Math is Everywhere: making your own “textbook”

Scott and I are making a book!

We flipped through the newspaper to find all the places math was being used and discovered it was… everywhere!

We decided to write a book. Our first step was to cut, cut, cut like crazy. Scott cut out some of the math we are used to seeing while I cut out more abstract concepts. Here is Phase One of our book:

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Phase Two will be to glue concepts from our textbook to match the real world math. In other words, the theoretical to the practical.

Phase Three will be to write stories to talk about how the math is being used.

Stay tuned!

Waldorf Education and the 21st Century: Compatable or Clashing?

In my perpetual quest to find the perfect education, I decided to check out the local Waldorf School for an impression of a different sort of school system. Situated on a quiet country road, surrounded by a forest, farms and large fields, I was most curious about how the school integrated nature into learning and how creativity was fostered. More significantly for our Digital Generation,  how did the lack of technology influence students and their education?

In 1919, Rudolf Steiner developed the notion of a whole-body/soul educational experience; he saw learning as an opportunity to unit the intellect with the body. One of the central pillars of this new pedagogy was to see the beauty in all things, from a math problem to a dance. Steiner began his quest by establishing the first Waldorf School to educate the children of factory workers in Germany. His system was simple; children’s development falls into three developmental stages:

  • From age 0-7 children learn through mimicry and imitation. In order to learn a concept, approach, or appropriate response, adults must first model the approach. We see this in children who play on plastic cell phones or pick up the language of the adults they are surrounded by. In a spiritual sense, these early years form empathetic humans who are conscious of the good in the world. They seek to please others, which is why they model the behavior around them so readily.
  • From 7-14 children learn by doing. At this stage, children begin to role play, create narratives and art of their own, and contextualize their learning from a personal, “egocentric” point of view. At this stage, the teacher becomes a facilitator, guiding students and creating the scaffolding for their learning. Within the classroom setting, students create artistic portfolios of their learning. Everything is given a sense of beauty and personalization: number lines, mythology, music, biology and so forth.
  • From 14 onwards, children learn by judging situations and applying critical thinking. In today’s education, the “Inquiry” based approach is equivalent. Students look at the big picture and dismantle each piece in order to fully understand; learning is deep and thorough. At this stage, students are asked to link learning to the real world and apply it to their own lives- both present and future.

Many of the early teaching practices are still applied today. For instance, the fact that Steiner started these schools for working class, and often poor, families meant that materials for learning came from their own lives. Hence the wooden blocks and rudimentary learning materials. Still today, Waldorf schools use chalkboards and do not use textbooks. Learning materials are created BY the students, through drawings and plays, crafts and hands-on experiences. This can be a difficult philosophy for many, as today’s gadget infused world implies that better learning is equal to better technologies and tools.Waldorfschule-Klassenraum

Many of the Waldorf’ Schools around the world apply the concept of simplicity to the physical school itself. Waldorf Schools are more often than not unassuming and modest structures. Some may even be build out of natural materials, such as cob. They are subtly colourful within; you will not find stark white corridors and classrooms. In keeping with a modest architecture, desks are wooden, the room is not cluttered with posters, shelves and displays. Instead, student work is featured in the hallways. P1010052In the younger grades, classrooms are cozy and almost ethereal: linens are draped, small nooks are created with cloth tents, and little chairs and tables dot the room.

One of the most significant characteristics of Waldorf education, perhaps more poignant in today’s world, is a true sense of order and discipline. This is especially obvious as student’s transition from one activity to another. They bring out their work and copy down lessons with artistic individuality and focus. There are perhaps two reasons why lessons appear to be so fluid and orderly. For one thing, they are! Each lesson is linked to a previous day’s lesson; this is because each morning students have a devoted block of core learning on a subject that will continue for several weeks. In other words, if students are learning about fractions, each morning for several weeks, they will continue their lesson on fractions. Once this unit is complete, they will begin an ecosystems unit, for example, and continue that for the morning lessons. This is, in many ways, similar to a traditional education. Imagine each course (Science, Math, SS) as a lane in a pool. Students in traditional schools learn by swimming up and down individual lanes, with each lesson being taught at its own pace, side by side with other lessons. On the other hand, the Waldorf curriculum is more like diving, where each topic is tackled one at a time (though I have to point out that Language Arts is also taught each day) and there is much more of an emphasis DEEP cross-curricular learning.

The approach to Waldorf teaching is largely Socratic. imagesAs I observed a grade four class, I was interested to see how well the teacher used open-ended questions to gauge students understanding and recall. It was simple to see who “got it” and who was still in the dark. An important skill to master is to call on all students throughout the lesson, rather than the ones who put up their hand. This can be done by drawing names written on Popsicle sticks out of a jar, but also in creating a really safe learning environment in which all answers are considered. Waldorf, like so many other modern teaching methods, guides students and redirects their thinking not through criticism but with graciousness. Rather than, “Oh, that is not right,” a teacher might say, “This number is doing something tricky here. Let’s see if we can make sense of it.” While this may seem a little bit belabored, it creates a genuine sense of compassion for learners.

My lasting impression of the Waldorf system is primarily positive. I believe that the tools and styles of teaching implemented are practical and thorough. I enjoyed being in a class that used colour and art to create meaning and personalized materials, rather than simply filling in worksheets and textbooks. I also appreciated the emphasis on nature, and on natural materials for learning. That being said, there were a few questions in the back of my mind as I left the school. The first was my confusion at why Waldorf insists on abiding by principles adopted in the early 20th century. I feel that Steiner would frown at the way the curriculum has been stagnated. His emphasis, after all, was on using the most applicable, current tools for teaching. If he was using wooden blocks and spindles to teach math in 1940, would it not stand to reason that in 2014 we should be using technology that is applicable to the work force today? I do not suggest that an iPad should be placed in each child’s hand; I simply mean that playing movies, researching on the internet, utilizing cameras and video and so forth have benefited so many students. I myself could not have helped certain students without the direction of these tools. I also feel that the curriculum and method of teaching are incredibly binding; there is little room for autonomy and flexibility in the curriculum. It seemed, from my first impression, that students learned the same thing, with the same projects, year after year after year. I would not be surprised if a Waldorf student from 1950 produced the exact same portfolio, project or art project as a child today. And perhaps this is the reason so many people are either drawn to or discouraged from Waldorf Schooling. While many people find the predictability and consistency of the system to be exactly what they want for their child, there are others who see the benefit of a changing, malleable education system that moves with the times.

After spending some time watching and researching Waldorf education I feel that I have a better sense of the education system Like so many philosophies and pedagogues, I see the value in taking the best from this system and applying it liberally to my own ideals and experiences. With perhaps more modern tools and more autonomy in the planning and execution of learning, I feel that Waldorf will continue to be a strong alternative to the public learning system.

If you are interested in hearing more details about my visit to the school, or would like more information, please feel free to contact me any time.

For more information, visit:

http://www.whywaldorfworks.org/02_W_Education/

http://www.whywaldorfworks.org/07_Community/marketplace.asp

Self Smart/ Intrapersonal Intelligence

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This poster reminded me of Dr. Bruce Tobin‘s art therapy lesson “Magic Shop.” Last year I improvised the lesson with my students and couldn’t believe the positive long term effects.

The lesson is simple. Provide students with three cue cards. Have them write down three qualities/virtues they admire about themselves: caring, friendliness, happiness, patience, kindness, loving, organization, courage, honesty, etc.

0003576_virtues_poster_gifts_of_character_300While students are writing their virtues, create several of your own cards with the following labels: anger, ambition, efficiency, commitment, enthusiasm, disappointment, happiness, kindness, patience, thoughtfulness, empathy.

Once students have written down their virtues, demonstrate the way the roll-play “game” works. Explain to them that you run a shop outside of teaching hours. It is a special shop that specializes in trading feelings and virtues. No money is ever exchanged; people simply come to your shop and trade one of their feelings for another they might be in need of.

Ask a student to volunteer to demonstrate. The student will come with their cards to your “shop” and look at the ones that you have on display. Once they have decided on a virtue they would like to trade, they will give you one of their cards in exchange for one of yours. Before they do, however, ask them to explain their reason for the trade (they do not have to get too personal here!). An example: “I have a lot of happiness in my life, but feel like I need more patience.”

Be sure to ask one of the student’s who enters your shop if they are sure they don’t want any ambition or frustration. Explain that too much of something is a bad thing, but sometimes it is helpful to get frustrated instead of pretending everything is okay. Explain that it is also okay to get angry, as long as there is not too much of the emotion. for example, if someone is being treated badly or being taken advantage of, they may need anger instead of complacency to take action.

Optional: allow students to fill out one more cue card with a feeling they might have TOO much of (so called negative feelings *in this exercise there is no such thing as a negative feeling, only an excess of…)
Once the trade is complete, the student’s card becomes a part of your display and the next student comes to make the trade. Once you have demonstrated for the class at least three times, explain that you are having an open house where people can come and swap cards one their own. The only condition is that they explain the swap.

Students will mingle for 10-15 minutes. During this time, circle the room and encourage students. (*One student approached me and said “I would like to create a gift certificate.” She handed me her “kindness” card and asked me to give it to another student. The student smiled happily when she received the card and was really grateful for the gesture!)

At the end of the lesson, allow for a reflection time. What worked well? What did students struggle with? What surprised them? What would they do differently next time? How will they use their new cards?

A few months later, when students were doing a locker clean up, I noticed that most of them had taped these cards inside their locker. It was a good reminder, I think, to build new virtues and to share the ones we have.

Twas the Night …

nightbeforechristmasTwas the Night Before Christmas Gift Exchange

Read fairly slowly pausing at punctuation.

The group forms a circle or sits in a straight row (separate circles or rows if males and females are present). Each holds the gift he brought to the party. While the poem is being read, each person passes his gift to the person on his right when reader says RIGHT; when reader says LEFT, each passes the gift he has to the left. The gift each person has in his hands at the conclusion of the poem is his to keep. NOTE: No one will receive the gift he brought if all pass gifts as directed.

Twas the night RIGHT before Christmas when RIGHT through the house
Not a creature was LEFT stirring, not even a mouse–
The stockings were hung RIGHT by the chimney with care,
in hopes that St. Nicholas soon would be RIGHT there.
The children were nestled RIGHT snug in their beds,
while visions of sugarplums danced RIGHT in their heads,
And mama in her kerchief, and I in my cap,
had just settled RIGHT down for a long winter’s nap,
When RIGHT out on the LEFT lawn there rose such a clatter,
I sprang RIGHT from my bed to see what was the matter.
Away to the RIGHT window I LEFT like a flash;
tore open the shutters and threw up the sash.
The moon on the breast of the new-fallen snow
LEFT a luster of midday to objects RIGHT below.
When, what to my wondering eyes should appear,
but a miniature sleight and eight tiny reindeer.
With a little old driver RIGHT lively and quick;
I knew RIGHT in a moment it must be St. Nick.
More rapid than eagles his coursers they came;
and he whistled and shouted, and called them RIGHT by name:
“Now, Dasher! Now, Dancer! Now, Prancer and Vixen!
On Comet, on Cupid, on Donder and Blitzen!
To the RIGHT top of the porch! To the LEFT top of the wall!
Now dash away, dash away, dash RIGHT away all!”
As dry leaves that before the wild hurricane fly
when they meet RIGHT with an obstacle, mount RIGHT up to the sky,
So up to the housetop the coursers they LEFT flew,
with a sleighful of toys and St. Nicholas, too.
And then in a twinkling, I heard RIGHT on the roof,
the prancing and pawing of each little RIGHT and LEFT hoof.
As I drew in my head and was turning LEFT around
down the chimney St. Nicholas came with a bound.
He was dressed all in fur, RIGHT from his head to his LEFT foot,
and his clothes were all LEFT tarnished with ashes and soot.
A bundle of toys he had flung RIGHT on his back,
and he looked like a peddler just opening his pack.
His RIGHT and LEFT eyes, how they twinkled! His dimples how merry!
His cheeks were like roses, his nose like a cherry!
His droll little mouth was LEFT drawn up like a bow,
and the beard LEFT on his chin was as white as the snow.
The stump of a pipe he held RIGHT in his teeth,
and the smoke it encircled his head like a wreath.
He had a broad face and a round little belly,
that shook when he laughed, like a bowl full of jelly.
He was RIGHT chubby and plump, a RIGHT, RIGHT jolly old elf,
and I laughed when I saw him in spite of myself.
A wink of his LEFT eye and a LEFT twist of his head,
soon gave me to know I had nothing to dread.
He spoke not a word, but went RIGHT straight to his work,
and filled all the stockings; then turned with a jerk
And laying his finger to the LEFT of his nose,
and giving a nod, he LEFT up the chimney he rose.
He sprang RIGHT to his sleigh, to his team gave a whistle,
and away they all LEFT like the down of a thistle.
But I heard him exclaim, ere he LEFT–out of sight,
“Happy Christmas to all and to all a good night!”

Awesome Factors and Multiples Math Lesson

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I recently taught a great math lesson and thought I was would share it with you. Let me know what your think!

Materials:

– iPad or device for Apps

– Apps: FactorSamurai & MiddleSchoolMath HD

– projector or AppleTV (something to connect iPad to projector)

– worksheet or workbook

 

Extension:

Flocabulary (LCM/ GCF)

– factor tiles

 

Lesson Plan:

1. Begin with a quick brainstorm about multiples and factors. What are they? Where are they useful? How can our understanding of multiples help with factoring and visaversa?

2. What challenges prevent us from understanding of multiples (example: not memorizing multiplication table; difficulty counting on, etc).

3. Help students visualize multiples and factors. Visual tools for multiples: VennDiagram or 100’s chart. Visual tools for factors: factor rainbow or factor tree.

4. Hand out worksheet or workbooks. Help students to visualize problems (work on the board to guide students through the first questions).

5. At this point in the lesson, many students may feel frustration at not understanding multiples or factors. Typical areas of difficulty are multiplication, skip counting and prime/composites…

SOLUTION to frustration: have some fun!

6. Hook up the iPad/device to projector. Begin to play FactorSamurai. Tell students that you only a Grasshopper but really want to become Apprentice and need their help. Students will immediately want to play. Ask them to watch and try to figure out the  pattern. Once students have figured out the pattern, allow several students to try and beat your high score.

7. Soon students should start to see the pattern, even the one’s that were not so sure before. They understand that (yes, this is exactly like fruit ninja!), they are trying to break the numbers into their factors. But you can’t break a prime!

DID YOU KNOW: factor comes from the Latin word “done”. Kind of makes sense!

8. Next, demonstrate the game “sorting multiples” on MiddleSchoolMathHD. Again, ask students to look for the pattern before allowing them to play. The crabs should be sorted into three bins: numbers that 2 goes into, 3, or both, for example. Soon, students should start to see another pattern: some numbers have “common multiples”

9. Finally, students will return to their worksheet. Ask students to explain how the game is like the worksheet. This will be their ticket out the door.

 

Hint: factors are what you multiply to get a number. So the App FactorSamurai actually asks players to slice the end product (multiple)  into factors. For example, two times two is four. Four is a multiple of two; two is a factor of four.

Hint: multiples are what you get after your multiply.

 

Extension Lesson:

10. Students watch flocabulary “LCM and GCF”, completing the fill-in0the-blank worksheet

11. debrief on the difference between multiples and factors.

12. Allow students to use factor tiles to visualize how different numbers can be be broken up in various ways. For example: 1×12, 3×4 or 2×6

Links:

Greatest Common Factor

Primes and Composites

factor tiles

factor and multiple classroom game

explanation of factors and multiples

Happy Teaching!

Organizing Your Classroom Day, Week, and Term

One of the first questions I had as a new teacher was about how to organize my days. How was I going to fit in every precious lesson, every field trip, every silent reading break, every test, every activity? Moreover, why didn’t they teach this to me in University!!

Over the years I have borrowed some great ideas for day , weekly  and term planners. If you have an idea of your own, please post it in the comments below, or direct readers to you own helpful resources.

Happy Planning!

DAILY PLANNERS:

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–  schedule on one side and the lesson plan notes/ behaviour notes on the other. One the right side, for example, write the goal of the lesson: “expository lesson 1/4”. On the other side of the paper, write down notes on how the lesson will unfold: “introduce new essay style, brainstorm as a class, pick topics out of a hat, begin planning stages, assign due dates for rough draft. NOTE: book computer lab for final copy type up.”

– Use coloured pens, highlighters, etc: highlight meetings, important lessons/ tests, etc.

– only use information that you will need to avoid unnecessary clutter/ added work. Pre-fab planners may not be as useful as your own templates for this simple reason.

– Detailed daily notes have the added bonus of being ready-to-go for SUB teachers

 

WEEKLY PLANNERS:

not a replication of the daily planner (ie, your own notes). Make a plan at the beginning of the term. This is the planner that you give to parents/students, admin, as well as post in the classroom so that everyone knows what is expected on each day.

– PLAN silent reading time, tech time, library visits, etc. If they don’t make it onto the class schedule, they likely won’t happen at all 😉

iTeach_Schedule

– if you are a teacher who has more flexibility when planning your schedule, you probably wonder how many hours of each class you should fit into each week. As a rule, math and language arts are given the most time allotment. For math, it is especially helpful to plan in a “comprehension skills” day, devoted specifically to drills and new skills. Stagger lessons: plan for science on Monday afternoon and Thursday morning, for example.  Student’s have different energy levels at different times of the day, as well as the fact that classroom interruptions will not impact a staggered schedule as much as a regular schedule.

– On Monday morning, include a 30 minute “high light/low light of the weekend” share time. Students LOVE sharing about their weekend (they have 30 seconds to share). This activity is great for building classroom culture.

–  Post the daily version of this schedule on the whiteboard/ at the front of the room.

– Homework days can also be assigned on this schedule. For example, Monday and Thursday Math and Science

– Try to plan one-on-one time with each student. I know teachers who use silent reading time to go over assignments with students, listen to them read, or check in with them. Learning-Materials--Magnetic-Daily-Schedule-Chart--LER3233_L

TERM PLANNERS:

– map out field trips, unit tests, guest speakers, projects, meetings, report cards, term-planneretc

– try to fit everything on to one page, on a week-by-week schedule

– SCHEDULE IN MAKE UP TIME. Whether it is for projects or falling behind in the schedule, plan a week or days here and there that can be used as “flex days”

Check out the following websites for more information on Lesson Planning:

New Teacher Survival Guide: Planning

Planning with Mandi

DIT homeschool plan

ErinCondron.com

Additional tips:

– Keep all your notes and schedules in ONE binder. This includes classroom/ behaviour notes, project outlines, check lists for assignments handed in, grades, important dates, etc.

Happy Planning!

Long-term memory, here we come!

Can multiple intelligences enhance long-term retention of information, facts, or ideas?

Why is it that we all remember, as adults, the projects and science labs we completed in school? More to the point, how does a grade seven Ancient Egypt banquet hold more sway with the ol’ hippocampus than the trigonometry we spent hours labouring over? The answer is simple. Humans learn through context-based, personalized, tactile-based activities.

One of my favourite multiple intelligence activities is the body/picture smart task “create a plasticine/ claymation scene.” Students never cease to amaze me with their creativity and imagination; but what surprises me more is that this small task creates such deep learning.Screen shot 2013-02-24 at 8.56.30 PM

The first claymation task I developed was designed as a “choice activity” for Lit Circles. Body Smart Character Detectives were asked to recreate four key scenes from their novel and to provide page numbers and a caption to support their plasticine work; Visual Smart Detectives were asked to sketch four scene and so forth. The results were phenomenal. Although I had only provided students with three small pieces of clay, they creates wonderfully detailed scenes.

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I have since used this activity for math, science, and social studies, as way of engaging students with a particular topic on a level that might otherwise be somewhat one-dimensional (read: dull).  From models of the earth’s layers and thematic poetry to fraction circles and ancient Egyptian tablets, visual and tactile learning pushes students to personalize their learning. Unlike a worksheet that asks students to uniformly present their ideas either correctly or incorrectly, these activities engage students and involve them emotionally with their learning- hence the long-term retention.

Case in point: I assigned students a small homework task. I provided them with a “pinwheel” worksheet (see samples on my website http://www.mi-classroom.com). The eight MI activities were designed to draw out the student’s understanding of power in Ancient Egypt. 8/12 students chose the visual task: recreate the Palette of Narmer. What was interesting was that as they explained their favourite part of the task to the class the next day, they went into detail about the unification of upper and lower Egypt, the symbolism of power and the ideals of ancient kings in more depth than I could have anticipated; each student offered a unique Palette, with a detailed synopsis of its key information.

LOGIC SMART and SELF SMART SAMPLES

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VISUAL SMART SAMPLES

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I strongly believe that the reason science labs and field trips appeal so much to us, is the same reason these small tactile activities also appeal: haptically acquired information = unconscious learning.

Essentially, students who use visual and tactile tools to complete a task encode information differently than those completed completed on paper; they store information in their long term memory because it is a) interesting b) personal and c) contextual.

Words can certainly help us in the short term, but there just might be a strong case to be made for tactile, musical and visual learning tools. And if this can be proved than can we make a case for extending these forms of “learning through play” to Senior School students?

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