A Year in the Life: Ambient Math Wins the Race to the Top!
Day 250
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.
Wow, 50 more posts to go! I have decided to stop at 300 days. This process has been pretty labor-intensive, so stamina has thinned considerably. One of my original purposes in writing this blog was to provide a reference to the Common Core in tandem with Math By Hand, for those who need or want it, since I am not able to change the California State and National standards with which the Math By Hand curriculum is currently aligned.
Not able to, and really not wanting to, because I do feel that the former standards are far superior to the Common Core. So I will end with Grade 4, which aligns with Math By Hand anyway. I’ve been thinking that I’d like to convert the whole blog into an e-book so it would be easier to use as a reference. Any comments/feedback on this would be appreciated!
Operations and Algebraic Thinking 4.OA
Gain familiarity with factors and multiples.
4. Find all factor-pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given 1-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.
This standard is easy-peasy! Factors are first taught early in Grade 1, then repeated through the grades. Prime and composite numbers are taught pictorially and intensively in Grades 2, 3, and 4. As always, a picture is worth a thousand words. See the factor and prime numbers examples below, as they are illustrated at different grade levels in the Math By Hand curriculum.
“12 is the King of Numbers because it’s the richest! Even though 13 is a bigger number, it only has two jewels: 1’s and itself. 12 has many jewels: 1’s, 2’s, 3’s, 4’s, 6’s, and itself!” The factors are introduced early on in Grade 1, only through story and pictures, and very concretely and colorfully, as shown.
Factor trees are created early in Grade 2, as a way of finding patterns and factors within the tables, after creating a large times tables chart. Individual trees are created for each table, giving a concrete sense of how they break down into factors.
The prime numbers are taught playfully at the end of Grade 2, using the fable, The Rooster and the Pearl. The chart on the left shows the prime and composite numbers to 100, after taking part of the chart to “sift” the prime numbers or “pearls” from the corn kernels.
Magic Squares are introduced at the beginning of Grade 4, both to reinforce factor concepts and as an introduction to fractions. This puzzle can be constructed by moving the numbers 1-25 as shown above to create columns that all add up to 65: horizontally, vertically, and diagonally. This particular pattern is useful for gaining mental flexibility and for addition practice. Other Magic Squares’ patterns are more directly focused on factor concepts.
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 4 math CCSS and their ambient counterparts.
The post 4.OA 4: Factors & Primes, Early On & Colorful (#250) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 249
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 4.OA
Use the four operations with whole numbers to solve problems.
3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Looking back over the Common Core Grade 3 standards, I found this one:
Operations and Algebraic Thinking 3.OA
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing in for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Why are these two standards so similar, and how significant are the slight differences? The prevailing feeling here is that overall, the Common Core math standards were too thoughtlessly cobbled together. And in both cases these standards are addressed and fulfilled with reams of worksheets. Instead and alternatively, straightforward concepts like estimation and rounding can be taught and learned quickly and easily, with little need for constant, repetitive practice and testing.
Requiring completion of multiple worksheets with abstract problem scenarios is a sense-dulling endeavor, and as such thwarts the true purpose of mathematics: experiencing the basic joy and beauty that numbers and their meaning and patterns can bring to our lives. If this is placed ahead of a fear-based reliance on repetitive work and constant testing, learning will occur. And it will occur with gusto and enthusiasm, laying the groundwork for genius and creativity, in service to a world that so sorely needs it!
The Math By Hand Grade 4 approach is creative, exploratory, hands-on and fun, with a solid grounding in the basics. A lively mix of reviewing factors and times tables through magic squares and other math patterning and tricks, along with form drawing, trickster tales, and learning long, complex verses and classic poetry by heart begins the math year.
This is followed by a thorough and concrete approach to teaching and learning fractions and decimals, their relationship, and how to compute with them. The year ends with an introduction to the number line with positive and negative numbers, mixed numbers and fractions, and a clear picture of how to use the 4 processes with it. Only then, at the very end of Grade 4, are basic algebra concepts introduced.
A methodical journey that exhibits a clear progression from one step to the next makes sense to the child who is struggling to grapple with too much information. Isn’t it our sacred duty as teachers and parents to make this journey doable for every child? And beyond doable, shouldn’t the journey be joyful, inspiring, and creative? Which brings us back to worksheets. No worksheet can meet the parameters and demands of a math approach that’s truly alive and engaging.
No amount of worksheet drudgery can match the mystery and exquisite presence of math as it’s found in nature, all around us. Open the child’s eyes to this wonder, while relating it to mathematical principles, and s/he will carry it forward into a life that meets the world with genius and love. Math is all about the mystery of life. Unless we acknowledge this, we’ve missed its essence and cannot convey it in our teaching. William Blake’s poem, Auguries of Innocence, begins with this verse, a testament to the mystery that at the same time confounds and sustains us.
To see a world in a grain of sand
And heaven in a wild flower,
Hold infinity in the palm of your hand,
And eternity in an hour.
Both this sunflower and lobelia display the spiral of the Fibonacci sequence. Unless we acknowledge and teach the mysterious majesty of math, and instead bury it under mountains of meaningless worksheets and tests, we have missed a golden opportunity, while robbing our children of their very humanity.
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 4 math CCSS and their ambient counterparts.
The post 4.OA 3: A Love of Math Is the Answer (#249) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 248
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 4.OA
Use the four operations with whole numbers to solve problems.
2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
Word problems! The bane of many teachers, teacher/parents, and students. There is something very cold, calculating, and alienating about scenarios thinly disguised as math problems, wherein strangers perform unfathomable tasks or disconnected acts. Love this one from the comic strip Peanuts.
In both the Waldorf and Math By Hand systems, there is a steeping in the four processes and how they relate to each other. Differentiation between them is deeply rooted and easily accessed, so that there’s a natural, instinctual reflex as to which process is appropriate to each particular situation or need. The sort of drawings required by this standard are less than optimal. In fact, they tend to be repetitive and demeaning. Here’s an example, from a Homeschool Addict blog post.
Is this rigorous and deep? Or is it counterproductive, in the sense that math now becomes a drudgery rather than a creative and exciting endeavor? Let’s not waste our children’s time and ability with this sort of repetitive, labor intensive work. Drawings that are more complex and promote true flexibility of thinking are more appropriate, like this form drawing from Tara Gregory’s Pinterest page.
Of course, we want our children to be flexible thinkers, to be able to think on their feet, and be open to solving any problem that comes their way. Waldorf simply says that this is a quality that needs to be carefully nurtured and grown, through many, varied means. That this quality can not be hammered in, can not be tested to death, that it must be beautifully taught and learned.
I will close with a clip from one of my favorite movies, Desk Set, with Spencer Tracy and Katherine Hepburn. Watch the whole clip if you like, because these two are just magic together. Or cut to the mathematical chase at 3:23 to see Kate handle any complicated word problem that’s thrown her way. I think it’s a pretty safe bet that the Hepburn character was not subjected to Common Core type math, but attained her prodigious math talent through a broad and eclectic education.
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 4 math CCSS and their ambient counterparts.
The post 4.OA 2: Word Problems. Are They Problematic? (#248) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 247
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 4.OA
Use the four operations with whole numbers to solve problems.
1. Interpret a multiplication equation as a comparison, e.g., interpret 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
This standard is a variation on the Grade 3 version (see blog post #186). I’ve copied most of that post because it is also relevant here. The Common Core’s stated objective is to delve deeper with fewer but more rigorous standards. I’m wondering if in the effort to economize with fewer standards, thoroughness was sacrificed, since it does seem that there’s a lot of slightly tweaked repetition from grade to grade.
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. This is the 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.
Cross stitch is the handwork focus in the Waldorf fourth grade. Besides adding another skill to the craft repertoire, cross stitching serves a distinct purpose at this age. As previously mentioned, the growth process can be a challenging one, with “growing pains” occurring on more than just the physical level.
We must think of our children as fragile, in the sense that we set them on a crash course of acclimating to our more than daunting modern world. It’s incumbent upon us to safeguard their well-being, by not expecting too much too soon. Grade 4 is a milestone in its leap into the geography and zoology of the real world, asking “What is our place on the planet, and with what creatures do we share our world?”
Because overwhelm can happen far too easily, fail-safes need to be in place and the act of cross-stitching can serve this purpose. Symbolically, the “x” that’s sewn again and again reinforces a sense of protection that can be relied upon in the sometimes treacherous waters the 9-10 year old navigates. Here is an example of Grade 4 cross stitched bags, found on Barbara Hernandez’ Pinterest page.
Cross stitch can be related to math as well, counting stitches, designing geometric patterns, and seeing the x’s themselves as examples of arrays! 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 4.OA 1: The Algebraic “X” . . . Not Quite Yet! (#247) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 246
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 4 overview in blue, followed by its ambient counterpart as practiced by Waldorf Education and Math By Hand.
Operations and Algebraic Thinking
Use the four operations with whole numbers to solve problems.
Gain familiarity with factors and multiples.
Generate and analyze patterns.
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 are taught mid to end of Grade 3. Factor patterns are explored as “trees” in Grades 2 and 3, then gone into at greater depth at the beginning of Grade 4, as a segue into fractions. A great emphasis is placed on math patterns and corresponding number “tricks” in both the Waldorf and Math By Hand curriculums.
Number and Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
Use place value understanding and properties of operations to perform multi-digit arithmetic.
Place value is taught in Grade 2 using hands-on materials and manipulatives, and used primarily in regrouping with addition and subtraction. Regrouping is also used with short multiplication and division at first, then in mid-Grade 3, the long versions of both are taught with hands-on materials and manipulatives. Multi-digit arithmetic is performed with regrouping in all 4 processes from mid-Grade 2 on.
Number and Operations – Fractions
Extend understanding of fraction equivalence and ordering.
Build fractions from unit fractions by applying and extending previous understanding of operations on whole numbers.
Understand decimal notation for fractions, and compare decimal fractions.
There’s a readiness for the concept of breaking apart the whole in Grade 4. Fractiousness, along with the chaotic storms of growing up in a complex world are more real and present now, echoed in the Norse Myths or the trickster tales from other cultures. At the same time, caution must be taken with presentation. When new concepts are presented abstractly without concrete references, much harm results. Opportunities for teaching fractions concretely abound! Math By Hand begins with cutting up color coded squares (1 whole = red, 2 halves = green, 4 fourths = blue, etc., so equivalence can be readily grasped from the start. A set of playing cards is used with familiar, classic games that are adapted to learning fraction equivalence, and the rules for using the four operations with fractions are clearly laid out in a simple booklet that can be used as a learning aid as often as needed. Using coin rubbings to introduce decimal-fraction equivalence (see below) is both fun and effective.
Measurement and Data
Solve problems involving measurement/conversion of measurements from a larger unit to a smaller unit.
Represent and interpret data.
Geometric measurement: understand concepts of angle and measure angles.
Both time and measurement are introduced slowly, carefully, and creatively through anecdotal historical stories and lots of hands-on, real, and experiential application in Grade 3. This is expanded upon in Grade 4, with increasingly complex measurement, along with conversion to metric measurement. Data can remain informal, through collections and notebook recording (no Excel spreadsheets just yet). Angles and polygons wait until formal geometry in Grade 6, when instruments are used, featuring accuracy and aesthetics. One of Common Core’s mistaken principles is that if advanced concepts are pushed down to lower grades, math proficiency will more likely be achieved. False! Slowing down with generous slices of play and artistic expression all through the grades, while solidifying the basics, is so key!
Geometry
Draw and identify line and angles and identify shapes by properties of their lines and angles.
As has been previously shown, form drawing is more than adequate to address all aspects of this standard. Here are two examples from Math By Hand Grade 4 form drawings. The compass rose is used to orient, as surroundings and local environment are mapped, beginning with home and radiating out from there. The second form is an example of the complex weaving and braiding found in many cultures’ symbolic figures, most notably the Celtic.
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 to continue with Common Core Math Standards and their ambient counterparts.
The post Grade 4: CCSS Math Overview (#246) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 245
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.
Why Trickster Tales? Here’s an excerpt from the Math By Hand Grade 4 Form Drawing/Stories Book:
Tricksters are magnetic figures who have inspired fascination in every culture, since the beginning of time. They’ve always played an important role as boundary keepers, and have also crossed or created new boundaries. The trickster’s realm is ambivalence, for s/he is at once divine and beastly, innocent and wicked, creative and destructive, fooler and fooled, giver as well as taker. S/he’s amoral, yet at the same time is the supreme prompt or source for/of morality. The trickster greatly delights in seeing that any and all rules are bent, broken, or twisted, no matter the cost, to self or others. S/he rides the edge with a ready willingness to suffer even the deepest personal humiliation as a result.
Living on the edge as an outsider, the trickster often serves as wily messenger between the human and the divine. Always on the periphery, never mainstream, the rebel is the persona most often taken up. Arbitrator or peacemaker is another one of the trickster’s guises, since s/he has the ability to simultaneously inhabit and/or penetrate complementary or opposing spheres or views. Perhaps most importantly, the trickster will carry the dark side, lightly and with much humor, for those who are unwilling or unable to carry it. Needless to say, this sort of behavior can be challenging, as well as boisterous and fractious.
Enter the fourth grader, ready to take on the world. There’s a confidence that is often over the top, in need of the sort of “comeuppances” that usually are the trickster’s stock in trade. An overly rambunctious mood, one that may be all too prevalent at this age, can be well met by these tales. Fourth graders love tricks and puzzles too, as well as secret codes and formulas. Present the mysteries and magic of math (such as magic squares and other wondrous ways that numbers can work) along with the telling of these tales. And let the trickster juggle and play!
A good story is the learning aid of choice now, because the elementary years are best approached with the arts. Notice that the caption here has been written in cursive script (the lines to the right are indications of handwritten text). Recent research has shown the many benefits of handwriting, as just one of many lost arts. Here’s an example of blending trickster tales with math tricks and patterns like Pascal’s Triangle, from the Math By Hand Grade 4 Binder, a math-infused illustration of the story “Nail Soup” from the Form Drawing/Stories Book.
So do let your Grade 4 jester/trickster play! Math By Hand includes juggling lessons along with instructions for making a set of juggling balls. As always, 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, as we begin Common Core Math Standards and their ambient counterparts.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 244
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.
Fractions! The fourth grader’s fractiousness signals a readiness to take on the task of breaking apart. Until now, wholeness was essential for healthy growth and development. But the leap into the real world that happens at this age makes it possible to hold strong in the face of all else fracturing. If the foundation is solid, this stage of the growth process can be met with confidence.
With the Waldorf approach, the elementary grades can be seen as a journey that begins at age 7 with a readiness to learn that’s still enveloped in the magical world of the fairy tale. Then at 8, the juxtaposition of the fables’ animal antics with the legendary goodness of heroes and saints paves the way for first tentative steps into the world. Followed by the mixed joy and sadness that accompanies the 9 year old as s/he moves more decisively away from the innocence, joy, and safety of childhood.
Basic survival tools acquired in third grade is a preparation for taking stock of the world close to home, and orienting to that place, wherever it may be. So along with the fractions’ breaking apart, the fourth grader can find structure and security in mapping home. Here is an example of a first map drawn in a main lesson book. This is from waldorftoday.com / Rejoyce InLight, pinned with the caption, “It is not an easy matter to draw a map for the first time. For how can you possibly fit in all the interesting things you see on the way to school!”
And here is a wonderful example of combining fractions with mapping from Catie Johnson’s website, Chalkboard Drawings in the Waldorf Classroom. 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 4 wonders!
The post Grade 4: Local Geography & Fractions! (#244) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 243
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.
In Grade 3, the garden of childhood was left behind, so that in Grade 4 the journey outward could begin in earnest. I’m reminded of the famous Cloth/Wire Mother experiment, in which baby monkeys were kept in close proximity to life-size cloth covered or bare wire mother figures. Even when the bare wire mothers provided food, the baby monkeys visited them only to feed, spending most of their time cuddling with the cloth covered figures.
As I write this, I am struck with the short-sightedness of this scientific method. In fact these experiments were instrumental in provoking the heightened awareness of animal abuse in science laboratories. These experiments were questioned along the lines of, why subject these babies to this stress just to gain abstract data? Relevance and importance of data fades in light of the potential harm done.
Anyway, obviously the cloth mother monkeys were the preferred surrogates because they were the more nurturing of the two. The monkeys tended to adapt to strange or new surroundings by venturing out to explore and repeatedly running back for comfort and assurance. This should be the model of choice for child development.
Slow and steady wins the race. Not sink or swim. We need to give all children all the time they need to leave the nest. It’s short-sighted and abusive to throw a 4 year old into the cold water of abstract learning, as it is abusive all along the way to rush the natural process of growing up (and out). Let’s stop experimenting with our children. Just as it was seen as cruel to isolate those baby monkeys, so it is just as cruel to force feed and over test our children.
So perhaps we should give the tests themselves a big, red F and fail anything and everything that gets in the way of healthy, natural child development. Because 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 4 wonders!
The post Grade 4: Is Common Core & Testing A Failed Experiment? (#243) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 242
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 feature a block lesson plan for the Grade 4 entire year. The advantages to teaching in blocks are many. Yearly planning is easier, and because the lessons are taught in 1 – 2 hour blocks in the morning, teacher / student focus is greater. Afternoons are freed up for art, handwork, games, field trips, family time, etc. Here is a suggested block plan from the Math By Hand Grade 4 binder:
September . . . Cultural Mythology / Grammar & Composition
October . . . Math / 4 Processes Review / Factors
November . . . Local Geography & History
December . . . Zoology / The Human & Animal
January . . . Math / Fractions
February . . . Cultural Mythology / Grammar & Composition
March . . . Local Geography & History
April . . . Math / Fractions Review / Decimals
May . . . Cultural Mythology / Zoology / Grammar & Composition
June . . . Math / The Number Line & Algebra / Class Play
From Catie Johnson’s wonderful page, Chalkboard Drawing in the Waldorf Classroom, an excellent overview of the Grade 4 human and animal study:
“In the fourth grade year, a new connection to nature is established. The first of several connections to be made in the upcoming elementary years, the animal kingdom is studied. The study of animals is brought to the students through imaginative pictures and descriptions of how the animal is seen in relation to the human being. The children learn all the various ways animals have adapted to their environment and how they have become specialized in one or a few particular areas. Below the Great Blue Heron is depicted with its sharp eyes, long fishing bill and lengthy legs for wading in water in search of its next meal. This was an animal chosen as well for its presence in this particular geographic location, easily relating to local studies.”
A couple more chalkboard drawings from the same page: the lion and the Carolina chickadee.
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 4 wonders!
The post Grade 4: Year Block Plan & Human/Animal Study (#242) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 241
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 4! Another milestone, a marker in the child’s journey, one that echoes Grade 2, in that it’s another confident leap into the world. And with this confident exuberance comes a certain rambunctiousness that is nicely mirrored by trickster tales!
Just as the fables’ animal antics displayed these qualities for the 7-8 year old, the Norse myths and other trickster tales serve the same purpose for the 9-10 year old. The deeply good qualities found in the stories and legends of the saints served to balance the fables’ mischief, as the Norse myths balance elements of the light and dark side by side.
As with all good, classic world literature, the Norse myths embody cultural archetypes that impart meaning and depth. We are sorely missing this element in modern times, and our children are hungry for it. Why are we stripping education of all the so-called “frills” subjects? Isn’t it time we woke up to the fact that we are starving our children? Because, just as we feed their bodies and are careful to provide all necessary nutrients for health and growth, we must do the same for their minds. Right-brain teaching and learning is not a fad, it’s a vital balance.
A picture is worth a thousand words, as is a good story. So here is a story for you, from Bullfinch’s Mythology, about The Three Norns, three archetypal women who show up in many of our ancient tales, followed by a wonderful chalkboard rendering from Catie Johnson’s page, Chalkboard Drawings in the Waldorf Classroom.
The Norns’ Web
The Norns sometimes wove such large webs that one of the weavers stood on a high mountain in the extreme east, while another waded far out into the western sea. The threads of their woof resembled cords, and varied greatly in hue, according to the nature of the events about to occur, and a black thread, tending from north to south, was invariably, considered an omen of death. As these sisters flashed the shuttle to and fro, they chanted a solemn song. They seemed not to weave according to their own wishes, but blindly, as if reluctantly executing the wishes of Orlog, the eternal law of the universe, an older and superior power, who apparently had neither beginning nor end.
Two of the Norns, Urd and Verdandi, seemed very beneficent indeed, while the third relentlessly undid their work, and often, when it was nearly finished, tore it angrily to shreds, scattering the remnants to the winds of heaven. As personifications of time, the Norns were represented as sisters of different ages and characters, Urd (Wurd, weird) appearing very old and decrepit, continually looking backward, as if absorbed in contemplating past events and people; Verdandi, the second sister, young, active, and fearless, looked straight before her, while Skuld, the type of the future, was generally represented as closely veiled, with head turned in the opposite direction from that where Urd was gazing, and holding a book or scroll which had not yet been opened or unrolled.
This beautifully intricate imagery is deeply taken in by the children, not analyzed per se but rather taken at face value, digested, and allowed to nourish and nurture elements of the personality that will manifest later as deeply moral and complex human qualities.
As always, 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 wonders from Grade 4!
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