More From the Trenches: Interleaving to Maintain Math Mastery

We are continuing our series of posts by Beth Guadagni, who shares the strategies she uses in her Colorado classroom. Today, she looks at how she uses interleaving to help students maintain math mastery.

Purpose:
To help students retain math procedures they’ve already learned.

Materials:
Math problems from previously studied units

Procedure:
I put together review sheets that students complete a few times a week. A simpler approach would be to flip backward in a textbook, choose a few pages at random, and do a problem from each section. Note that students should have a way to check their answers* if they’re going to tackle this independently.

Why This Works:
Like many students, my group generally does a good job of performing newly learned procedures once they’ve had some practice. Performing that procedure a few weeks or months down the road is a different story. To combat this, I use interleaving, one of Dr. Yellin’s most useful and widely applicable strategies.

One thing we know about memory is that we’re able to store a lot more things than we’re able to find easily, rather like a very large, disorganized closet. Brains are good at keeping thought processes efficient, and so information that we have to access often is stored in a place that makes it easier to find. Information we don’t need often, however, takes a lot longer to find, and sometimes we can’t find it at all. Here in Colorado, my students spend a lot of time enjoying the outdoors, so I use a trail analogy to explain this to them. A pathway that is traveled often is well worn, making easy to find and follow. You can hike faster along a trail that’s been traveled a lot, just like one’s brain can quickly find information that has to be accessed frequently. A less popular trail, though, like a seldom-referenced memory, is much more challenging. You might lose it altogether, and if you can follow it, your progress is going to be slowed by rocks and overgrown plants.

Back to math: Constantly circling back to concepts we covered earlier in the year causes my students continually access procedures they’ve stored in their long-term memories, communicating to their brains that this information is important and so the pathways to it need to be efficient. My students complete only a problem or two from each past unit of study at a time, and we spend only five to ten minutes reviewing every few days. This small investment pays off in a big way, though; when I graded their math finals at the end of the last semester, I was pleased to see that they recalled concepts from August just as well as the ones they’d learned in mid-December.



*See our previous post on Photomath, a free app that uses smartphone cameras to scan and solve math problems.

.
Photo by Matt Gross on Unsplash

From the Trenches - Photomath

We are delighted to welcome back Beth Guadagni, one of our all-time favorite bloggers. We'll let Beth explain what she has been doing and what her posts will be about...

I’m excited to be collaborating with The Yellin Center on a new series of blog posts! 

I was lucky to work as a learning specialist alongside Dr. Yellin for several years when I lived in New York. Before I attended graduate school and subsequently worked at The Yellin Center, I was a classroom teacher, and when I moved from New York to Colorado I returned to a classroom setting. Currently, I teach math, reading, and language arts at Hillside School in Boulder. All of the students at our small, private school have dyslexia. I teach our oldest students, a mixed grade group of high school students. They are bright, curious, and simply delightful.

I certainly miss many things about The Yellin Center, but the wealth of knowledge I gained working alongside Dr. Yellin has made me a far better teacher than I was before. I find myself designing lessons inspired by the brain-based strategies I learned to recommend to students who came to The Yellin Center for assessment. My students learn more quickly, and they really enjoy learning about how their brains work and why we approach learning tasks in certain ways.

We thought that others might find value in suggestions from someone who has applied these tactics in a real classroom with real students. I’m excited to share a variety of games and teaching techniques, and the rationale behind them. I hope you enjoy reading this series as much as I’ve enjoyed working on it!

****************************

One thing every high school teacher learns pretty quickly is that students will almost always know more than she does about technology. One of my freshman was aghast to learn that I didn’t know about Photomath and I’ve been using this remarkable app, and encouraging my students to do the same, ever since.

Photomath is an app for both Apple and Android that uses a smartphone camera to scan a math problem. Within a second or two, the app displays the answer.

Here, in no particular order is a list of reasons I love this app:

• It scans typed or handwritten math problems. (It cannot, alas, solve word problems.)
• It produces an answer in just a second or two
• It displays the steps used to attain the solution, along with brief, clear explanations. Users can access multiple explanation modes for some problems. 
• There are animated instructions for many problems, showing the steps in a sequence like the one I’d show a student on the whiteboard. 
• When it scans the formula for a line, it will display a graph.

As a teacher, it’s frustrating when a student proudly hands in a completed problem set and every answer is wrong. Without an answer key (which some textbooks feature but many worksheets do not), students often don’t know if they’ve been using a procedure incorrectly. Photomath eliminates that uncertainty.

Of course, it’s imperative that students don’t abuse Photomath. I’ve given my group a few guidelines. First, they are to use it only after they’ve completed a problem. If their answer was wrong, they are not allowed to simply change it and move on; they must check their work (using the Photomath’s explanation, if they want) to find their error. My students raise their hands only when they’re still confused, meaning that fewer hands go up. I get more time with the students who really need my help, and they spend less time sitting around waiting for me. It’s a win-win.

Watch for more suggestions from the trenches in future posts!

Assistive Technology

We often get questions from parents that send us back to our blog to see what we have written about a particular subject. Sharing the link to a blog will often help a student or family who has questions about a particular topic that we have discussed - and written information that can be reviewed and even printed can be particularly helpful.

Such is the case with the issue of assistive technology (AT). In response to a question from a New York City mom, we took a look back at our past posts on this subject -- and found a wealth of information that we hope you might also find helpful. As we hope our readers know, our blog has a "search" feature that lets you find posts by topics, key words, or even the date posted. It's a quick way to check on any subject about which you may have questions.

There is a simple video that explains the basics of AT with information about finding out about how to locate AT resources throughout the U.S.

Our posts about various aspects of AT go all the way back to 2012, so some of the tech we discuss as "new" may not be so new anymore. But we think that you will find these posts a useful starting point for understanding what AT is, how it works, and how it can help you or your student with specific issues.

• Back in 2012, we looked at CAST (The Center for Applied Special Technology) and the wealth of resources they offer 
• We recommended a wristwatch that sent a vibrating reminder signal and an app that might help teenage procrastinators 
• We discussed audio books that have highlighting features, something we often include in our recommended strategies for students
• We shared information about a blog from the folks who bring you TED Talks about how to navigate educational technology
• We look at the accessibility features available from Google
• We describe some top time management and homework resources, a number of which we frequently recommend to students
• In a post from 2017 we review a number of excellent AT tools for managing dyslexia.

And we also wrote about the low tech subjects of handwriting and the benefits of teaching children to write by hand and other kinds of low tech AT

Finally, there is a helpful blog post from earlier this year on the InsideSchools blog about high tech tools for students with a variety of disabilities and the New York City Department of Education has a web page with information about the nuts and bolts of getting appropriate technology for students with disabilities in New York City.

New Book Series for Young Music Students

A new series of books, Having Fun with Music - The Young Child's Piano Book is a wonderful and creative way to introduce young children to the joys of music. The first and second volumes of this series are now available and the third book is due out this summer. The books were written by Lori J. Lerman, who has taught voice and piano to children and adults for over 30 years, along with other accomplishments too numerous to mention. Your blogger has been friends with the author since seventh grade and can attest to her deep love of and experience with teaching music. Each book incorporates teacher's notes, explaining the concept behind the lesson, how to use the lesson, and additional activities to extend what is being taught. The books are designed for children from kindergarten through third grade, but can be used for younger children who show an interest in piano or older children with little or no musical background. 

In a few years, this baby will be ready to learn piano with this excellent series.

. 
When I asked Lori why she wrote this series, she explained, "My Master’s degree is in Reading and Language Education, so I’ve always been particularly interested in the connection between learning language and learning music. Young children learn language in well-known stages. First they learn to understand speech, then they learn to speak themselves. Eventually, once they're fluent in spoken language, they learn to understand it in written form. Music is a language, and it should be taught to young beginners in the same series of steps. It would be ridiculous to teach children to read and write before they know how to talk, and it’s just as silly to teach them to read music before they actually understand what it means.

"I’m writing the Having Fun with Music series to try to incorporate what we know about language into the process of learning music, using the same series of steps. The early activities use listening, singing, movement, and keyboard improvisation to create “fluency” in the language of music. Once this process has gotten started, the child then begins to learn written notation as a way to take the sounds they already recognize and understand, and recreate them on paper.

"The most important part of the series, I think, is that its main goal is to make piano lessons enjoyable for young children. Every lesson has instructions for parents and teachers on the facing page, including suggestions for optional activities and ideas for using a floor keyboard or incorporating movement. Songs are introduced through singing and games before the child is asked to play them. The parent or teacher is urged to use whatever ideas and suggestions seem appropriate for their own child and to spend as much or as little time on each activity as their individual child seems to prefer. Since young children love repetition and need to repeat skills they have mastered, reviewing activities already completed is greatly encouraged. Rather than progress quickly through the book and then move on to the next, children can spend as much time as they like repeating and enjoying their favorite songs and games."

COPAA Advocate's Training

Parents sometimes ask how they can learn about special education law, to help them advocate for their own child or to help other parents who need guidance. A terrific opportunity to learn about special education advocacy has just been announced by COPAA - the Council of Parent Attorney's and Advocates, a dedicated group that includes both attorneys and non-attorney advocates.

Registration begins this coming Friday, April 5th, for COPAA’s Special Education Advocate Training (SEAT) 1.0 – Beginning Advocacy. This annual program is the first module in a a several part training that can lead to a competency as a special education advocate. You can go to the COPAA website to learn more about the role of advocates in the special education process and how the COPAA SEAT training works. There is also information on other organizations involved in training advocates.

Information on dates, fees, additional training programs, and COPAA membership (although membership is not required to participate in these trainings) is also available on the COPAA site. This course is expected to fill quickly, so don't delay in signing up if you are interested.

The New York Institute for Special Education

There is a hidden gem in New York City that has served children with visual and other impairments since 1832. The New York Institute for Special Education was founded as The New York Institution for the Blind and was located at several Manhattan locations, the most recent of which was at Ninth Avenue and 34th Street. When this land was needed to build a huge postal facility, arrangements were made to move the Institute to its current location on more than 17 landscaped acres on Pelham Parkway in the Bronx, where it began operations under its current name in 1924.

Over the years, the Institute's mission has both expanded and contracted. Its original program, and still center of its mission, is the Schermerhorn Program for visually impaired or blind students from ages five through 21. The program is designed to provide students with the tools they need for independence and includes New York State exams and Regents exams for those who are able to work at that level. Those who are not at grade level receive remedial instruction as needed.  Related services, such  as occupational therapy, speech and language therapy, orientation and mobility training, and counseling, as well as training in social skills and activities of daily living are provided as appropriate.  Students participate in pre-vocational and skills development and can earn college credit starting in their junior year as part of a partnership with area colleges. There are a variety of extra-curricular activities, including sports, student government, music, and art.

Another program at the Institute is its Readiness Program, a full-day program for Bronx children from ages three through five who have developmental delays and who are referred by their Committee on Preschool Special Education.

Still another program, Van Cleve Program, was established in the late 1980's to serve children with learning and emotional disabilities from ages four through 13. The goal of this program is to remediate the behavioral and learning deficits of these young students in a highly structured setting that includes counseling services for both students and families. At this time, however, the Van Cleve Program is not accepting new students.

The spacious facilities at The Institute include dormitories for students from the Van Cleve Program and those in the Schermerhorn Program who can benefit from the five-day residential program . Students return home on weekends and holidays and during the week receive homework help, learn independent living skills, and participate in numerous recreational activities.

Graduation 2018

The Institute is led by the amazingly knowledgeable and dedicated Bernadette M. Kappen, Ph.D. Dr. Kappen leads a team of dedicated educators and works with a Board of Managers that includes Dr. Yellin, who tries to attend graduation every year!

Advanced Placement for All

We recently had an interesting conversation with a New York City Department of Education (DOE) administrator, who shared his experiences with the DOE AP for All Program. The DOE has put extensive resources towards expanding access to Advanced Placement Exams, which measure college level competency and can reduce the number of courses required for graduation at some colleges.  At some NYC high schools, they are introducing AP classes for the first time, and at others they are expanding from two or three courses to eight or nine. Since this takes a lot of work from teachers and a lot of materials, the DOE provides funding to participating schools to encourage and support involvement. The DOE has stated that its goal is that by fall 2021, students at all high schools will have access to a full slate of at least five AP classes, thereby increasing college and career readiness for all students.

AP Exams are administered by the College Board, which charges $94 for each exam. NYC schools cover some or all of the cost of the exam for their students.

In addition to funding, the DOE provides ongoing training and curriculum to all partner schools. Week-long trainings in the summer, with workshops and updates throughout the year, help first-time and repeating AP class teachers to build the best curriculum. They also provide extra support to students at Saturday Study Sessions where students receive additional support to prepare for exams. This all comes together to provide access to a high-quality AP Course experience for students who may not have previously had the opportunity. The "For All" focus also means schools are pushed to allow access to those not traditionally scheduled for AP classes, like ENL (English as a New Language) students or students with disabilities.

Having all students take AP exams has had a mixed result in some states, as noted in a NY Times article from 2017. However, the College Board reported, that same year, that in New York City, "The number of students taking and scoring a 3 or higher increased in every borough, and across all ethnic groups." And 2018 data from the DOE shows gains in both numbers of students taking AP exams and passing them.

Computer Science for All, Algebra for All, and College Access for All are similar, full service type initiatives that provide funding to schools, materials to teachers, support for students, and training for all involved parties. These types of programs were previously limited only to specialized schools or to certain groups of students, but the ideal in the DOE now is that every student is deserving of these opportunities.