Wednesday, May 22, 2019

"Calling In" to Build Classroom Tolerance and Learning

We are living in an era when statements that are racist, sexist, cruel, or just ignorant or unkind, are no longer given a pass in our society -- and that's a real step towards making a better world. But "calling out" people who make such offensive statements can often involve harsh language and humiliation. And when an inappropriate (or worse) statement is made in a classroom setting, it is important that teachers respond in a way that not only challenges or corrects the statement, but also educates the speaker and the listeners.

An excellent discussion of a technique for handling such situations in a classroom appears in an article by Loretta J. Ross in the Spring issue of Teaching Tolerance magazine - "Speaking Up Without Tearing Down". Ms. Ross proposes that when teachers are faced with language or an argument that is wrong or offensive, that rather than "calling out" the student, that the teacher "call in". As she explains, 

"Calling in is speaking up without tearing down. A call-in can happen publicly or privately, but its key feature is that it’s done with love. Instead of shaming someone who’s made a mistake, we can patiently ask questions to explore what was going on and why the speaker chose their harmful language. 

"Call-ins are agreements between people who work together to consciously help each other expand their perspectives. They encourage us to recognize our requirements for growth, to admit our mistakes and to commit to doing better. Calling in cannot minimize harm and trauma already inflicted, but it can get to the root of why the injury occurred, and it can stop it from happening again."

Ms. Ross makes clear that calling in is not for every situation. She notes that when people use bigotry, fear, or lies to hurt others, that they should be called out for such speech or conduct. But she explains that a classroom is a special setting, where mistakes and misunderstandings need to be acknowledged and opportunities for learning abound. She gives a number of examples as to how a teacher can begin "a call in conversation" to address offensive or ignorant statements, and to educate and enlighten his or her students. Her examples include:

  • “I need to stop you there because something you just said is not accurate.”
  • “I’m having a reaction to that comment. Let’s go back for a minute.”
  • “Do you think you would say that if someone from that group was with us in the room?”
  • “There’s some history behind that expression you just used that you might not know about.”
  • “In this class, we hold each other accountable. So we need to talk about why that joke isn’t funny.”
This article should be required reading for every educator -- and everyone who lives or works with others. 

Wednesday, May 15, 2019

Skip-Counting – The Threes & Sixes, Plus a Game

Today's post winds up our "From the Trenches" series by Colorado classroom teacher and former Yellin Center Learning Specialist Beth Guadagni. In Beth's prior posts, she explained how our brains learn math facts and how she uses songs to help her students -- all of whom have dyslexia -- learn the fours multiplication facts.

Our last post gave background and instructions for teaching multiplication facts for four and eight. Using different songs, Beth explains how the same techniques can be used to teach the math facts for threes and sixes.

Skip-Counting by Threes

“Three” is repeated three times to get the rhythm to work out. We add “and thirty-six” at the end in the same way people add “and many more” to the “Happy Birthday” song. Jazz hands, while optional, are highly recommended.

Row,                   row,                      row                      your                     boat,

Three,                 three,                   three,                   six,                        nine

Gently                down                    the                       stream,

Twelve,               fifteen,                   

Merrily,             merrily,                   merrily,                 merrily,

Twenty-one                 Twenty-four                   Twenty-seven

Life is but a dream.

Thirty   thirty-three

…and thirty-siiiiix!

Skip-Counting by Sixes

Happy                birthday                to                     you,

Six                      twelve                    eighteen          twenty-four

Happy                birthday                to        you,
thirty                  thirty-six               forty-two

Happy                birthday               dear           [name]

Forty-eight               and                 fifty-four

Happy                birthday                 to you!

Sixty                   sixty-six                 seventy-two!

Game: Domino Draw

To give students practice applying skip-counting sequences to real math problems.

Materials for the game:
A set of dominos, turned face-down or in a bag.
If you don’t plan to play long enough to go through a whole set of dominos, use a timer so that students play for a set amount of time. Be sure, once it goes off, that everyone has had the same number of turns.
There are two variations here.

1. To target the sequence students are learning:
On his turn, each player draws a domino at random. He adds the number of dots on the domino, then multiplies that number by the sequence you’ve been practicing. For example, if his domino had 11 dots on it and you were practicing the threes, he’d get a product of 33 and earn 33 points.

2. Once students have learned all the sequences, try this variation:
On her turn, each player draws two dominos at random. She adds the number of dots on each domino, then multiplies them together. For example, if one domino had four dots on it and the other had twelve, she’d get a product of 48 and earn 48 points.

Wednesday, May 8, 2019

Skip-Counting by Fours ... And a Multiplication Game

In her last post, Colorado teacher Beth Guadagni shared the concepts behind one of the methods she uses to  help her students (all of whom have dyslexia) learn number sequences. As part of her advice "from the trenches" we share the specific techniques that she uses in teaching them to work with fours, getting them ready to do multiplication and division. 

To help students memorize number sequences that will help them with multiplication and division.

First, make sure the students know the song. I like to start with the fours and use "Take Me Out to the Ballgame"  because the rhythm of the song fits perfectly with the number sequence, which is not always the case. Don’t try to teach the whole song-number connection at once! I usually like to start with the first five or six numbers, or the first two lines. In this case, the song breaks nicely after 28.

1. Write out the numbers from 4-28. Sing the first line and then ask the students to repeat it. Do this a few times.

2. Next, ask the students to close their eyes. Cover a number, then ask them to open their eyes. They should sing the line, filling in the missing number when they get to it. Do this a few times, covering different numbers each time.

3. Once they seem to be comfortable, add the next line of the song and repeat the procedure.

4. Cover or erase all of the numbers in your chosen lines and sing through them with the students once or twice.

5. Ask students to write the sequence as far as they’ve learned it.

For additional reinforcement, I like to hand out a sheet on which I’ve written the sequence they’ve learned a few times. Each time, it is missing more and more numbers. They have to complete the sequence by filling in the missing numbers, then cover the top part of the sheet when they’re ready to tackle the next, more challenging section. At the end of the sheet, they have to write the whole thing from memory. I also like to include a few multiplication and division problems from that family that they have to solve, using the memorized sequence to help them. They are not allowed to peek at the sequences from the top of the sheet unless they’re really stuck!

Teach the whole song, bit by bit, this way until you’ve taught the whole thing.

Take            me              out                    to the                     ballgame, 

Four          eight            twelve                sixteen                    twenty 

Take me out                to the crowd, 

Twenty-four               twenty-eight 

Buy me some                 peanuts and                      cracker-jacks, 
                             Thirty-two                      thirty-six                          forty 

I don’t care                           if                           I ever get back…. 

Forty-four                   and                            forty-eight

Once they’ve memorized the song, there’s one more part to add: students have to count on their fingers while they sing it. (I allow my too-cool high school students to keep their hands on their laps, as counting on hands that are held in the air feels babyish to some of them.) This is essential if they’re going to use the song to solve math problems.

Each time they say a number, they have to hold up another finger, so that by the time they get to, say, “thirty-six,” they are holding up nine fingers and will know that thirty-six is the answer to four times nine. This is trickier than it sounds. At first, when they have to both sing and track on their fingers most kids lose their place in the sequence. To practice this skill, we sing the song until I call out “Stop!” and students have to write down the last math fact they sang. For example, if I stopped them right after they said “twenty-four,” they should have six fingers extended and so they’d write “4 x 6 = 24.”

Why This Works:
Songs are incredibly powerful mnemonics. Most students seem to remember tunes easily, and this prompts them to recall the number that goes along with each change in tone and matches the number of syllables for that particular line. Students see the number sequence while they are hearing the sequence and the song, meaning that they store the information in several formats in their memories. Eventually, they count on their fingers while singing as well, adding a tactile element. Teaching the song in segments is quite important, too; as with any new skills, students must demonstrate mastery before they can tackle new material.

Once students have gained some comfort with skip-counting, you may want to introduce a game to help reinforce their skills. My kids like the card game "War".

Game: Multiplication "War" 

To give students practice applying skip-counting sequences to real math problems.

Materials for the game:

One or two decks of cards (Use two decks shuffled together if you’re playing with three or more students)
  • Ace = 1
  • Jack = 11
  • Queen = 12
  • King =0

Because War can take ages to wrap up, I often set a timer for around seven minutes while my students play, and the winner is the one with the most cards when their time is up.

There are two variations here.

1. To target the sequence students are learning:
Each player lays down a single card, face-up. They have to multiply the card by the sequence you’ve been practicing and say the product aloud. The player with the highest product keeps the cards from that round.

2. Once students have learned all the sequences, try this variation:

Each player lays down two cards at once. The player with the highest product gets to keep all the cards from that round.

If two players get the same product, they lay down two cards face down, then use a second pair to get the tie-breaking product.

Why This Works:
Students who aren’t focused don’t learn well, and games keep kids engaged in the learning task. This game is fast-paced enough to ensure that students have to use the skip-counting sequences they’ve learned many times during the allotted interval.

Friday, May 3, 2019

Strengthening Paired Associate Memory with Song

We are continuing our series of posts by Beth Guadagni, who shares the strategies she uses teaching her students with dyslexia in Colorado. 

Like many students, mine have struggled to learn their math facts. Automaticity with the multiplication tables is essential for math far beyond simply multiplying numbers; students use multiplication when working with fractions, doing long division, calculating area and volume, and in so many other applications that it seems rather silly to try to list them!

Perhaps most importantly: students need to have a sense of multiplication to determine whether a solution to a math problem makes sense. As Dr. Yellin will tell you, memorizing math facts involves a particular part of memory called paired-associate memory. Paired associate memory involves linking and storing two related data bits, retrieving one piece of information when presented with the other piece (eg., a sound with a symbol, or the number 28 when presented with 4x7).

Paired-associate memory is what we use when we learn someone’s name, remember that the color of the sky is called “blue,” pair the /ch/ sound with a "c" and an "h" together, etc. There’s no immediate context for these associations (although savvy students and educators can invent contexts to make information “make sense”); they just have to be memorized. Paired-associate memory is generally not a strength for dyslexic students, like mine, although people who don’t have dyslexia may struggle with this skill as well.

I learned skip-counting songs from a colleague and was amazed by the ease with which her fifth graders learned the number sequences. I was eager to try this concept in my class, but I was a bit apprehensive, too. Would my high school students be willing to sing strings of numbers to the tune of “Twinkle, Twinkle Little Star” and “The Wheels on the Bus”? The answer was a resounding “yes!” Although they were a little hesitant at first, my students were as pleased as I was that they could commit number sequences to memory with only a little practice. In fact (and this is true), one day one of my students, frowning darkly, exploded, “I’m really mad that I made it to eleventh grade before anyone taught me this!”

I’m going to spread the sequences over a few posts, which also is what one should do when teaching these songs. I’ll share a game for practicing math facts in each post, too. Learning the songs is important, but it’s not enough; one has to practice using the sequences to answer actual math facts, too. We'll present detailed instructions on how to use this technique in your classroom in our next post, but you can get a sense of how this process sounds from this YouTube video, posted by another teacher who used this technique. 

Friday, April 26, 2019

Pictionary and Charades to Learn Vocabulary

We are continuing our series of posts by Beth Guadagni, who shares the strategies she uses in her Colorado classroom. Today, she writes about ways to help learn vocabulary.

To help students learn vocabulary words, in English or in other languages.


  • words to be studied, each written on a slip of paper
  • list of words’ definitions
  • something to draw with, and on
Students take turns picking words at random by drawing slips of paper. They must get the other players to guess the word by drawing it, or by acting it out. The first one to guess the word correctly gets to select the next word and draw it/act it out.

Why This Works:
My students can’t get enough of this game, so one of the primary reasons it works is that it keeps them engaged. Even my most introverted student thinks it’s great fun because I allow him to choose who will go next if he guesses the word correctly. The game allows the students to move around, as well, and research indicates that movement helps some kids learn faster and stay engaged longer.

People remember information more reliably when concepts are stored in their memories in multiple formats. Memorizing a list of words and their definitions gives students only one format in which to interact with, and remember, material. Having a mental image to associate with a word—whether it comes from a classmate’s drawing or the memory of a classmate performing an action—seems to help my students remember new words more quickly than any other exercise we’ve tried. Further, as they guess which word is being presented, they pore over the list of definitions with more vigor than they would to complete any worksheet or test I could give them. And in a surprisingly short time, they don’t need to reference the list at all.

My students’ memories for vocabulary have improved, and I’ve found that the Pictionary/charades approach helps my students to understand the new words more deeply as well. Even seeing vocabulary words in the context of sentences—a valuable learning experience, to be sure—pales in comparison to playing with the words. When deciding how to portray a word’s meaning to their classmates, my students have taken to connecting personally with the words. For example, one of my students hates to sit still. He loves nothing more than working up a good sweat. His drawing for the word “laborious” showed a stick figure mowing a lawn and smiling. My whole class now remembers that word easily because they connect it to this young man, who has developed a reputation for enthusiasm about chores the rest of them hate to be assigned at home. Charades and Pictionary have helped my students see how to use these words in their lives to express information about themselves or people they know. The information feels relevant because they’ve given it a context.

Although this activity really works only in a group setting, a student studying independently could use it as well. Spending a few minutes imagining how one would draw or act out vocabulary words on a list will still help a student to translate concept from one format (verbal) to another (visual or kinesthetic), leading to deeper and more lasting memories of the words’ meanings.

Photo by Nicole Honeywill on Unsplash

Thursday, April 18, 2019

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.

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


Math problems from previously studied units

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

Monday, April 15, 2019

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!