Decoding Learning Differences with Kimberlynn Lavelle

Addition is such a common math skill and yet, you may have found yourself wondering HOW to teach it!

To begin with, kids need a few “pre-adding skills”, skills that they must be comfortable with before they can successfully learn to add.  They must be able to count, they must recognize numbers and the plus and equals symbols, and they must have 1:1 correspondence.

All math skills should be taught first with concrete exploration, then pictorial representation, and finally with abstract practice (such as standard algorithms). 

Early Addition (K - 1st)

Addition starts with just adding small numbers within 5, then within 10, within 20, and within 100.  Each step takes on a new level of difficulty for a child.  Some progress quickly but others need time to work through each new challenge.  

Rushing kids through any level is likely to cause difficulty later on.

When introducing addition to your child for the first time, be sure to have lots of practice with physical objects.  To start with, your child will just be exposed to conversations about addition. “You have two carrots.  If I give you two more, you’ll have 4!”

When the concept of adding objects is solid, they can be presented with pictures and discuss the addition represented by those pictures.

Finally, the algorithm can be presented.  In the course of all of these (concrete, pictorial, and abstract), stories about the numbers should be used.  This helps to make the connection between numbers/addition and story problems, helping to prevent difficulty with “word problems” later on.

Before moving into double-digit addition, addition of multiple addends should be introduced (5 + 4 + 3 + 2).  

Multiple-digit Addition (2nd - 4th)

Once kids are adding single digit numbers to double-digit numbers with confidence, they’ll move into adding 2 two-digit numbers, first without regrouping (also called carrying), and then with regrouping (carrying).  

Again, we want to introduce this concept with concrete and pictorial before jumping to the abstract with just numbers and symbols.  The tendency to rush kids through these skills can lead to kids knowing tricks and performing the addition task without truly understanding how the numbers are working, which can cause difficulty later.

I highly encourage the use of base ten blocks, or the Montessori “Golden Beads” to support the understanding of place value with addition.  A 100s Number Table is also beneficial in moving from concrete through to abstract (and in supporting abstract).

Decimal Addition

After children have mastered adding multiple-digit numbers with regrouping, they can start to add decimal numbers.  First, they’ll add numbers that have the same number of decimal places.  (3.56 + 4.12) But then they’ll start to have numbers with different numbers of decimals places. (3.56 + 2.3)

To be successful at this level, kids need to have a strong understanding of place value and exactly what decimal places are representing.  Many kids will think that 2.567 is a larger value than 35.3, for example.

One way to support this understanding of place value is to use those same base ten blocks as before, or something similar, perhaps using a different color for decimals, to avoid some confusion.

Once at the abstract stage, I would suggest setting the problems up horizontally so that the child has to then “stack” the problem accurately, understanding how it must line up.

Fraction Addition

Around the same time, and possibly prior to, decimal addition, children will often be taught fraction addition.  First, the numbers will have the same denominator.  Working with fraction tiles, legos, or evenly sliced foods (such as pie) are all helpful concrete representations of what a fraction is and how it works.  

 And it is critical for kids to truly understand what numerators and denominators represent before attempting to manipulate fractions by adding them.

When moving from concrete and pictorial to abstract in this step, I often encourage kids to think of the denominator as “apples” to help them remember not to add the denominators!  Instead of ⅜ + 2/8 they might say, “3 apples plus 2 apples”.  This can help them to remember that denominators are the name of the size of the object, not a number to be manipulated during addition. Side warning: never teach multiplication and division of fractions at the same time as addition and subtraction.  The different rules can be very confusing to keep straight!

Once adding small fractions of the same denominator are solid, you’ll add in adding fractions more than 1, and learning how to turn an “improper fraction” (also called “a fraction greater than 1”) into a “mixed number”.  

Then kids will add different denominators, first less than 1, and then more than 1, and mixed numbers together. 

Again, having something physical to represent those numbers is important in demonstrating why ⅔ + ¾ does NOT equal 5/7, as they are likely to want to try.  They need to see and feel why different denominators require first finding a common denominator (or “cutting all the pieces to be the same size”).

With fractions, use concrete and pictorial representations for longer than you think necessary as anything with fractions tend to be confusing to kids, even after they seem to have mastered it.  Also, be sure you are practicing it frequently after it is mastered so that it stays fresh for them.

Algebraic Addition

Having letters and symbols represent a missing number can happen early on, as soon as a child seems to have first mastered adding using an algorithm.  This makes them truly understand all of the pieces of the algorithm and what each piece represents.  It may not be how you were taught, but it can be beneficial for your own kids!

Takeaway

Addition requires skills to be mastered before beginning and new skills before increasing the difficulty.  Use concrete, pictorial, and then abstract when teaching addition (and all math skills).

Your spouse/partner comes to you and says, “Hey, I need you to organize the shelves in the garage this weekend.”

-OR-

“Hey, I’d love to get the garage organized this weekend!  Would you be willing to handle the shelves?  Or would you rather tackle the pile of tools?”

Which would most get you on board with their project?

I am certainly MUCH more motivated when I’m not being told what to do, but being given choice.

As promised, I’m back with more ideas on what TO DO to motivate your learner!

Back in January, I had a fabulous discussion with Vibha Arora in which she suggested giving a child autonomy if they are shutting down and refusing to work.

I agreed with Vibha on so many things, and this was no exception!

Autonomy is very motivating!

When a child is told that they “have to” do something, a child’s autonomy is being removed and they will fight to get it back.  “You have to ____” is instantly going to make a child less willing and interested in doing that thing.

Autonomy’s definition is: “the capacity to make an informed, uncoerced decision”.  When we are using rewards and punishments, we are using coercion.

How do we boost autonomy and motivation?

Give Choices!

Give developmentally-appropriate choices.  Two choices for some kids, and many more for others.

Give meaningful choices.  Asking “do you want to use the crayon or colored pencil?” is less meaningful than “do you want to practice counting or do you want to practice your letters?”  Both kinds of choices can boost autonomy, but more meaningful choices will go further in this aim.

When kids feel powerless, they fight back.  Which then causes us to up-level our authoritarian instincts (or is it just me?).  We start to threaten or punish and they feel more powerless and things just spiral…

But the opposite is also true: the more often we give choices, the more empowered they feel.

When giving choices, you can give information about what is important to you.  “It is important that you work on learning your letter sounds.”  Then asking them how they’d like to do it, but offering choices that they can select from.  

Younger kids will have had less exposure to all the different options in how to learn something, so giving them a variety to choose from is helpful in their selecting a choice.  Older kids won’t necessarily need specific choice, but just the freedom to come up with ideas on how to achieve the goal.

Give Responsibility

When you are giving meaningful choices, you are giving kids control over something and allowing them to recognize that their choices are important.

Don’t force the responsibility, but allow for it.  Allow them to engage meaningfully in the family and participate in what needs to happen.

Rather than choosing a curriculum for your child, allow them to choose for themselves.  This might be between two choices you’ve looked at, or it might be more open-ended and allowing them to do all the research behind it (for older kids).  (“Would you like to use A or B for your reading curriculum? Look at these features…”  or  “We need a reading curriculum for next school year, do you want to take the lead on researching and choosing one?”)

We might also allow our child to choose how or where they go to school.  Maybe they can choose between two nearby schools, or maybe they can choose home school or public school.  Maybe you homeschool, but are open to them selecting the style of homeschooling.

You can allow them to take responsibility over their work space.  And with that and other responsibilities, you can give parameters around what is acceptable to you, and establish what is important to them.  “You need a clear space where you can focus on your studies.”  and “I need this desk kept cleared off when you’re not using it because having clutter in the living room doesn’t work for me.”

Give responsibility as a gift.  Responsibility comes with benefits and consequences.  It can allow for more freedom, but also more opportunity for messing up and needing to make repairs.  Give responsibility and trust in your child.

Follow Their Lead

Whatever a child is already interested in, they’re already intrinsically motivated toward.  Encourage and support these interests as well as doing whatever you can to encourage them in developing new interests.  (These are the WORST times to utilize rewards!)

Takeaway: Autonomy can be very motivating!

How do YOU foster autonomy?

When asked to add two numbers, what is your child’s strategy?

Kids like “Freddy” add by always starting at 1, instead of “counting on” from one of the two numbers.

For kid’s like Freddy, there is a lack of number sense that is slowing them down and can cause bigger problems later, so it’s worth fixing now!

What worked- Asking Questions

“How many fingers are on that hand?” 

“What comes after 5?”

For a lot of kids, these questions aren’t enough because they haven’t practiced counting on so they aren’t able to.

What worked- Practice Counting On

Build into your routine regularly starting the count from numbers other than 1 and zero!

As you’re out on a walk or driving in the car, just start counting on from a different number and then stop to let your kiddo take over. “3, 4, 5…” “32, 33, 34….”  

At home, start counting on, and then mime handing the mic over to your kid for them to then continue.  Then switch and have them start and hand you the mic.

*Keep in mind that the biggest challenge in counting on for most kids is “29…” (and 39, 49, 59, etc).  I would recommend practicing this after they’re more comfortable with the easier ones, and then be sure to practice this one A LOT!  You’d be shocked how many older kids still struggle with this!

Model

“7 + 2.  Okay, 7, 8, 9! 7 + 2 is 9!”

Explicit Instruction

You can explicitly teach a child to use the counting-on strategy.  This should be a quick 5 minute lesson in which you show your child.  “I’m going to show you a way to add a little faster! Watch me.”

Specific Practice

Once your child has learned this strategy, let them know that they are going to practice it and then  have them do a few problems on a worksheet to practice.  You can also play games instead.  I like using cards or dice to mix things up a bit.  I might roll two dice and have my child write down the numbers and then I’ll cover the die that has the higher value, encouraging them to count on from that number.  With cards, I’ll do essentially the same.  (I also might practice without writing anything down)

“When you finish that math worksheet, you have the reading comprehension one from yesterday to finish.”

Does that sound reasonable?

To most of us, it does.  We have likely heard and maybe said something very similar ourselves.

In a society focused on how “productive” a person is, we expect kids to finish worksheets like it is their job.

We even talk about school being a child’s job, and some parents pay kids for how well they do at their job! (Please see the episode “Motivation Killers” on why I don’t support this practice)

But learning is way more important than a job.  We can choose to quit a job, and we can choose to quit doing a “learning activity”, but the actual learning is happening.  Kids are constantly learning, especially when they are having fun and are interested in what they’re doing.

The more focused we are on a particular task being completed, the more likely it is that our child will find the task unpleasant and learn little from it.

Instead, ask yourself, “what is my goal in giving my child this task?”

Now, a worksheet to practice a particular math strategy is totally valid.  I recommend starting with hands-on learning first, and then worksheets can provide good practice and review.  

However, the goal of the worksheet is to allow for that practice, not to finish a worksheet.  And maybe completing two problems is sufficient practice.  Maybe two full pages is more appropriate.

And there are plenty of times that a worksheet is too easy and not helpful practice, or too difficult and getting the child to complete it leads to a child who has a finished worksheet that they have no idea how to do or what they were supposed to have learned from it.

I see this last one all the time.  The other day I was given an incomplete comprehension page that one of my students was supposed to finish with me because they didn’t do it in class.  I immediately could see that the worksheet was at a much higher reading level than this child’s ability, and was not on a topic the child was interested in.

I certainly could have gotten that worksheet finished with the child, but I have limited time with these kids and I want the time that I do have with them to be used wisely.  So, instead of doing the worksheet, we worked on what I had planned already- some reading and math activities that were at her level.

The next time you are about to ask your child to complete something, question yourself: what is the purpose of this activity?  At what point will it have fulfilled its function?  Is it an appropriate level for my child? And then make an appropriate plan with that information.

Phonics is all about the relationship between sounds and letters and using that letter-sound knowledge to read and spell words!

With a strong phonics knowledge, your child will be able to read and spell unfamiliar words.

But phonics can also be confusing!  In English, there are 44 sounds, 26 letters, and 75 basic phonograms (single or multi-letter representations of sounds).

And kids with dyslexia REALLY struggle with phonics!

If you show your child a nonsense word (like fisp), can they read it?  If you ask them to spell ‘plit’, how do they do?

If your child is struggling with phonics development, there are things we can do to help them!

First of all, there are Orton-Gillingham based programs that provide a strong phonemic awareness and phonics foundation.  

But you can also follow the same basic process at home, by following a few steps:

Step 1: Start by developing phonemic awareness!  Check out the episode on phonemic awareness for specific steps on how to do this part yourself!

Step 2: Be sure your child knows the letter and sound correspondences.  For most kids, this is just about plenty of exposure and practice.  It could be flashcards, but multi-sensory approaches typically work best.  

• Write letters in sand, build them with playdough, make whole body dance moves about letters and sounds!  

• Keep in mind that there are 75 basic phonograms and many of those 26 letters have multiple sounds

Step 3: Have your child put their letter-sound knowledge to use!  Reading is typically easier than spelling for most kids, so reading will develop faster.  Take each at their own pace!

Get progressively more complex (C = consonant sound; V = Vowel sound): 

• CVC

Step 4: Next come the multisyllabic words!  

• Take individual words that they can read and make compound words.  

Many multi-syllabic words are VERY phonetic, making them easy to read and spell once a child knows how to chunk them and use phonics skills!

Takeaway: Phonics is important, but can be difficult for those with dyslexia.  A systematic intervention is necessary (but it is also something that you can provide completely for free!)

If you suspect your child may have dyslexia, take the quiz “Is My Child Dyslexic?” here to find out how likely it is!  (This is not a diagnostic tool, but a simple pre-screener that you can use to help guide you!)

Stop with the sticker charts, cookies, threats, and bribes! Put down the gold star!  Don’t say, “if you ….” ever again!

There’s a better way! 

To be completely transparent, this better way is not likely to be faster… at first.

But as I talked about in the episode “Motivation Killers”, all of those bribes don’t work very well in the long term.  You have to keep upping your game, promising more and more.

However, there is something that doesn’t require any upping of the ante, or any tricks.  And it works to motivate your kiddo in the long-term.

Actually, there are SEVERAL somethings that work like that!

Today though, we are talking about RELATIONSHIPS!

The relationship between a parent and child can be very powerful in motivating a child to do something that we are asking them to do.  Or in motivating them to learn something specific.

When our children feel seen, loved, and respected, they are much more likely to be helpful.  And when they feel respected by us, it opens them up to be interested in what we are doing.

A strong relationship with your child can lead them to be interested in what we are interested in, or in feeling free to explore something that they are interested in!

When children feel that they are in conflict with us and that we are threatening their autonomy, they aren’t very likely to be cooperative (especially as they get older and need to express their autonomy!).  But when we have a mindset based around respect and being on their side in all challenges, they see us as someone who they can come to with difficulties, and maybe even someone with interesting ideas!

What are you doing to foster the relationship you have with your child?

I want to tell you about Rita.

Rita was a student I worked with MANY years ago (more than I can believe!).  

I was a new teacher and knew almost nothing about dyslexia.  I had heard of it, but got no training on it in my credentialing classes to become a special education teacher (education specialist).  Can you believe that?!

Poor Rita.  She couldn’t rhyme, blend, or segment in kindergarten.  And I didn’t really know what to do about it except to practice MORE rhyming, blending, and segmenting.  For a few years, we kept at it, while also working on sight words and other reading skills.  

Rita was able to stay at grade-level in her reading but couldn’t rhyme, blend, or segment much at all.  (Despite all of the practice we had been doing!)

I’m a researcher by nature.  I love to read and research any topic I’m interested in, and especially ones around problems I’m trying to solve for myself, my family, or my students!

So I read and read and realized I needed to do something more fundamental than the rhyming, blending, and segmenting that I had been doing!

Eventually, we found success and Rita was able to segment and blend and read unknown words, although rhyming was never her strong suit!  She became a strong reader who could figure out some rhymes.

The first things that helped a little was just an overall increase in Rita’s exposure to rhyming.  We played rhyming games, practiced rhyming, books, poems, songs, videos.  This was the stuff I did early on that seemed to help some, but not nearly enough.

Eventually, I used a systematic phonemic awareness instruction.  It included a lot of specific segmenting and blending practice.  For more on how that works, check out the episode/blog on Phonemic Awareness and Dyslexia.

Takeaway:

If you want to learn how to teach your own child with dyslexia, email me at [email protected]

In the quiz “Is My Child Dyslexic” there are ten questions.  Knowing the purpose of each of these questions can help you to best determine what your best next steps are.

And if you want to work with me directly, check out Word Warriors!

Kids with dyslexia struggle with Phonemic Awareness.  But what does that mean?

Phonemic Awareness Skills

Kids who are strong in Phonemic Awareness are kids that are able to  segment, blend, delete, and rhyme!

Segmenting means taking a word and breaking into individual sounds. Example: you tell your kid, “Cat” and they are able to tell you: “/k/ /a/ /t/”.  This is all by sound!  No looking at words, using letter tiles, or writing anything down!

Blending means taking individual sounds and turning them into a smooth word.  Now you’re reversing the task for your kid.  You say something like “/k/ /a/ /t/” and they can say, “cat!”  Again, this is all by sound, not reading the letters for help.

Deleting means taking one sound out of a word.  You might ask your child, “Say ‘cat’ without saying /k/” and they have to be able to say: “at”.  (Again- no letters! No pictures, all just by sound.)

And rhyming, of course, is deleting the initial sound(s) and replacing it with (a) new initial sound(s). “What rhymes with cat?” “bat, fat, hat, rat, mat, sat, that, flat…”

Bonus- pig latin!  This is a manipulation of a word, removing the initial consonant sound(s) (if there are any), moving that sound to the end of the word, and adding “-ay” to the end of the word.  “Cat” becomes “atkay”.  “I can speak pig latin” becomes “Iay ankay eakspay igpay atinlay.”

Why it matters

Phonemic Awareness leads to the ability to read and spell unknown words.  This allows individuals to independently read increasingly complex texts and write about what they are spelling.

Some kids with dyslexia, or with insufficient phonemic awareness and phonics instruction, become great sight readers.  They memorize how to say a word very well and are able to progress with grade-level reading ability.  However, as words become increasingly complex, and as they are presented with less and less auditory input for what they are reading (fewer read alouds!), they are going to start to really struggle to know what they are reading.

Phonemic Awareness is hindered by dyslexia

Phonological Processing is necessary for Phonemic awareness and kids with dyslexia have a phonological processing deficit.  Therefore, phonemic awareness is unlikely to develop easily in a child with dyslexia. 

What do we do about it?

What can we do to support phonemic awareness development in those with dyslexia?

Developing phonemic awareness in a child with dyslexia is a worthwhile endeavor, allowing them to be more successful in their reading and spelling!  However, it isn’t easy.  It requires specific, structured, intentional instruction over many months, or even years.

One of the most strongly recommended types of programs for those with dyslexia is Orton-Gillingham based strategies.  These can get pricey.  They are well-developed and worth the cost for those who can afford it and want a specialized tutor or want a ready-made program. 

But you can also implement all of these strategies for free yourself!

Step 1: Start by dragging out a word until your child can hear each sound. Example: saying “Caaaaat!” while also moving your hand across their visual field (in front of them) to help them notice when one sound is changing into another.

Step 2: Next you want your child to be able to delete one of the sounds after they’ve said all of the sounds.

Step 3: Trade a sound: “Say ‘fip’. Say all of the sounds in ‘fip’. Say /d/ instead of /f/ Now what is the word? (dip)”

Step 4: Notice when and how a nonsense word changes

Step 5: Rhyming the words.

When they’ve mastered one level, repeat the above, getting progressively more complex (slowly!)  General progression (C= consonant sound; V= vowel):

CVC

VCC

CCV

CVCC

CCVC

CCVCC

If step 1 above does not work for your kid, try Step 0!

Step 0: break compound words into the component words. (pancake is made up of pan and cake!)

For some kids: even those start points are too difficult. They need to start by feeling the sound of a letter in their mouths.  You want them to feel what each sound feels like in their mouth. You want them to notice whether or not the voice box is on, what is happening with the tongue, teeth, and the lips.

Takeaway:

Phonemic Awareness is important, but is difficult for those with dyslexia.  A systematic intervention is necessary to truly meet the needs of those with dyslexia.

Each month on the Decoding Learning Differences podcast, I’ll be digging into motivation.  And to kick off the year, I’m starting with what NOT to do, so that we can spend the rest of the year diving into what TO DO!

This episode goes into three “Motivation Killers”: Punishments, Rewards, and Praise.  (Although praise is actually a type of reward).

Punishment

Now that corporal punishment (physical abuse/hitting) is very rare and illegal in most states, punishment is usually about taking something away from a child (called a negative punishment).  Punishments you may have seen in schools:

“You didn't do your work, you don't get to go out to recess.” 

“You didn't do well enough, you get an F.” 

“You get a zero.” 

“You have a missing notice that has to go home and get signed by your parents.” 

Now, that last one can also be a type of communication between parents and teachers and doesn’t need to be punitive.  It really depends on the teacher’s mindset.  Do they want to punish or just communicate?  Is the note given privately and with empathy or is the kid put on blast in front of the whole class?  Is the tone of voice kind or upset?

Similarly, at home we tend to not spank much anymore (there is a lot of evidence around the harm that spanking causes) but we will take things away (negative punishment):

“You didn’t do your homework, you don’t get to watch TV” (or ride your bike, or play on the tablet, etc)

All of these punishments send the message that you believe the child has willfully chosen to do the “wrong thing” or to not do well enough on an assignment, etc. All of these punishments create a power struggle between child and adult.  All of these punishments can cause kids to feel like they are bad or dumb.

Rewards

We can also flip some punishments to be rewards: “you don’t get to watch TV until you do your homework.”

Or we can use bribes, “If you read this page to me, you get an M&M!”

We’re letting kids know that doing the homework or reading is not worth doing unless they are being “paid” to do it.  “If you do A, I’ll give you B” let’s the child know that A is a bad thing and B is a good thing.  If they already like A, they quickly start to realize that they’re not supposed to.

If your kid loved eating broccoli, you could kill that love pretty quickly by telling them they only get ice cream if they eat their broccoli and then one day stop giving them ice cream.

Reading is a wonderful and pleasurable activity for people to engage in.  Writing, mathematics, athletic endeavors, and playing music are also.  If we start rewarding a child for engaging in any of these, we are sending the opposite message.  We are telling kids that they shouldn’t like these.  They should only like TV, tablets, candy, etc.

Because I never want my young children to lose their love of books and reading, I will never bribe or otherwise reward them for reading with me.  Reading is already intrinsically motivating and enjoyable.

Praise

Praise is a specific type of reward.  Saying, “good job” tells a child that they are being evaluated.  It lets the child know that there is a right and wrong way to do things and that they better be careful not to do the wrong thing.

This can kill creativity.  If a child comes up to you with their drawing and you say it’s a beautiful drawing, expect to see lots more just like it.  They’re less likely to risk drawing something different because you might not like it.  They’ll stick with the safe drawing.

If a child is working on writing, and you tell them, “great hook!” you are giving a specific praise, but you are still evaluating them and they’re likely to use the same type of hook in their next piece of writing. (A hook is the beginning of the writing that grabs a reader’s attention)

Keep in mind that many famous, award-winning authors were rejected by dozens of publishers before being picked up and then going on to become famous.  Those professionals didn’t think that book was good enough but now it’s being taught in classes on literature.  It doesn’t matter what those particular professionals thought of the book and it really doesn’t matter whether or not you like the hook.

It does matter whether or not your child is able to learn and grow from what they are doing.  It does matter how they feel about their writing.  So, ask them questions: 

“How do you feel about the hook?”

“What part do you feel you really nailed?”

“What are you going to work on improving next time?”

“Are you aware of the conventions around dialogue?  May I show you how we mark dialogue in a text?” OR “Do you know how most English writers show when characters are speaking to each other?  May I show you?”

You can guide and teach without your child feeling evaluated.

What to do instead

Motivation is tricky.  In Alfie Kohn’s book, Punished by Rewards, Kohn goes deep into why rewards are problematic.  And yet, he doesn’t offer much in the way of what to do instead.  And that’s because it’s rather complicated and there aren’t any easy and quick answers.

In the coming months, we’ll be going into various strategies that you can put into place that will motivate your child!  Be sure to subscribe so that you don’t miss any new episodes/posts!