Using Apprenticeship to learn to solve a Rubik's cube

A Lego covered Rubik's Cube!

In the previous blog post, I explained how I used the Trivium to help me learn to solve a Rubik’s cube. When my son asked me to help him learn, I wondered how I would be able to teach him.  He was only 6 years old, and I knew nothing about the cube.  But after about a month of practice, I was able to solve a 3x3 on my own.  Now I needed to help my son learn. 

The second tool I used to help my son solve a Rubik’s cube is Apprenticeship.  I spent hours learning the steps to solving a cube, memorizing algorithms, and solving the cube, one layer at a time.   By this time, he had already found some strategies to solve the white face by himself.  I let him solve the white face.  Then I showed him over and over again how to solve the second layer.  Finally, he was able to take a little ownership.  I sat beside him while he practiced the second layer.  He asked questions.  When he was able to solve this layer without any help, I showed him the next step.  Over and over again.  We chanted algorithms.  We looked for patterns.  (In the final step to solving a cube, there is a yellow 2x2 square that spins around the top layer as we are moving the cube through the algorithm. It is fun to watch, and if the square disappears, we know that we have not completed the algorithm correctly.)

An apprentice to a blacksmith will not start making nails on his first day.  Instead he will stand beside the master blacksmith and watch him maybe thousands of times.  Gradually the master will start giving the apprentice a little more responsibility.  Eventually the apprentice will be able to make a nail, while the master blacksmith will continue to make horse shoes.  This process is one of my favorite tools for teaching.  It takes a long time.  It takes a lot of work.  But the rewards are infinite. 

Apprenticeship works for more than just Rubik’s cubes and blacksmithing.   I use this tool with my daughter when she studies Language  and Writing.  When we study the English Language, I model how to parse sentences into parts of speech.  We have a series of questions to ask.  For example, the sentence might be: “ Jonny solved a Rubik’s Cube.”  We would ask: Who solved a Rubik’s Cube? Jonny: Subject Noun.  What is being said about Jonny? Jonny solved: Verb transitive.  Solved What? Cube:Direct Object.  What kind of cube? Rubik’s: Possessive Noun Adjective.  When I first exposed my daughter to this series of questions, we started very simply.  The sentences only had two words.  “Suzy sang.”  I told my daughter I would not allow her to say anything.  She just needed to listen to me over and over again.  Who sang? Suzy: Subject noun.  What is being said about Suzy? Suzy sang: verb intransitive.  I repeated this pattern many times.  Tommy danced.  Who danced? Tommy: Subject noun.  What is being said about Tommy? Tommy danced: verb intransitive.  After about the 10^th sentence, my daughter finally said, “Mom, can I do it please?”  And you know what?  She did it perfectly.

I also use apprenticeship when I teach my daughter to write.  I model making keyword outlines, writing from the keyword outline, adding dress ups like adverbs and adjectives, varying sentence openers, etc.  When we first started using Institute for Excellence in Writing (IEW)’s writing program, I wrote most of the assignment myself, with my daughter sitting at my side.  Andrew Pudewa, IEW’s founder, says, “You can’t help your child too much.”

 The teacher in me feels like this is cheating.  It isn’t.  Of course, I do not let my daughter take credit for my work, but I want to model good writing so that students can learn from a master.  Just like in English Grammar, my daughter started out by just observing, then gradually took ownership of her own writing.

This fuzzy picture shows my son's first cube
that he solved entirely by himself!

 

Apprenticeship is a beautiful and effective way to teach. My children learn with me.  They know that learning is a lifelong process because they see me continuing to learn.  My children are better writers, readers, and thinkers because of the way we learn together. 

On Easter day 2017, my six year old son solved his first 3x3 completely on his own.  Later that month he had major surgeries and several complications.  He was sick for months, so he decided to take a hiatus from solving Rubik’s cubes.   He has just recently started to solve them again.  I will continue to sit beside him, cheering him on.

Using the Trivium to solve a Rubik's Cube

My six year old held a Rubik’s cube in his hand.  Turning it slowly, he looked at me.  “Mom.  I want to learn how to solve a Rubik’s cube.”

I could tell he was serious.  This was not a whim of a little boy.  I remembered the promise I made to one of his doctors.

“Help him find things that he can be good at.  Adaptive sports are fine if that is what he wants, but also invest his time in things like music, history, robotics.” 

 Dr. Timothy Brei is one of the most celebrated physicians in his field.  Dr. Brei and my son have something in common.  They both have Spina Bifida.  The Rubik’s cube seemed to be a way to keep my promise to Dr. Brei.  But I knew nothing about Rubik’s cubes. How on earth was I going to teach my son how to solve a Rubik’s cube? The first thing I needed to do was learn to solve a cube myself.

I used two major tools to help my son solve the Rubik’s cube. In this post, I’m going to focus on the first tool: The Trivium.  I will explain how the second tool, Apprenticeship, helped us to solve the cube in the next blog post.

I love Classical Education.  I educate my children classically at home, and we are part of a classical homeschool group that meets once each week called Classical Conversations.  When I first started studying Classical Education thirteen years ago, I thought it was kind of stuffy and dry.  Students learn Latin.  The memorize declensions.  They read old books.  It didn’t sound quite as fun as traditional learning to me.  But I have changed my position on that.  Classical education is not dry.  It is rich.  And the tools of Classical Education can be used to learn just about anything.  To show you how versatile the tools of Classical Education are, I am going to explain how I used the Trivium to learn to solve a Rubik’s cube.  (Not quite as stuffy and dry as it sounds, eh?)

In ancient Greece and Rome, students used the Trivium to learn new skills. Trivium means “three roads”  in Latin.  The three parts (or roads) to the trivium are Grammar, Dialectic, and Rhetoric.  During the Grammar stage, students memorize definitions and facts, with very little concern to meaning. While students can work through all the stages, young children naturally fall into the Grammar stage because they are able to memorize facts without a lot of effort.   Have you ever met a preschooler that can name all different kinds of dinosaurs?  My five year old loves Pokemon cards.  He can tell me the names of each of the characters on the cards, and he can remember how much health and damage each one has.  (I, however, have no idea what that means.  Nor do I care.)  The Grammar of the Trivium, not to be confused with English Grammar, is the basics of the topic you are studying.  Students in the Grammar stage memorize names and dates in History, math facts in Math; they memorize lists in Science such as the five kingdoms of living things. They memorize the list of prepositions for English Grammar. They memorize the states and capitals. Their brains are wired to memorize facts, so classical educators try to fill their long term memory with as many good facts as possible.

To use Grammar  to learn how to solve a Rubik’s cube, I first memorized the colors of the cube: white is always opposite yellow, green is opposite of blue, and red is opposite of orange.  Then I memorized the 7 steps to solving the cube. (White cross, white face, top layer, middle, yellow cross, yellow face, and bottom layer.)  I memorized the notation.  R means turn the right layer clockwise.  R’ means turn the right layer counter clockwise.  I learned how to orient the cube.  Then I started memorizing algorithms.  (I’m probably the only Rubik’s cuber that sings algorithms to herself.) If I have a yellow bar, then I need to use these steps to get the yellow cross; but if I have a yellow hook, then I need to use a different set of steps to solve the yellow cross.  All of this memorization began my journey of helping my son learn how to solve a Rubik’s cube.  While I was memorizing these facts, my son started playing with a 2x2 cube (instead of a traditional 3x3).  The 2x2 uses some of the same algorithms as the 3x3, but there are not as many steps to solve the cube.  This was a great introduction to learning to solve the 3x3.  He also had a pyramid puzzle with 4 faces.  He was able to solve it just by playing with it for a while.  These two simpler cubes helped him to understand the more complex 3x3.

The next stage of the Trivium is Dialectic.  As I said before, learning a new skill can take a student through all the stages, but children naturally fall into this stage around age 10 or 12 to middle school and early high school.  This is the time that students start questioning everything.  They tend to disagree with authority and argue about many things. During the Dialectic stage, students study logic.  They ask questions and answer many.  They use the grammar they have memorized and start to make sense of it.  They see how the facts they memorized fit into the world.

I used Dialectic tools to learn to solve the 3x3 cube.  I started with the memory work I had acquired.  I watched Youtube videos of skilled Rubik’s cube solvers show how to solve a cube step by step.  I practiced each algorithm many times.  I called a few Rubik’s cube solving friends to help me when I got stuck.  We had 5 cubes around the house, so I practiced each step five times before going on to the next step.  I first solved the white face on all five cubes.  Then I solved the middle of all five cubes.  And one day, I finally solved a 3x3 without any assistance.   This process took me about a month.  (I am sure there are many skilled cube solvers that learned to solve a cube in less time than me.)

The final stage of the Trivium is the Rhetoric Stage.  This is when you take the skills you have acquired from the Grammar and Dialectic stage, and you are able to teach what you have learned.  I started  a Rubik’s cube solving club that met at my house.  I was ready to help my son learn to solve a cube. I did use grammar and dialectic stages to help my son learn the cube, but there is also another tool I used to help him. I will explain how I used Apprenticeship to teach my son to solve a 3x3 Rubik’s cube in the next blog post.

Suzuki and IEW

As an Essentials tutor, I get a lot of questions about why we use Institute for Excellence in Writing's (IEW) History Based Writing Lessons.  I can see their point.  After the following techniques are introduced, students are required to have an ly adverb, a quality adjective, a strong verb, a who or which clause, and subordinate clause in each paragraph.  Students are also required to vary their sentence openers.  One sentence should start with a prepositional phrase, another with an adverb, and so on.  Each paragraph also needs an alliteration, a metaphor or a simile.  If the assignment is a five paragraph essay, then each paragraph must contain all these stylistic techniques, dress ups, and decorations.  It can make the writing seem a little awkward and forced.  So why do I choose to have my children in this program?   

To understand the reasons why IEW requires such a strict rubric, it is helpful to understand a little bit more about Andrew Pudewa, IEW’s founder.  Mr. Pudewa is a violin teacher.  He actually studied under Shin’ichi Suzuki.  I am a cellist, and when I heard that Pudewa studied with Suzuki, I could easily see the parallels between IEW and the Suzuki method.

 I am not a certified Suzuki teacher and I am not a certified IEW instructor, but I am very comfortable with both methods of teaching. I learned to play cello with the Suzuki  method.  In high school, I was so inspired by Suzuki’s methods that I wrote a report on his book, Nurtured by Love.  It is on my shelf today and I try to read it each summer as one of my inspirations for teaching.  Today I am a cello teacher for beginning cellists and I tutor seven children with the IEW method.  I also homeschool my ten year old daughter using IEW.

Here are 4 of the components of the Suzuki Method of learning music:

1. Scales, Arpeggios, and drills.  (This is not exclusive to the Suzuki method for learning an instrument. Most musicians spend much of their practice time playing scales, drills, and arpeggios.  A soloist will not play a concert of just scales, but music often consists of these things.  A soloist who has practiced drills will be able to play difficult passages with ease. 

This is why IEW has a checklist that requires students to practice stylistic techniques, sentence openers, dress ups, and decorations. While it may seem like a lot of fluff, practicing these techniques will enable students to use them when they need them in any kind of writing.  I remember studying metaphors and similes in school, but I was never asked to use it in a paper.  IEW students write a metaphor or simile in every paper. This is just good practice.  The assignments from IEW may not produce good writing, but it does help to produce good writers.

2. Parental help.  When Suzuki took a new young student, he first taught the student’s parents.  He asked the parents to hold that tiny violin (sometimes 1/16 the size of a full violin) and learn to play Twinkle, Twinkle, Little Star.  He gave the parents a few lessons in front of the child, but would not allow the child to participate.  The parents had to complete assignments at home.  Watching and listening to the parent, the child wanted to mimic what they did.  The result of this was two-fold. The young child was motivated to learn to play like his parents, and his parents were able to help him learn. 

Similarly, Pudewa says that parents cannot help their child too much.  In IEW, parents are given so many tools to help their children. From live seminars, to the Teaching With Structure and Style dvds, to webinars, articles, books, and teachers’ manuals, there are so many resources to equip parents.  I have taken advantage of the live webinars that Mr. Pudewa holds each month for Essentials tutors, which walks us through a mock lesson that we will teach later in the semester.  IEW is designed to walk students through all 9 units each year.  In the first few years, the student is somewhat like an apprentice to their parents.  My ten year old sometimes needs help selecting an appropriate –ly adverb, or rearranging a sentence so that it starts with a prepositional phrase.  IEW allows me to model and provide those things for her.  This is not cheating.  This is equipping.  Eventually, she will not need me to help her find the correct word.  Next year, she will be more independent in her writing.  

3. Ear Training. Suzuki students listen to recordings of master musicians who play the pieces they are studying.  These young musicians sometimes listen to the piece hundreds of times.  This trains their ears to play in tune, follow the complicated rhythms, and play with expression. 

In IEW, Pudewa recommends daily reading great literature aloud to children, even older children.  This trains students’ ears to hear what good writing sounds like.  Reading aloud has done wonders for the lyrical writing of my own children.  They write with expression.  They know when something doesn’t sound right.

4. Gradual increase in difficulty.  Suzuki’s music books gradually get more difficult and the student learns a little more with each piece of music.  For example, a student may be asked to play an already familiar piece in a different key, or with a different fingering and a different position on the fingerboard.  Cellists are required to learn 3 different staves.  The Bass Clef is the simplest.  When a cellist has mastered the Bass Clef, she will need to learn the Tenor Clef.  Suzuki gently introduces this by allowing the student to play familiar pieces in a different key and notation.  When the Tenor Clef notes seem more familiar, the student will be asked to play a new piece of music in the Tenor Clef.  The same process is repeated with the Treble Clef.

Writing five paragraphs about Amelia Earhart

Vygotsky called this teaching technique of gradually increasing the difficulty scaffolding.  Mr. Pudewa calls it Easy + 1.  Although there are many components to the paragraph checklist in IEW’s writing assignments, every student starts by adding just one –ly adverb to the paragraph.  When that becomes easy, the child will add an –ly adverb and new skill, like a quality adjective.  When the –ly and quality adjectives become easy, they will have a third requirement for their paragraphs. This continues until all the skills are mastered and practiced in each paragraph.

It is easy to see how Pudewa’s educational journey with Suzuki has helped him to mold the IEW program into what it is today.  Suzuki’s methods made me the cellist I am today, and I know that IEW will continue to sharpen the writing skills of my students.

Defeating a Dyslexic's Nemesis: Reading Aloud

“What’s the best way to defeat an enemy?”- Sensei Wu, Ninjago: Masters of Spinjitzu

It has been about a year since I intentionally decided to read out loud more.  Honestly, I would go weeks without reading a single book to my children.  We homeschooled.  I taught Math, and Science, and Spelling, and reading mechanics.  They did workbooks.  It was dry.  It was missing something.  I knew what was missing, but I didn’t know what to do about it.  I love reading.  I really do.  To myself.  But out loud… Shew. That’s another ballgame.  When I read out loud, dyslexia rears its ugly head.  I suddenly can’t remember how to pronounce a word I’ve said many times.  I find an unfamiliar word that I just skipped while reading to myself.  The words get jumbled up in my head.  On paper they sometimes magically rearrange themselves into a big hairy mess.

            Reading out loud has been my nemesis for years.  In college, reading aloud sometimes kept me from getting the parts I wanted when I auditioned for plays.  I was the kid in grade school who would count how many paragraphs until my turn to read out loud during reading circle.  Then I would read ahead, practicing the words in my head for the paragraph I knew would soon be mine.  I would be so focused on that paragraph that I would have no idea what was going on in the story, and I would miss my cue.  I missed a lot of recess because of this.  I remember visiting my cousin’s church in maybe sixth grade.  The Sunday school class was reading The Horse and His Boy, one of the Chronicles of Narnia books.  Each student took turns reading a WHOLE CHAPTER.  A whole chapter of British literature?  I asked if I could stop at after one page.  When studying teacher education in college, I sometimes had to read to different classes during my field experiences and internship.  It scared me.  One year a teacher asked me to read The Secret Garden out loud to her class.  Have you read The Secret Garden?  Some of it is written in Yorkshire.  Yorkshire.  I figuratively broke into hives.

            When my children were very little, I found the Five in a Row curriculum. It is a sweet way to introduce picture books to your littles.  I loved it. Each week we read the same book five days in row (hence the name…)  We read Madeline, and The Story about Ping, A Pair of Red Clogs, and so many other sweet stories.  We found the countries where they were located on the map.  It was easy and sweet. We counted and cooked. My children and I have many fun memories from that time.  Picture books are no big deal for me to read. Twenty-four pages with simple words? I can do that.

            Chapter books are a different hairy deal.  As my children got older, I wanted to introduce them to some of my favorites:  The Lion, The Witch, and the Wardrobe, Holes, The Tale of Despereaux, The Secret Garden, Ramona and Her Father.  I just didn’t have the stamina or the confidence to do it.  We would start a book and then never finish it. 

            By the end of the day, I’m exhausted.  My dyslexia kicks in and words on a page look like an unscramble the word puzzle.  (I’m actually really good at unscramble the word puzzles, because that is how words look to me all the time.) Reading out loud at bedtime just won’t work for me about 80% of the time.

            I was beginning to feel like this was hopeless.  My children would never experience listening to chapter books with me.  Then I started to listen to Sarah MacKenzie’sRead Aloud Revival Podcast.  Sarah says that you should read out loud even to your older children.  I had never really thought about it, but I was worried that I was losing the window of opportunity to read aloud with my oldest child.

            Here is how I went from reading almost nothing with my children each day to reading for several hours each day.  It was a gradual process. 

            The first thing I did was try to identify why reading aloud was intimidating for me.  The main reason was that I was just too tired at bedtime to read, and for some reason I had it in my head that I had to read chapter books at night to my kids in order to be a good parent and educator.

I decided to implement a Morning Time. Your morning time probably won’t look like mine.  I started just with Bible, a history storybook and some poetry.  Last year, I used Our Island Story about British history.  This year we are reading A Child’s Story of America.  I also love James Baldwin’s anecdotal history stories, and the Story of the World.  Our Morning Time at the beginning was Bible and History, and Poetry.  Already I was reading more.  I’m most alert in midmorning, so we usually started 8:30 or 9:00 am.  Then the kids did their workbooks and math and we went on with our day.  After the children got used to a few subjects for morning time, I gradually added one more.  (I think I added 1 subject each month.)   Here is our Morning Time schedule after 14 months (on a day when we don’t have any appointments or anywhere to go. You can read about how I modify this when we have a busy day here.) Our current schedule includes Bible, Precepts, Storybook of Science, A Child’s History of the United States, The Blue Fairy Book, and a chapter or two of whatever chapter book we are reading.  I finish Morning Time by reading Life of Fred, our math curriculum.  Then we move on to our next part of the day.  When we are home, my oldest two children can listen for up to two hours. They play quietly, or draw, paint, or do something.  I love using “living books” as our source of information.  Our history, science, and Life of Fred are all living books.  Living books draw children into a story to help them remember details.  The term living books was made popular by Charlotte Mason, an educator in the 1800s. Mason believed that history is best learned when you study famous people by looking at their childhood.  George Washington and Cherry Tree is an example of an anecdotal history story.  (I know that is just a tall tale, but it does help children link a relatable story to a famous person). I’m much too eclectic to use Charlotte Mason’s method exclusively, but I do love living books, and her ideas about nature walks, and narration.  I don’t require a lot of writing or worksheets about what we read. But we do discuss.  Yesterday, I read “The White Cat” from The Blue Fairy Book.  My seven year old chimed in that the story reminded him of Repunzel because the white cat, who was really a princess under a spell, was locked up in a tower for years when a prince tried to rescue her by climbing the tower.  I didn’t prompt him to tell me that.  My children are used to making connections because we do this many times each week.  I continue to add things to our Morning Time.  I want to do some music and art appreciation.  I want to read simple biographies.  I want to add a Five in a Row picture book. 

Here are some benefits that I have seen in the 14 months we have made reading aloud the focus of our day.  I am a much more confident reader.  Many of the books I read were written in the 1800s, with a broad vocabulary and complicated sentences. That makes reading chapter books a piece of cake for me, and it strengthens my children’s vocabularies and sentence structures.  Also, not to brag, but my Yorkshire is en pointe now!

My daughter studying the art of writing in her Essentials class using Institute for Excellence in Writing (IEW)’s History Based Writing Lessons.  When I read out loud to her, she is able to identify strong verbs, quality adjectives, -ly adverbs, different kinds of sentence openers, alliterations, and much more.  Reading aloud makes her a stronger writer. If you are familiar with the Suzuki method for learning an instrument, you know that a major part of Suzuki is that children listen to the pieces they will eventually play hundreds of times.  This trains their ears to play a piece like a master.  Similarly, reading out loud trains a writer’s ear to write like a master.

Another added perk of reading out loud is that my children have become better readers.  They read out loud for ten to fifteen minutes out loud each day.  They do it because they see me model reading out loud all morning.  My son is a good reader, but he has never really liked reading to himself.  In the past month, I have actually seen him pick up a book to read for pleasure. This is so encouraging to me.  I want my children to be vivacious readers, and I feel like we are starting to take a step in the right direction.  My daughter also has dyslexia, but she now reads above grade level, and her out loud reading is much better than mine was at her age.

Reading with friends on a cozy, rainy day

I have found that at bedtime we do read a little more now.  Like a snowball rolling down a hill, our reading amount is continuing to grow.  Picture books are my choice for bedtime, but my daughter and I recently took turns reading Flora and Ulysses (one of our new favorites) and last night, my youngest requested a chapter from Winnie the Pooh.

“What is the best way to defeat an enemy?”

“It is to make him your friend.”- Sensei Wu

Our family has made a friend out of reading aloud.  (Leave it to me to use a CARTOON to illustrate a blog post about reading.)

Shakespeare Camp: "Though this be madness, yet there is method in it."

I’ve been called a special kind of crazy on more than one occasion.  I’m usually told this after I announce my plan for the summer’s Shakespeare Camp. 

What is it that makes Shakespeare so unapproachable? The Bard of Avon intimidated me in high school.  I had this idea in my head that my dyslexia would keep me from understanding the language. During my freshman year, I completely fell in love with the story of Romeo and Juliet.  It’s the first real tragedy I studied, and I still get that heart wrenching feeling when Romeo doesn’t receive the letter in time.  It is one of the most moving stories I have ever read.  For extra credit, I memorized Juliet’s lines in the balcony scene.  I’m sad to say that they were the only Shakespeare words that I memorized while I was in school.  When I was rereading the play this week, the words of the balcony scene greeted me like a familiar friend.  I wish I had memorized more Shakespeare in my youth.

After I got married, I got a job as a teachers’ aide at a classical school.  I completely fell in love with Classical education, and I was inspired by young students who studied Shakespearian plays.  The next year, I was hired as a fourth grade at a traditional school, and I decided that my students would perform The Fifteen Minute Hamlet, a play my college drama troop had performed, as a big end of the year program.  The Fifteen Minute Hamlet is a one act play by Tom Stoppard.  It is pure Shakespeare, ultra-abridged.  I loved it.  The quick pace makes the tragedy almost comical.  My class of 7 boys and 2 girls loved it. Who wouldn’t love ghosts, and poison, and sword fights, and skulls? In fact, many years later (am I showing my age?!) I got this lovely note from one of the students who had been in that first fourth grade class.

“Dear Mrs. McAdams,  

So a couple of days ago, we started reading Hamlet in my AP English class. My teacher was and still is extremely impressed that I had been exposed to Shakespeare in fourth grade. As I'm reading through it though, all I can think about is our absolutely fantastic performance that we did. It's almost next to impossible to read it because I'll hear Noah and Jacob and Isaac and Kelly and everyone else saying the lines! However, just that little edited version we read has made a world of a difference for me. I cannot thank you enough for making us read through something that people eight years above us were reading and helping us understand it. You've made AP English easier!"

This is the number one reason I teach Shakespeare to children: to build confidence.  When you expose children to something that seems hard and they understand a little bit about it, it makes them believe that they can do even more.  I love teaching hard things to young children.  It’s my philosophy of education in a nutshell.  Some of my other reasons for teaching Shakespeare are the story, the language, the poetry, and the fun.

FAQ about Shakespeare Camp

Where did you get the idea for a Shakespeare Camp?!

 I’m not going to bore you with all the details of how Shakespeare camp came to be.  Here’s my abridged version.  I was very familiar with teaching The Fifteen Minute Hamlet to kids.  I also spent five summers in high school and college as a camp counselor.  My husband moved me out in the country on some land that feels “campy” to me.  Naturally, all this begs the question: Why NOT have a Shakespeare Camp? (“Why not” is also a part of my philosophy of education.  Just call me Vygotsky. )

What Is Shakespeare Camp?

This will be my third summer to host a Shakespeare Camp.  I call it camp because we play campy games like Capture the Flag (Capulets versus Montegues), my version of Giants, Wizards, and Elves (Midsummer Night’s Dream- Fairies, Humans, and Elves), archery, etc. 

Every day we have devotions by the cross.

We make crafts and sing songs. 

It is a day camp, with a Shakespearian theme.  Each year we study and perform a play.  We have performed Hamlet, Midsummer Night’s Dream, and this year we will perform Romeo and Juliet.

We have memory work set to music.  (Side note: Today my lovely daughter said exasperatingly, “This is what my mom does.  She takes perfectly good music and turns it into school!”  She is not wrong.)  The memory work is pure Shakespeare.  We study iambic pentameter.  We study the life of William Shakespeare. I wrote a song about the Bard's life set to the tune of the Beverly Hillbillies. We study tragedies and comedies.  We practice and preform an abridged version of the play.  We have fun with language and poetry.  Shakespeare camp makes Shakespeare memorable and enjoyable.  I do not strive for a perfect performance.  It is not a drama camp.  I’m more focused on learning and enjoying the story.

What about all the heavy themes?

Yes.  That’s a tricky one.  Some children are not ready to hold a skull and lament, “Alas. Poor Yorik.” Honestly, I’m still wrestling with Romeo and Juliet.  It’s such a sad story.  I always go back to the Bible.  What does the Bible say about this? Was the decision to end his life a good one?  Did anything good come out of Romeo and Juliet’s deaths? Can God use tragedy for his good and glory?  I believe He can and He does.  I have had a few students that request to take a role other than the ghost in Hamlet, or to be a character that lives. I always honor those requests.  A few parents have kept their sensitive children home instead of performing in the tragedies.  They join us when we do a comedy.  At the moment, I’m considering Taming of the Shrew for next year.

And the question you are all waiting for:  When is the next Shakespeare Camp?

We will meet at my house on Friday June 1, and the week of June 4-8 from 9am to 12:30 pm.  Our performance will be on Friday, June 8 at 7:00 pm.

The cost is $35 per child and $30 for each additional child in the same family. *As always, if money is an issue, please let me know.  We will work something out! The cost goes toward supplies, memory work CD, copies, and my time.

Students must be ages 5-12.  This is for any child.  Every year I have children who are in traditional school as well as homeschoolers. If your child is part of the Challenge program, they are welcome to apply to be a Counselor in Training (CIT). This is a volunteer position that would count for service hours. 

I prefer to have parents stay.  If you need to drop off your children, please arrange that with me in advance.

Please let me know if you are interested!  We would love to have you!

Cool Tricks to Multiply Numbers 6-9

If you have been reading my blog, you probably noticed that I get way too passionate about educational tricks. (Once I was moved to tears when I found out there was a reason for the Silent E in the word "have.") 

Today is no exception.  You guys... This is LIFE CHANGING.  I was excited to show you the first trick I learned. 

But then last night, I learned an even more nifty multiplication trick that you can do ON YOUR FINGERS.  And I literally jumped up and down for joy.  I need to work on my self-control a little bit.

Today I want to show you a quick trick to help your child memorize multiplication tables.  This only works with numbers 6-9.  The nines and tens facts have their own tricks, so I would focus on multiplying 6-8 which are usually the hardest to remember anyway.)   If your child needs help learning to multiply 3s and 4s, I really love Times Tables the Fun Way.  It has little pictures and stories that help you remember the math facts. (You have to be 16 to drive a 4x4, etc.)

Ok, here we go... I learned this trick from Speed Math for Kids. It is the basis for all kinds of mental math multiplication tricks.  Using the same method, I can multiply numbers like 97 x 98 in my head.  (It's 9506, by the way.) I highly suggest you get this book.  It's fun for kids and challenging enough for adults.  I spent all summer wading through it, and I still have a lot to learn.

I will do one more:

I hope that mostly makes sense.  Are you ready for the coolest part of all? Last night, I learned from Pintrest that you can do this ON YOUR FINGERS!  Life Changing, My Friends.  I am going to put the finger method next to the circle method so that you can see we are doing the same thing.  (Spoiler alert: The finger method is easier.)

Step 1: Assign numbers to your fingers and touch the fingers you want to multiply together.

 

 

 

 

 

 

Step 2: Count the number of fingers that are touching and below.  Multiply that number by 10.

 

 

 

 

 

Step 3: Multiply the number of fingers on each hand that have not yet been counted. Add that product to the step 2 answer.

I'm curious to hear your thoughts.  Do you think this could help a child who is struggling to learn multiplication?

Need more help?

Check out these videos :)

Circle Method for Multiplying numbers 5- 9

Finger Method for Multiplying numbers 6-10

Play Your Way to Higher Math Skills: Simple Games to Develop Number Sense

 

When I tutor children in math, the first thing I do during their assessment is to find out where their number sense falls away.  Can they subitize the number 4?  7?

Subitize means to look at an amount of something (like four blocks, or two forks) and know how much it is without counting.  

I need to distinguish between number and numerals.  Number is an amount.  Numerals are the written representation of that amount.  1, 2, 3, 4 are numerals.  While recognizing and writing numerals is important, it doesn't necessarily mean that a child has a strong number sense.  

 



This cutie is demonstrating the equation
1 - 1 = 0.  Genius little cousin of mine
Peekaboo!

My general rule of thumb for children aged one through five is that the amount a child can subitize directly corresponds to their age.  So, a three year old can usually understand the amount of three, but the number four is a little trickier.   

You may be thinking that a one year old can’t understand the number one.  But they do.  When they play Peekaboo, they see one thing (like your face) and then it goes away (behind a blanket).  The equation 1-1=0 is hysterical to them.  Even though your one year old probably will not recognize the numeral 1, he or she CAN understand the amount of one.  Your baby is a genius!

Playing some simple games with your three to five year old will help them develop a better Number Sense.  This process is also VERY helpful for early elementary students who struggle to understand number concepts.  (I ALWAYS assign these games to my struggling math students.)

 

Many of the games I will present today come from the book Developing Number Concepts Using Unifix Cubes by Cathy Richardson.  Sadly, this book is out of print, but it is worth tracking down a used copy.  Amazon and Ebay usually have several inexpensive copies available.  This book has activities that strengthen skills in addition, subtraction, multiplication, division, patterns, and so much more.  I think it is worth every penny. 

You don’t need fancy schmancy math manipulatives to help children develop a Number Sense. One of the first things I do with my young learners is to find an age appropriate small toy that they like to play with to use as counters. 

Shopkins are popular for girls.  Or you could use Lego Mini figures for boys, or just some plain Legos.  Beans are cheap, but not as motivating.  M&Ms are just a little too tempting for my taste. If you have Unifix cubes, this is a great way to use them.  Get a butter container or a plastic cup- anything that is not see through and that is large enough to fit all the counters inside.

We are going to focus first on the number (amount) as opposed to the written numeral.  We’ll get to numerals eventually.

 

 

Game 1 : How many are in the tub?

 

Secretly put a number of counters under a plastic cup.  Have the child peek under the cup and quickly subitize (know the amount without counting) the answer.  Repeat with another amount.

 

 

 

 

Game 2: Matching Number and Numeral Correspondence

Put one counter under the first cup, two counters under another cup, three under a third cup, four under another cup, and five counters under the last cup.  Mix them up.  Make a numeral card for each of the number amounts used.  Turn them over and mix them up.  Take turns looking under the cup to subitize the amount, and turning over a numeral card.  Try to match the amount with the numeral card.

 

 

 

Game 3: Making Equations

Step 1: Start with one less toy than your child’s age.  My son is 5, so I’m going to start with four Lego Mini figures.  Show your child all of the toys.  Then secretly put one of the counters under the butter tub.  Put the remaining toys on top.  Ask the child how many are under the cup.  Most children should be able to know how many are in the cup. If the child has no idea, start with a smaller amount.  If this seems a little two easy, you can increase the beginning amount by one. 

Step 2: Repeat Step 1, but put two counters under the cup instead of one.  Then three, etc.  Do not go on to a higher beginning amount until you have completed at least steps 1-5.

Step 3: When you feel like your child has an understanding of how many are in the cup, start using some math language.  “There are 3 on top of the cup.  How many are inside the cup?” “One” “Yes.  One counter is inside the cup because one plus three equals four.” And “I have four counters.  I’m going to put some inside and 2 on top. How many are inside?” “Two” “Yes, because four minus two equals two.”

Step 4:   Now each time you play the game, show the child the written equation.  1 + 3 = 4.  2 + 2 = 4.  3 + 1 = 4.  This is also subtraction . 4 – 1 =3.  4 – 2 = 2. 

Step 5: Feeling daring?  Did you know this game is really ALGEBRA?  Your four year old is a smartypants.  Use the term “unknown.”  Say this: “I’m going to start with four counters.  I’m going to put an unknown amount under this cup.  There are 3 on top of the cup.  What is my unknown amount?” After the child answers, show your child this equation.  x + 3 = 4.  (This step is not from Developing Number Concepts.  It's just from me.  I learned the value of exposing Algebra to young children from the Life of Fred Books.  You can read my LoF review here.)

This game can take just five minutes each day.  You could start with the first two steps, then add a step each day. After a week, increase your beginning number of counters by one, and follow the steps. 

Step 6: Eventually you can have your child copy the equations on a marker board or a piece of paper.

Step 7:  See if they can write the equation on a piece of paper without any prompts.  There are three different ways to write any representation.  1+3 = 4.  4-1=3.  x +3 = 4  are all the same thing.  You could also have them practice writing them vertically.

 

These are just a few of the games found in Developing Number Concepts Using Unifix Cubes that I use with so many of my students.  Whether your child is in PreK or Kindergarten or is struggling to retain math facts in elementary school, these games are sure to help your child succeed in math.

Need more help?  I love tutoring elementary children in Math! Let me know how I can help your child.