going, right?

What if we use technology to visualize new concepts and interact with math to investigate and learn? What if we pair a process learning progression with a content learning progression?

I can explain and illustrate that a fraction a/b is the quantity formed by a parts of size 1/b, and I can represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0.

AND

I can apply mathematical flexibility to show what I know using more than one method.

Have you previewed the Building Concepts series on fractions?

Everybody knows that you must have common denominators to add fractions, right? Do we know why? If asked to construct a viable argument, could we? Can we draw it, i.e., communicate why visually)?

How mathematically flexible are we when it comes to fractions?

From Jo Boaler’s How to Learn Math: for Students:

…we know that what separates high achievers from low achievers is not that high achievers know more math, it is that they interact with numbers flexibly and low achievers don’t.

What if we facilitate learning that leverages technology, that blends technology and visible thinking, a. k. a, note taking, but creative visual note taking?

Let’s focus on the journey not the destination. How will we know if appropriate tools are used strategically? What if we change our essential assessment questions from What is ____? to Show how to solve ______ to focus on process and understanding? How might we encourage our learners to use technology to see, to ask, and to think?

Jill Gough, Director of Teaching and Learning, Trinity School

@jgough

Blog: https://jplgough.wordpress.com

]]>I just returned from the most excellent trip to Washington, D.C., where I collaborated with great math and science teachers and shared practices and needs with people from NSF and the White House Office of Science and Technology Policy. Best of all, I shook hands with President Obama when he presented the Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST) to me! What an incredible experience, and one that I want all of my science and math teacher friends to experience, so I thought I would share a little about the application process and the lesson that I submitted.

Presently the application portal is open for K–six and seven–12 in alternating years. There is talk of combining them, however, so you could apply any year regardless of grade. The application is usually due in April or May. You have to be nominated, but you can nominate yourself. My first year, I was nominated by my district supervisor and did not receive the award. The next time, I nominated myself and won. The application is almost like a small National Board Portfolio. It requires a 45-minute video and written entries about instructional strategies, assessment and leadership outside the classroom. Easy peasy, right?

My Lesson:

I chose to submit a video of my lesson, Discovering the Equation of a Circle. My lesson began with giving the students sets of ordered pairs and asking them to find the mathematical model that would fit the data. I gave them a linear set, a quadratic set, an exponential set and a set of ordered pairs that did not make a function (it was a circle). Some groups did not plot the points. They just looked at the relationship between x and y and created the equation, so when they got to the circle, they had no idea what the equation or the shape was because they hadn’t plotted the points. This was a good opportunity for the students to collaborate with other groups. Once they figured out it looked like a circle, I asked them if they could prove it. This led to using Siri to find the definition of a circle, and each group tackled the job of proving the points were equidistant from a center point. Some groups used the Pythagorean theoremTheorem from the given points to the point they thought was the center. One group used points they thought were the endpoints of diameters. Another student, Shauna, used her TI-Nspire™ CX handheld to plot the points and then used the equation template to find the circle that went through the points.

I had never shown the equation templates to the students, so she found this on her own. A great way to start the class the next day was by showing how her discovery can help us study equations of all circles and their transformations. She did not work through the math of the Pythagorean theorem (distance formula) that I had wanted the students to do, but her method led to an excellent discovery (as well an excellent use of TI-Nspire™ CX technology).

When teachers are able to provide students with tasks that they can explore and attack in their own way, beautiful discussions, learning and discovery takes place. Using a task like this I believe was helpful in me earning the PAEMST. I want to encourage you to apply. As your momma would say, “It’s good for you.” All of the planning, videoing and reflection will only make you a better teacher. If you don’t get the award at first, try again! That’s what I did.

Julie Shouse Riggins

@jrigginsEFHS

]]>When I was first introduced to a Computer Algebra System (CAS) device, I thought it was a great tool for my AP Calculus class. The more I used CAS activities the more I realized it would be a great tool for all math students.

I believe student investigations are key in deeper understanding of mathematics.

CAS devices such as the TI-Nspire™ CX CAS handheld and the TI-Nspire™ CAS App for iPad® give students the opportunity to investigate the why’s and how’s of math.

As I think about important skills for students, percentages stand out to me as an important skill for both elementary and middle school students to learn that is not understood completely. The students memorize the algorithms we set before them but never really reach the mathematical understanding of why and how we use them. Using the TI-Nspire™ CX CAS handheld and some teacher preparation, students can delve into the why’s and how’s of percentages. For example, start the lesson by putting the following slide on the board or send to student handhelds.

Ask students the following questions:

- What stays the same?
- What changes?
- Why do you think the last one is false?

Using a Quick Poll in the TI-Nspire™ CX Navigator™ system or a cooperative learning strategy facilitates student discussions on their answers. The students can use their devices to investigate other percentages to see if their theories hold true. Teachers can use the activity Solving Percent Problems from the Math Nspired website as a follow-up activity or intro activity for the lesson on using percentages to solve problems. As the unit progresses, other investigations and discussion starters could look like this:

Ask questions such as:

- What do you notice about the numbers?
- What is the relationship between the numbers?
- What conclusion can you make based on this pattern?

Also show some other percentages such as the slide below asking similar questions.

Of course as in any good unit of study, opportunities for practice and hands-on applications are needed throughout the unit to master the skill but getting students motivated to understand the math is the first step. Investigations such as these will allow students to delve deeper into the math instead of skimming the surface with algorithms only.

Michelle Bonds

@mibonds

https://usemorecas.wordpress.com/

]]>

How do your students experience learning right triangle trigonometry? How do you introduce sine, cosine, and tangent ratios to them?

NCTM’s Principles to Actions includes **build procedural fluency from conceptual understanding** as one of the Mathematics Teaching Practices. In what ways can technology help us help our students build procedural fluency from conceptual understanding?

Until I started using TI-Nspire Technology several years ago, right triangle trigonometry is one topic where I felt like I started and ended at procedural fluency. How do you get students to experience trig ratios?

I’ve been using the Geometry Nspired activity Trig Ratios ever since it was published. Over the last year, I also read posts from Mary Bourassa: Calculating Ratios and Jessica Murk: Building Trig Tables about learning experiences for making trigonometric ratios more meaningful for students. Here’s how this year’s lesson played out…

We first established a bit of a need for something called trig (when they finally get to learn about the sin, cos, and tan buttons on their calculator that they’ve not known how to use). I showed a diagram and asked how we could solve it. We reserved “trig” for something they couldn’t yet solve.

We use TI-Nspire Navigator with our TI-Nspire handhelds, and so I can send Quick Polls to assess where students are. Sometimes Quick Polls aren’t actually so “quick”, but these were, along with letting students think about what we already know and uncovering a few misconceptions along the way (25 isn’t the same thing as 18√2).

Next I asked each student to construct a right triangle with a 40˚ angle and measure the sides of the triangle.

I sent a Quick Poll to collect their measurements.

Then we looked at the TNS document for Trig Ratios. Students can take multiple actions on the diagram. I asked them to start by moving point B. What do you notice? We recorded their statements for our class notes.

Then I asked them to click on the up and down arrows of the slider. What do you notice?

What ratio of side lengths is used for the sine of an angle?

You all constructed a right triangle with a 40˚ angle and recorded the measurements. What’s true about all of your triangles?

- The triangles are all similar because the angles are congruent.
- The corresponding side lengths are proportional.
- We know that sin(40˚) is always the same.
- So the opposite leg over the hypotenuse will be the same?

Will it? We sent their data to a Lists & Spreadsheet page and calculated a fourth column, opp_leg/hyp. What do you notice?

Of course their ratios aren’t exactly the same, but that’s another good discussion. They are close. And students noticed that one entry has the opposite leg and adjacent leg switched because the leg opposite 40˚ is shorter than the leg opposite 50˚.

We didn’t spend long looking at the TNS pages for tangent and cosine … students were well on their way to understanding a trig ratio conceptually. They just needed to establish which side lengths to use for cosine and which to use for tangent.

There’s a reason that #AskDontTell has been running through my mind as I have conversations with my students and reflect on them. Jill Gough wrote a post using that hashtag over two years ago: Circle Investigation – #AskDontTell.

What #AskDontTell opportunities can you provide your students this week?

-Jennifer Wilson, NCBT

@jwilson828

My Teacher Webpage

Blog: Easing the Hurry Syndrome

Blog: Slow Math Movement