Sacramento Homeschool Math By Hand

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 187

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math.  Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”  

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times. Why ambient?  A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful.  CCSS math standards are listed here in blue, followed by ambient math suggestions.  Note that this post is largely a repeat of yesterday’s because the two are so closely related.

Operations and Algebraic Thinking 3.OA
Represent and solve problems involving multiplication and division.
2. Interpret whole number quotients of whole numbers; eg., interpret 56 / 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.  For example, describe a context in which a number of shares or a number of groups can be expressed as 56 / 8.

Is this enough to drive any teacher crazy, or is it just me being dense?  Common Core proponents would say the latter.  But if looked at from a Waldorf perspective, this really is much ado about nothing.  This sort of standard, even though Common Core philosophy repeatedly says that CCSS is just standards and not scripted curriculum, is the source of all those scribbled diagrams, showing the above-mentioned shares and groups.  Not pretty to look at, and I am sure tedious and boring to create, these so-called arrays could be avoided by teaching all 4 processes together from the beginning.

With both the Math By Hand and Waldorf methods, this concept is begun in Grade 1, as division and subtraction are compared, side-by-side. Manipulatives help to make this clearer and more understandable. The glass gems pictured above are used to correlate division and subtraction as follows.

Color-coded strips differentiate each of the 4 processes:

addition/plus = green
multiplication/times = yellow
subtraction/minus = blue
division/divide = red

Each strip is folded into six 3″ square sections, with a white square that can be placed anywhere for the missing number. To compare division and subtraction, a red strip could be placed next to a blue strip, with corresponding equations. For the minus equivalent to the divide equation 10 / 5 = 2, 2 gems would be placed in each of 5 squares. Same principle as above, with smaller numbers.

If this is demonstrated repeatedly and consistently in Grade 1, with the 2, 5, and 10 times tables, it will easily translate to the higher tables in later grades. No need to have students draw endless arrays of dots or other objects to reinforce the concept.  And, on the subject of scribbling (because that is what it looks like when you draw 7 groups of 8 circles each), the Waldorf philosophy holds that it’s essential for everything the young child creates in the learning process to be beautiful.  (And beyond, as middle and high school Waldorf students’ work testifies.)

Math should be full of fun and games as well.  Here is a star/folding activity for learning or reinforcing the 6 times table. Both rote memorization and a deeper understanding of math concepts should coexist. The times tables do need to be memorized, and this is accomplished with games, rhythmic movement, recitation, singing, and handwork. Patterning, on the other hand, takes it all to a deeper level, so that math is appreciated for its complexity and compelling beauty.

Interest and beauty, as prime motivating factors for grade school age children, will carry the day as the love of learning grows into a lifelong quest. The “reasoning” or “putting it into words” aspect of Common Core math, as groups of students are required to discuss how they arrived at their answers, may very well be a mistaken goal for math as a whole, as well as for the child until age 12-14 when abstract reasoning first appears. Until then, we need to have a little faith that the process of learning will naturally occur if conditions are favorable and the right ingredients are gathered and presented.

Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Tune in tomorrow for more Grade 3 math CCSS and their ambient counterparts.

The post 3.OA 2: Grouping to Divide & Subtract (#187) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 186

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math.  Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”  And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times.

Why ambient?  A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful.  CCSS math standards are listed here in blue, followed by ambient math suggestions.

Operations and Algebraic Thinking 3.OA
Represent and solve problems involving multiplication and division.
1. Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each.  For example, describe a context in which a total number of objects can be expressed as 5 x 7.

In the Math By Hand and Waldorf methods, this concept is begun in Grade 1, as addition and multiplication are compared, side-by-side.  Manipulatives help to make this clearer and more understandable.  The glass gems pictured above are used to correlate addition and multiplication as follows.

Color-coded strips differentiate each of the 4 processes:
addition/plus = green
multiplication/times = yellow
subtraction/minus = blue
division/divide = red

Each strip is folded into six 3″ square sections, with a white square that can be placed anywhere for the missing number.  To compare addition and multiplication, a green strip could be placed next to a yellow strip, with corresponding equations.  For the plus equivalent to the times equation 2 x 5 = 10, 2 gems would be placed in each of 5 squares.  Same principle as above, with smaller numbers.

If this is demonstrated repeatedly and consistently in Grade 1, with the 2, 5, and 10 times tables, it will easily translate to the higher tables in later grades.  No need to have students draw endless arrays of dots or other objects to reinforce the concept.  

Both rote memorization and a deeper understanding of math concepts should coexist.  The times tables do need to be memorized, and this is accomplished with games, rhythmic movement, recitation, singing, and handwork.  Patterning, on the other hand, takes it all to a deeper level, so that math is appreciated for its complexity and compelling beauty.  Interest and beauty, as prime motivating factors for grade school age children, will carry the day as the love of learning grows into a lifelong quest.

The “reasoning” or “putting it into words” aspect of Common Core math, as groups of students are required to discuss how they arrived at their answers, may very well be a mistaken goal for math as a whole, as well as for the child until age 12-14 when abstract reasoning first appears.  Until then, we need to have a little faith that the process of learning will naturally occur if conditions are favorable and the right ingredients are gathered and presented.

Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Tune in tomorrow for more Grade 3 math CCSS and their ambient counterparts.

The post 3.OA 1: Grouping to Multiply & Add (#186) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 185

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math.  Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”  And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times.

Why ambient?  A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful.  Today’s post compares Grade 3 Algebra and Functions section of the California State Math Standards and the Grade 3 Operations and Algebraic Thinking section of the CCSS Math Standards.  

My hope is that discerning the differences between the two will result in your making a right decision for your child, and all children for that matter.  You may question the merits of the Common Core with your school, teacher, or school board if your child is in public school or homeschooling with a public charter school.  Or you may decide to opt your child out of the Common Core testing.

Math By Hand is aligned with California State Math Standards and will remain so, because these standards are more effective, functional, and developmentally appropriate.  (Math By Hand’s alignment, which is included in the binder in detail, is noted after each standard.)

California State Math Standards / Algebra and Functions / Grade 3

1.0) Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve simple number relationships.

The post Grade 3 Math: CCSS vs. California State Standards (#185) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 184

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math.  Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”  And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times.

Why ambient?  A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful.  Today’s post takes a time out to ask the question, “Is the Common Core rigorous or silly?”  It’s a serious question.  Serious because some seemingly irrevocable steps have been taken at great expense and very likely in the wrong direction.

A Wall Street Journal article by Marina Ratner, professor emerita of mathematics at the University of California, Berkeley, asks why $15.8 billion was invested nationally in the Common Core (according to a 2012 estimate by the Pioneer Institute) to replace individual state standards that may very well have been far superior.  California’s state standards for example, were considered the top math standards in the nation.  The Math By Hand curriculum is aligned to both the old California State and the old National Math Standards for this reason.

Ms. Ratner says,
“It became clear to me that the Common Core’s “deeper” and “more rigorous” standards mean replacing math with some kind of illustrative counting saturated with pictures, diagrams and elaborate word problems. Simple concepts are made artificially intricate and complex with the pretense of being deeper—while the actual content taught was primitive.

Yet the most astounding statement I have read is the claim that Common Core standards are “internationally benchmarked.” They are not. The Common Core fails any comparison with the standards of high-achieving countries, just as they fail compared to the old California standards.”  Here is a pictorial example, taken from the article, an illustration by Martin Kozlowski.

Read the entire article here, and see if you don’t agree that while the Common Core may be posing as “deeper and more rigorous,” in reality it may be merely repetitious, and downright irrelevant to the true nature, depth, and beauty of mathematics.

Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal.  Tune in tomorrow for more Grade 3 math CCSS and their ambient counterparts.

The post Common Core: Rigorous or Silly? (#184) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 183

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math.  Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”  And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times.

Why ambient?  A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful.  Today’s post features the Common Core Grade 3 overview in blue, followed by its ambient counterpart as practiced by Waldorf Education and Math By Hand.

Operations and Algebraic Thinking
Represent and solve problems involving multiplication and division.
Understand properties of multiplication and the relationship between multiplication and division.
Multiply and divide within 100.
Solve problems involving the four operations and identify and explain patterns in arithmetic.

The 4 processes are taught and learned side by side from the very beginning, so a relationship has been established, between and among all 4.  Equations are written horizontally at first in Grade 1, as number sentences.  Single digits totaling no more than 20 are worked with in addition, subtraction, multiplication, and division.  After briefly reviewing the Grade 1 content at the beginning of Grade 2, the horizontal format is changed to vertical, using double digits with no regrouping, in all 4 processes up to 100.  Since multiplication and division have been worked with so extensively, their long forms can be taught mid to end of Grade 3.  A great emphasis is placed on math patterns in both the Waldorf and Math By Hand curriculums.

Number and Operations in Base Ten
Understand place value.
Use place value understanding and properties of operations to perform multi-digit arithmetic.

Place value was taught in Grade 2 using hands-on materials and manipulatives, and used primarily in regrouping with addition and subtraction.  Regrouping was also used with short multiplication and division.  In mid-Grade 3 the long versions of both are taught with hands-on materials and manipulatives.  Multi-digit arithmetic has been performed with regrouping in all 4 processes from mid-Grade 2 on.

Number and Operations – Fractions
Develop understanding of fractions as numbers.

Fractions do not appear until Grade 4 in both the Waldorf and Math By Hand systems,  since both place a great emphasis on developmental appropriateness.  In the growth process, things need to be broken down and broken apart slowly and carefully.  Wholeness is retained in all that’s taught until the child is ready to accommodate the fracturing that occurs with complex, abstract concepts.  There’s not a full readiness for abstract learning until age 11 or 12, so teaching must be as concrete as possible until then.  Meanwhile, the introduction to abstract learning through reasoning should be gradual and incremental.  No rush!  Fractions can wait, but foundational lessons can be applied wherever possible.

Measurement and Data
Solve problems involving measurement and estimation of intervals of time, liquid volumes and masses of objects.
Represent and interpret data.
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
Geometric measurement: Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Il’s time!  Time and measurement can be taught now in Grade 3, as the child has left the relatively timeless world of childhood to the extent that these concepts can be meaningfully grasped.  Both time and measurement are introduced slowly, carefully, and creatively through anecdotal historical stories and lots of hands-on, real, and experiential application.  Data can remain informal, through collections and notebook recording (no Excel spreadsheets just yet).  Area and perimeter wait until Grade 5.  I remember struggling with my daughter over these concepts in Grade 6!  We used the kitchen floor tiles as examples again and again.  Mastering times tables and other basics is far more important in Grade 3 than forcefully forging ahead to inappropriate and far too advanced subjects.  This is just one of Common Core’s mistaken principles, that if advanced concepts are pushed down to lower grades, math proficiency will more likely be achieved.  False!  This sadly mistaken notion is what’s brought us all-day Kindergartens, with 4 and 5 year olds struggling through hours of worksheet seat work, both at school and at home.  Slowing down with generous slices of play all through the grades, while also getting the basics solid, is so key!

Geometry
Reason with shapes and their attributes.

As has been previously shown, form drawing is more than adequate to address all aspects of this standard.  Here’s one example of many Grade 3 form drawings from this Pinterest page.

Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal.  Tune in tomorrow for more Grade 3 math CCSS and their ambient counterparts.

The post CCSS Overview: Grade 3 (#183) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 182

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times.” Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. Today’s post will focus on Anne Sullivan, the miracle worker, as a prototype for being an effective teacher.

The Anne Bancroft/Patty Duke portrayal of Anne Sullivan and Helen Keller is riveting.  I’m sure I’ve seen it before, but I watched it again last night and was taken with the raw passion that Anne brought to the task of teaching Helen.  The two started out hating each other (I don’t think that’s overstating).  Helen was so violently resistant to Anne that the family was on the brink of letting her go as Helen’s live-in tutor.

But upon realizing their and Helen’s limited options, they agreed to Anne’s unusual plan: to take Helen away from her family.  They were not good for her, pitying and indulgent.  She needed strict discipline if she was to learn anything.  So Anne removed Helen from the family to a cottage on the property, and so began the mighty struggle.

Anne was given two weeks to accomplish her task, then Helen was to return to her family.  At the two-week mark, she was to give Helen back at 6 pm that evening, and says this:

“Give them back their child and dog, both housebroken, everyone’s satisfied. But me, and you. (HELEN’S hand comes out into the light, groping.) Reach. Reach! (ANNIE, extending her own hand, grips HELEN’S; the two hands are clasped, tense in the light, the rest of the room changing in shadow.) I wanted to teach you—oh, everything the earth is full of, Helen, everything on it that’s ours for a wink and it’s gone, and what we are on it, the—light we bring to it and leave behind in—words, why, you can see five thousand years back in a light of words, everything we feel, think, know—and share, in words, so not a soul is in darkness, or done with, even in the grave. And I know, I know, one word and I can—put the world in your hand—and whatever it is to me, I won’t take less! How, how, how do I tell you that this——(She spells.)——means a word, and the word means this thing, wool? (She thrusts the wool at HELEN’S hand; HELEN sits, puzzled. ANNIE puts the crocheting aside.) Or this—s, t, o, o, l—means this thing, stool? (She claps HELEN’S palm to the stool. HELEN waits, uncomprehending. ANNIE snatches up her napkin, spells:) Napkin! (She forces it on HELEN’S hand, waits, discards it, lifts a fold of the child’s dress, spells:) Dress! (She lets it drop, spells:) F, a, c, e, face! (She draws HELEN’S hand to her cheek, and pressing it there, staring into the child’s responseless eyes, hears the distant belfry begin to toll, slowly: one, two, three, four, five, six.)”

For me, this is a metaphor for everything we attempt to teach every child.  We must be adamant in our determination to bring the light of human heritage in its essence to those in our charge.  Nothing can preempt that urgency.  Not standards, not testing, not disjointed and inappropriate subject matter.  All that matters is the light.  Every child instinctively knows it and will settle for nothing less.  So much “misbehavior” is this questing for that light on the part of the child!  Let us not let them down, let us as their teachers strive to be equal to their passionate desire to know, to take their places in this challenging world, to do their parts to live their lives as vital players in the drama of the light making its way.

Here are the closing scenes, Helen’s discovering that water is the same as the word “water” and of Helen and Anne, student and teacher, finally recognizing each other as such.  Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of that knowledge as a worthy goal. More Grade 3 tomorrow!

The post Teach! As Anne Sullivan Taught Helen Keller (#182) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 181

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times.” Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful.  Today’s post will focus on excerpts from the Math By Hand Grade 3 Binder: the Grade 3 overview and suggested block plan for the year.

As the child grows away from childhood, s/he develops an increasing capacity for abstract reasoning.  Note that until age 12-14, which both Steiner and Piaget (among other child development advocates) designate as the borderline for learning abstractly vs. concretely, the child’s increasing appetite for knowing about the world must still be cloaked in the arts.

Here is a block teaching schedule for the Grade 3 year from the Math By Hand binder.

The post Waldorf Blocks & Introduction: The Grade 3 Year (#181) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 180

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times.” Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful.  

Grade 3: a favorite time.  For me, a home-arts and craftsperson, teaching Grade 3 was heavenly.  Although the signature of the 9 year old is an earthly one, in the sense that what Steiner described as the 9 year change is just one of many forays out of the garden and into the world.

Many such transitions occur in the course of growing up, but the first significantly major boundary is crossed now.  At every grade level, the curriculum content supports the stage of development.  And here in Grade 3, creation stories are told as the archetypal expression of leaving the garden.  This banishment so to speak, deeply resonates as a metaphor for the first pass at growing up and leaving childhood behind.

The Waldorf curriculum supports the child as s/he descends the ladder to live on the earth.  Alongside grieving of the loss of childhood the gifts of self-sustenance and independence are given.  In Grade 3 housebuilding, farming and many beautiful, practical home-arts and crafts accompany the child on this momentous journey.

When I taught a Waldorf Grade 3 class, we began our housebuilding block with an extensive survey of how houses were built in many different times and places.  I added each house as we studied them to a progressive chalkboard drawing, and then each child chose which house model s/he would build.  The houses were all wonderful and after they were built, a most memorable moment occurred.  One of the girls said that she’d had a dream the night the houses were finished that she and all her classmates visited each others’ houses!

Here is an excellent blog post on Waldorf 3rd Grade Housebuilding Projects, from Waldorf (Inspired) Moms.  Her son chose to build a Mongolian yurt, and later wrote about it, as shown below.  So from the history and cultural overview, to the 3-D experience of building a house, to creating a written and illustrated account, the act of housebuilding is thoroughly experienced, in many different ways.

The Grade 3 year may be the richest one of all because it’s so experiential.  As many believe, hands-on experience is the best teacher, and knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of that knowledge as a worthy goal.  More Grade 3 tomorrow!

The post Grade 3! A Home Away From Home (#180) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 179

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times.” Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful.  Today’s post looks at the polarity of Grade 2.

As the 8 year old moves away from the fairy tale and begins to take first real steps into the world, a powerful dichotomy appears.  The strong urge for growing up and being more independent takes the form of a sort of rebellion against authority.  And this is juxtaposed with a desire to “do the right thing,” conflicting feelings that need to resolve.

And here is where the strong moral pillar of the saints’ lives can serve to counterbalance the often reprehensible and always rambunctious antics of the fables’ animal characters.  Here is a link to Taming the Wolf, an institute for peaceful mediation and reconciliation, and their story of “Saint Francis and the Wolf of Gubbio,” who I’m sure was much like the fellow pictured below.

After telling this wonderful story, you might have the children write and illustrate St. Francis’ “Canticle to the Sun.”  Here is an excellent post from the blog, Wadorf Inspired Moms, that features a beautifully rendered version of it.

In contrast, there’s Mr. Reynard Fox, up to his old tricks again, in the fable, “The Fox and the Crow” by Aesop.

A Fox once saw a Crow fly off with a piece of cheese in its beak and settle on a branch of a tree.

     “That’s for me, as I am a Fox,” said Master Reynard, and he walked up to the foot of the tree.

     “Good day, Mistress Crow,” he cried. “How well you are looking today: how glossy your feathers; how bright your eye. I feel sure your voice must surpass that of other birds, just as your figure does; let me hear but one song from you that I may greet you as the Queen of Birds.”

     The Crow lifted up her head and began to caw her best, but the moment she opened her mouth the piece of cheese fell to the ground, only to be snapped up by Master Fox.

     “That will do,” said he. “That was all I wanted. In exchange for your cheese I will give you a piece of advice for the future: “Do not trust flatterers.”

So here we have the hapless crow, as so many of Mr. Reynard’s “victims” seem to be.  But there’s also a certain wily worldliness to his machinations.  One that may after all, be a necessary ingredient to growing up.  Even though this clever fox is never brought to justice per se, it could be said that his calculated, self-centered deeds keep the community on its collective toes by somehow pointing out each one’s foibles and shortcomings.

And so it goes in Grade 2.  I hope you enjoyed our sojourn as much as I did!  On to Grade 3 tomorrow, remembering that knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of that knowledge as a worthy goal.

The post Grade 2 Farewell: Saint Francis & Reynard the Fox (#179) appeared first on Math By Hand.

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 179

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times.” Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful.  Today’s post looks at the polarity of Grade 2.

As the 8 year old moves away from the fairy tale and begins to take first real steps into the world, a powerful dichotomy appears.  The strong urge for growing up and being more independent takes the form of a sort of rebellion against authority.  And this is juxtaposed with a desire to “do the right thing,” conflicting feelings that need to resolve.

And here is where the strong moral pillar of the saints’ lives can serve to counterbalance the often reprehensible and always rambunctious antics of the fables’ animal characters.  Here is a link to Taming the Wolf, an institute for peaceful mediation and reconciliation, and their story of “Saint Francis and the Wolf of Gubbio,” who I’m sure was much like the fellow pictured below.

After telling this wonderful story, you might have the children write and illustrate St. Francis’ “Canticle to the Sun.”  Here is an excellent post from the blog, Wadorf Inspired Moms, that features a beautifully rendered version of it.

In contrast, there’s Mr. Reynard Fox, up to his old tricks again, in the fable, “The Fox and the Crow” by Aesop.

A Fox once saw a Crow fly off with a piece of cheese in its beak and settle on a branch of a tree.

     “That’s for me, as I am a Fox,” said Master Reynard, and he walked up to the foot of the tree.

     “Good day, Mistress Crow,” he cried. “How well you are looking today: how glossy your feathers; how bright your eye. I feel sure your voice must surpass that of other birds, just as your figure does; let me hear but one song from you that I may greet you as the Queen of Birds.”

     The Crow lifted up her head and began to caw her best, but the moment she opened her mouth the piece of cheese fell to the ground, only to be snapped up by Master Fox.

     “That will do,” said he. “That was all I wanted. In exchange for your cheese I will give you a piece of advice for the future: “Do not trust flatterers.”

So here we have the hapless crow, as so many of Mr. Reynard’s “victims” seem to be.  But there’s also a certain wily worldliness to his machinations.  One that may after all, be a necessary ingredient to growing up.  Even though this clever fox is never brought to justice per se, it could be said that his calculated, self-centered deeds keep the community on its collective toes by somehow pointing out each one’s foibles and shortcomings.

And so it goes in Grade 2.  I hope you enjoyed our sojourn as much as I did!  On to Grade 3 tomorrow, remembering that knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of that knowledge as a worthy goal.

The post Grade 2 Farewell: Saint Francis & Reynard the Fox (#179) appeared first on Math By Hand.