If you are a WEA member looking for STEM clock hours, consider attending my Desmos workshop on July 29th at Prairie High School in Vancouver, Washington. We will explore the Desmos graphing calculator, Desmos Classroom Activities, and Desmos Activity Builder so that teachers are prepared to integrate this tool in their classrooms to facilitate and support student learning. View the agenda or click here to register!

# CL Byte #3: Give Card Sort Feedback

In this video I talk through how to use Desmos Computation Layer to give students feedback about the accuracy of their card sort. Here is the Desmos Activity Builder I used in this video. Enjoy!

# CL Byte #2: Giving Feedback on Table Entries

In this video I talk through how to use Desmos Computation Layer to verify if the values entered in a table are correct and then give feedback. Here is the Desmos Activity Builder I used in this video. Enjoy!

# CL Byte: CL note with input

This year I facilitated a Desmos Computation Layer PLC for teachers in my district. It has been a great opportunity to learn with and from my colleagues as we develop our CL skills! To help teachers learn more about CL, I am curating a collection of CL things and also plan to create a series of short tutorials for various CL elements. These ‘CL Bytes’ are meant to be bite-sized tutorials for those who may not have any formal programming experience from the perspective of someone who is trying to make sense of it all herself. 🙂 So here you go, CL Byte #1.

**CL Byte: CL note with input**

In this video I talk through how to use Desmos Computation Layer to create a CL note that changes based on an input. Here is the Desmos Activity Builder I used in this video. Enjoy!

# The Forgetting Curve

The Forgetting Curve is a model that describes how information is lost over time when there is no attempt to retain it. It originated in the late 19th century with German psychologist Hermann Ebbinghaus.

The graph above published in this article in Quartz shows the forgetting curve is initially very steep, but Ebbinghaus found that the amount of learning retained eventually leveled off. So the next day, he might remember just a few bits of the new information but he would remember those bits for many days.

Ebbinghaus also found that the curve of forgetting could be interrupted by spaced repetition. This graph published in this article in Medium shows that when the new learning is revisited, with space between repetitions, retention is increased and sustained over longer periods of time.

The blue line on the graph above dips into a curve to show that our memory of new facts we have learned declines over time, unless we revisit/revise that information regularly. There are 4 pink curved lines to represent how our memory retention will be higher if we revise the information we learn.

#### Applying to Classroom Practice

So how might we apply this in the classroom? One model from University of Waterloo suggests that we need spaced repetition, but of shorter duration over time, to retain newly learned information.

I know most math teachers will agree with this in theory. I also know many teachers find it challenging to work in this necessary review while still feeling they must march through a lesson a day to get through their curriculum and all the standards assessed on state-mandated assessments. So how can we do both?

**Warm-ups**: These must be more than filler. I realize the very real issue of trying to take attendance so you can start your lesson, but warm-ups can be prime times to revisit prior learning.**During the lesson**: Whenever possible, connect the current lesson to prior learning. This creates opportunities to revisit concepts while still moving forward.**Closure**: I can not overstate the importance of closure. If you have gotten out of the habit of ‘summing it up’, use the last few minutes of class to summarize the new learning and make connections to prior learning. It is one of the best ways I have found to improve student retention and understanding.

# Resources from YouCubed

Youcubed.org is a free K-12 math resource from Stanford University’s Graduate School of Education. Many of you are familiar with the Week of Inspirational Math, but here are a few of the other resources you’ll find on the site.

### Mathematical Mindset Algebra

Mathematical Mindset Algebra is a 4-week curriculum unit developed by Youcubed to introduce algebraic concepts at any grade level. In the Week 3 materials, students continue exploring linear functions, this time comparing them to quadratic functions while creating and analyzing multiple representations of both functions. Youcubed also has a discussion group on Facebook for those who would like to share ideas about the algebra curriculum with others, and Week 4 will be available on September 25!

### Mindset Mathematics for Grades 3-6

Created by Jo Boaler, Jen Munson and Cathy Williams, Mindset Mathematics is designed around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that:

- There is no such thing as a math person – anyone can learn mathematics to high levels.
- Mistakes, struggle and challenge are the most important times for brain growth.
- Speed is unimportant in mathematics.
- Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics.

With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.

### Online Courses for Teachers

Stanford offers two online courses for teachers: **Mathematical Mindsets** and **How To Learn Math For Teachers**.

The **Mathematical Mindsets** course helps educators inspire and boost math achievement. You’ll learn the latest neuroscientific research on the best methods by which students learn math, as well as the specific methods and approaches you can use to successfully help your students develop a growth mindset.

**How To Learn Math For Teachers** explores the new research ideas on mathematics learning and student mindsets that can transform students’ experiences with math. Whether you are a teacher preparing to implement the new State Standards, a parent wanting to give your children the best math start in life, an administrator wanting to know ways to encourage math teachers or another helper of math learners, this course will help you. Watch this video to view an overview of the online course.

Both of these courses are self-paced, and participants will receive a Record of Completion upon finishing the course. Tuition for each course is $99 payable to Stanford. I am currently setting up inservices in PD Place so that teachers who complete a course can be awarded clock hours through NSD (more details to follow).

### Free Online Course for Students (or anybody)

How to Learn Math is a free class for learners of all levels of mathematics. It combines really important information on the brain and learning with new evidence on the best ways to approach and learn math effectively. Many people have had negative experiences with math, and end up disliking math or failing. This class will give learners of math the information they need to become powerful math learners, it will correct any misconceptions they have about what math is, and it will teach them about their own potential to succeed and the strategies needed to approach math effectively. If you have had past negative experiences with math this will help change your relationship to one that is positive and powerful.

NOTE: Teachers are welcome to take this free course, but no clock hours can be awarded for this online course since the course doesn’t supply a Certificate of Completion. Teachers who wish to earn clock hours should consider taking the course, **How To Learn Math For Teachers** (see above).

### For Parents

Youcubed has a variety of resources and articles that may help parents (and teachers!) support their child’s mathematical learning. ~

#### Happy YouCube-ing!

*~Patty Stephens*

# Desmos Snowglobes

My Algebra 2 students have been studying function transformations. To give them an opportunity to apply their learning, we are creating Desmos Snowglobes!

The inspiration came from a tweet by Joanna Stevens and I created this activity based on a Desmos Activity by Julie Reulbach. In Desmos Snowglobes, students start off with some tutorials about circles, ellipses, and some Desmos features such as domain/range restrictions and using inequalities to color graphs. After completing the tutorials, students view some Desmos snowglobes created by others before using the Desmos graphing calculator to create their own. Please visit student.desmos.com and use code SA974 if you’d like to try this activity as a student! If you’d like to use this activity with your students, just click “Create Class Code” to get started.

If you would like help finding/creating a Desmos Activity for a particular topic or using a Desmos Activity with your own students, let me know! I am happy to help you plan a lesson, teach a model lesson, or co-teach a lesson with you. 🙂