
A Year in the Life: Ambient Math Wins the Race to the Top!
Day 240
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.
Farewell to Grade 3! This pivotal time is marked by many new things as the 9 year old takes the first real steps out of childhood. Consolation is found in the Creation stories by learning how many before us felt these same pangs of separation as they left their gardens, their innocence, behind.
Competence is nurtured and built through the many practical tools utilized in learning how to count time, measure objects and quantities, grow, cook, and preserve food, build shelters, craft beautiful, useful things, sing, play, recite by heart, and o yes, the three r’s as well. Here are some colorful images from all of these treasured disciplines, captioned with their sources.
FARMING: From the Michael Mount Waldorf School, Johannesburg, South Africa

SHELTERS: From the Toronto Waldorf School

TIME: A chalkboard drawing of the Dorothy Harrer verse from Heirloom Seasons

MEASUREMENT: From Boyceview Home School
SPANISH/FARMING: From the Waldorf School of Atlanta

CREATION STORIES/WATERCOLOR PAINTING: From Syrendell

FORM DRAWING: From waldorfteachers.com

HANDWORK: From the Waldorf School of Atlanta

MATH: From the Emerson Waldorf School
My Grade 3 Class: Oakland Steiner Waldorf School, Troy, MI
Farewell to Grade 3! 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 move on to Grade 4!
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 239
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.
The CCSS Standards for Mathematical Practice are meant to be used throughout the year, applied to all lessons and skills practices. The wording is pretty dense and unapproachable, certainly not child friendly and possibly not even teacher friendly. There have been attempts at translation, but the examples I’ve seen still tend to be somewhat dry. Well, I guess I’ve temporarily run out of steam here. You’ll find the CCSS standards listed in blue below, but not followed by their ambient counterparts, not today.
I came across an article called Common Core and the Death of Reading. Many of the points listed are similar to what I’m experiencing now. Here’s an excerpt that I found to be most compelling: “The Common Core approach to reading is like breaking a molecule down into individual elements. But as any science teacher can explain, once you break the molecular bonds that tie the atoms together, you lose all the properties of the original chemical. You now have hydrogen and oxygen, but you no longer have water. In Common Core students may learn skills, but they do not learn to love reading or to really understand sophisticated written material.”
I must echo this: in Common Core students may learn skills, but they do not learn to love math or to really understand its sophisticated, complicated beauty. Read the article here, and please allow me to simply say that true math is more than disjointed Common Core parts, along with endless testing to make sure that all parts are present and accounted for, but always sans math’s amazing, indomitable spirit. Here are the standards, along with the picture from the article that today expresses my sentiments, exactly.
5. Use appropriate tools strategically.
Mathematically proficient third graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use graph paper to find all the possible rectangles that have a given perimeter. They compile the possibilities into an organized list or a table, and determine whether they have all the possible rectangles.
6. Attend to precision.
Mathematically proficient third graders develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their own reasoning. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, when figuring out the area of a rectangle they record their answers in square units.
7. Look for and make use of structure.
In third grade mathematically proficient students look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to multiply and divide (commutative and distributive properties).
8. Look for and express regularity in repeated reasoning.
Mathematically proficient students in third grade should notice repetitive actions in computation and look for more shortcut methods. For example, students may use the distributive property as a strategy for using products they know to solve products that they don’t know. For example, if students are asked to find the product of 7 x 8, they might decompose 7 into 5 and 2 and then multiply 5 x 8 and 2 x 8 to arrive at 40 + 16 or 56. In addition, third graders continually evaluate their work by asking themselves, “Does this make sense?”

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 a farewell post to Grade 3!
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 238
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.
The CCSS Standards for Mathematical Practice are meant to be used throughout the year, applied to all lessons and skills practices. The wording is pretty dense and unapproachable, certainly not child friendly and possibly not even teacher friendly. There have been attempts at translation, but the examples I’ve seen still tend to be somewhat dry. Here’s my attempt, with a Grade 3 focus and a Waldorf lens. The CCSS standards are in blue, followed by their ambient counterparts.
1. Make sense of problems and persevere in solving them.
In third grade, mathematically proficient students know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Third grade students may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does this make sense?” Students listen to other students’ strategies and are able to make connections between various methods for a given problem.
Math is the underpinning of all life. By nature it likes to remain hidden, as a mystery that’s all the more compelling when discovered. Children understand this intrinsically, much more than we as adults do, with our more empirical mindsets. From this perspective, math in a Waldorf third grade takes a back seat to the rich tapestry of projects and activities that fill each day. But from that back seat, it presents itself beautifully as the universal bottom line. The meaning of a problem may be expressed through any practical examples such as small building projects, knitting patterns, recipes, etc. Discussing how a problem was solved takes a back seat to the finished product, which was accomplished together. The summary happens nicely when all steps of the project are colorfully written and illustrated in the students’ main lesson books. Here’s a page from a Waldorf Stone Bridge School measurement main lesson book.

2. Reason abstractly and quantitatively.
Mathematically proficient third grade students should recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities.
A Waldorf third grade student would have mastered this concept in first grade. Math By Hand introduces the Roman and then the Arabic numerals in depth, in the first Grade 1 math block. The abstract nature of the numbers we use is circumvented by the imaginative, pictorial, and historical treatment of the numbers as symbols. The Math By Hand Grade 2 place value block teaches the meaning of 1’s, 10’s, 100’s, and 1,000’s and their relationship to each other, in depth. Here is an example from Math By Hand: the evolution of the Arabic numerals 1-4.

3. Construct viable arguments and critique the reasoning of others.
In third grade, mathematically proficient students may construct arguments using concrete referents, such as objects, pictures, and drawings. They refine their mathematical communication skills as they participate in mathematical discussions that the teacher facilities by asking questions such as “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking.
A third grade group building project is a most ideal application here. Students literally construct arguments by working together and combining ideas and solutions as the project proceeds. Having seen Common Core videos of classroom scenarios where this is put into practice, the teacher asking the questions listed above often takes on an artificial tone. If however, the explanation of and responses to thinking occur in a group context, i.e., through the modification of building techniques, measurements, and specifications, the resulting teaching and learning is much more effective and successful. Here, from the Pine Hill Waldorf School, is a perfect example of mathematical communication skills in action: cooperatively measuring lengths of wood for a building project.

4. Model with mathematics.
Mathematically proficient students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart, list, or graph, creating equations, etc. Students require extensive opportunities to generate various mathematical representations and to both equations and story problems, and explain connections between representations as well as between representations and equations. Students should be able to use all of these representations as needed. They should evaluate their results in the context of the situation and reflect on whether the results make sense.
Waldorf students experience this sort of broad, varied approach to math from first grade on. Flexibility of thinking is paramount to math success, and it gets off to a flying start as the 4 processes are introduced side by side in first grade. A full spectrum of math expression and experience is employed by teachers and students alike in both the Waldorf and Math By Hand systems.
One of the best practical examples of experiencing math principles is Waldorf handwork. For all who practice it regularly, knitting engenders the best of math practice, by casting on and off, counting stitches, and creating geometric patterns. Most importantly, it stimulates neuron health and balance in the right and left brain, while it also enhances eye hand coordination by the repetitive and detailed use of the right and left hands. And all children most decidedly thrive on it, as can plainly be seen here, in a knitting class at the Tucson Waldorf School.

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 the last of the Grade 3 CCSS math standards and their ambient counterparts.
The post Grade 3: Common Core Standards for Mathematical Practice 1-4 (#238) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 237
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.
Common Core proponents claim that its methods promote a deeper (vs a rote or automatic) understanding of math’s underlying principles and logic. This may be true, in that students are required to break down equations into parts in order to see the sense of the operations: what’s really going on with the numbers. The overriding problem though is that the concepts are presented in an abstract rather than concrete way, which results in tears and frustration over a developmentally inappropriate approach. Here’s a typical Common Core worksheet:

Not very friendly is it? Not very clear and way too abstract. “Making 10’s” is a method used as a basic way to see the sense of subtraction. But in this form, it’s quite cold and alienating. Add the pressure of high-stakes testing to this, and it becomes a recipe for disaster.
Waldorf and Math By Hand teach all 4 processes together in the third Grade 1 math block, so that the relationships and characteristics of each process can be discerned early on. The same sort of deeper understanding is achieved, but with much friendlier, less abstract, and very concrete methods. Here is a page from an Earthschooling math main lesson book. Find the book on their website here.

Notice how the number 12 is broken down into factors for dividing. Look familiar? I believe Common Core has the students making the same dots and groupings, but please do see the difference here. There’s color and an engaging backstory, with everything fitting nicely into a whole picture. Perhaps most importantly. this is introduced very early on, enabling an economical understanding that doesn’t need to be repeatedly drilled and tested. Learning it once in first grade is enough!
If all concepts are introduced this way, depth and a love of learning is there. The 4 processes are given names and personalities so math becomes personal and friendly, circumventing any math fears or phobias. As pictured above, gnomes are often used to characterize the 4 processes, but Math By Hand chose 4 children instead.
Notice the dominant traits of each personality in the image below. Plus is green and growing, Minus is sadly blue, losing everything or giving it all away. Divide is red, decisive and fair (note that the sword pictured above is also a division sign). Times is the happy go lucky, more-is-better type, in yellow.
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 CC math standards and their ambient counterparts.

The post How Are Waldorf & Common Core Math Alike & Different? (#237) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 236
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.
Back to the Common Core for Grade 3 English Language Arts Standards. Math By Hand integrates language arts with math, and though the Waldorf curriculum is taught in blocks, none of the subjects are really taught in isolation. Integration is key, and the ambient standards posted here will reflect that. The Common Core language arts standards are listed here in blue, followed by ambient language arts suggestions.
LANGUAGE
Conventions of Standard English:
CCSS.ELA-LITERACY.L.3.1
Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
CCSS.ELA-LITERACY.L.3.1.A
Explain the function of nouns, pronouns, verbs, adjectives, and adverbs in general and their functions in particular sentences.
CCSS.ELA-LITERACY.L.3.1.B
Form and use regular and irregular plural nouns.
CCSS.ELA-LITERACY.L.3.1.C
Use abstract nouns (e.g., childhood).
CCSS.ELA-LITERACY.L.3.1.D
Form and use regular and irregular verbs.
CCSS.ELA-LITERACY.L.3.1.E
Form and use the simple (e.g., I walked; I walk; I will walk) verb tenses.
CCSS.ELA-LITERACY.L.3.1.F
Ensure subject-verb and pronoun-antecedent agreement.*
CCSS.ELA-LITERACY.L.3.1.G
Form and use comparative and superlative adjectives and adverbs, and choose between them depending on what is to be modified.
CCSS.ELA-LITERACY.L.3.1.H
Use coordinating and subordinating conjunctions.
CCSS.ELA-LITERACY.L.3.1.I
Produce simple, compound, and complex sentences.
At the risk of being overly simplistic, all of the above are covered quite indirectly in the Waldorf system, through timeless, classic literature, poetry, and anecdotal history and biography. Mechanics are taught and learned as well, but in a artful, storied, hands-on way. The parts of speech are given personalities and relevant characteristics, so they are humanized and interesting, not dry or boring. Colors are related to each of the parts of speech, relevant to their dominant characteristics.
VERBS: the DOING words are RED
NOUNS: the NAMING words are BLUE
ADJECTIVES: the PICTURE words are YELLOW
ADVERBS: the DESCRIBING words are PURPLE
ARTICLES: the POINTER words are GREEN
PREPOSITIONS: the POSITION words are PINK
Simple, color coded felt pouches could be sewn with the children, to hold the various types of words written in their corresponding colors on small squares of paper. Words could continually be added to the pouches, then used together, to construct whole sentences. Using this sort of colorful approach with adult/child hand-made learning tools is most effective and successful!

Here’s how to make the pouches:
Cut 6″ (or larger) felt squares, one each of all the above parts of speech colors.
Sew a 1/2″ running stitch all around with yarn, starting and ending in one of the corners.
Knot the yarn 1/2″ from the ends, then pull both ends tight, gathering the edges and forming the pouch.
Tie the the yarn in a bow to close, filling each pouch with words!
CCSS.ELA-LITERACY.L.3.2
Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
CCSS.ELA-LITERACY.L.3.2.A
Capitalize appropriate words in titles.
CCSS.ELA-LITERACY.L.3.2.B
Use commas in addresses.
CCSS.ELA-LITERACY.L.3.2.C
Use commas and quotation marks in dialogue.
CCSS.ELA-LITERACY.L.3.2.D
Form and use possessives.
CCSS.ELA-LITERACY.L.3.2.E
Use conventional spelling for high-frequency and other studied words and for adding suffixes to base words (e.g., sitting, smiled, cries, happiness).
CCSS.ELA-LITERACY.L.3.2.F
Use spelling patterns and generalizations (e.g., word families, position-based spellings, syllable patterns, ending rules, meaningful word parts) in writing words.
CCSS.ELA-LITERACY.L.3.2.G
Consult reference materials, including beginning dictionaries, as needed to check and correct spellings.
Knowledge of Language:
CCSS.ELA-LITERACY.L.3.3
Use knowledge of language and its conventions when writing, speaking, reading, or listening.
CCSS.ELA-LITERACY.L.3.3.A
Choose words and phrases for effect.*
CCSS.ELA-LITERACY.L.3.3.B
Recognize and observe differences between the conventions of spoken and written standard English.
Vocabulary Acquisition and Use:
CCSS.ELA-LITERACY.L.3.4
Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3 reading and content, choosing flexibly from a range of strategies.
CCSS.ELA-LITERACY.L.3.4.A
Use sentence-level context as a clue to the meaning of a word or phrase.
CCSS.ELA-LITERACY.L.3.4.B
Determine the meaning of the new word formed when a known affix is added to a known word (e.g., agreeable/disagreeable, comfortable/uncomfortable, care/careless, heat/preheat).
CCSS.ELA-LITERACY.L.3.4.C
Use a known root word as a clue to the meaning of an unknown word with the same root (e.g., company, companion).
CCSS.ELA-LITERACY.L.3.4.D
Use glossaries or beginning dictionaries, both print and digital, to determine or clarify the precise meaning of key words and phrases.
CCSS.ELA-LITERACY.L.3.5
Demonstrate understanding of figurative language, word relationships and nuances in word meanings.
CCSS.ELA-LITERACY.L.3.5.A
Distinguish the literal and nonliteral meanings of words and phrases in context (e.g., take steps).
CCSS.ELA-LITERACY.L.3.5.B
Identify real-life connections between words and their use (e.g., describe people who are friendly or helpful).
CCSS.ELA-LITERACY.L.3.5.C
Distinguish shades of meaning among related words that describe states of mind or degrees of certainty (e.g., knew, believed, suspected, heard, wondered).
CCSS.ELA-LITERACY.L.3.6
Acquire and use accurately grade-appropriate conversational, general academic, and domain-specific words and phrases, including those that signal spatial and temporal relationships (e.g., After dinner that night we went looking for them).
Writing should develop organically for the most part, with concentrated lessons and direct teaching beginning in Grade 4. For now, playful practice like that described above for learning parts of speech, could be employed to hone all of the above skills. Remember that exposure to excellent literature, both hearing it and eventually reading it, will do more for acquiring all of the above skills than almost anything else.
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. Back to a bit more of the CCSS Grade 3 math standards tomorrow, before bidding farewell to Grade 3!
The post L 3.1 A-I, L 3.2 A-G, L 3.3 A-B, L 3.4 A-D, L 3.5 A-C, L 3.6: Really, It’s Not All That Complicated! (#236) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 235
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.
Back to the Common Core for Grade 3 English Language Arts Standards. Math By Hand integrates language arts with math, and though the Waldorf curriculum is taught in blocks, none of the subjects are really taught in isolation. Integration is key, and the ambient standards posted here will reflect that. The Common Core language arts standards are listed here in blue, followed by ambient language arts suggestions.
SPEAKING AND LISTENING:
Comprehension and Collaboration:
CCSS.ELA-LITERACY.SL.3.1
Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 3 topics and texts, building on others’ ideas and expressing their own clearly.
CCSS.ELA-LITERACY.SL.3.1.A
Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion.
CCSS.ELA-LITERACY.SL.3.1.B
Follow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion).
CCSS.ELA-LITERACY.SL.3.1.C
Ask questions to check understanding of information presented, stay on topic, and link their comments to the remarks of others.
CCSS.ELA-LITERACY.SL.3.1.D
Explain their own ideas and understanding in light of the discussion.
These might just as well be rules and protocols of behavior at a corporate board meeting! Certainly not suitable for healthy, active, curious 9 year olds. First, notice “grade 3 topics and texts” since it’s italicized and meant to be noticed. There’s no need to water topics down to reduced levels, rather all material needs to be presented integrally whole so no talking down is necessary. The difference is that all material is cloaked in art and story, so it’s translated and understandable at a third grade level.
Discussion requires logical thinking on the part of all participants. Not yet, not until age 11 or 12 when reason becomes accessible and developmentally available. The word “idea” comes from the late Middle English via Latin from Greek meaning “to see the form or pattern.” Again, this is the product of clear, logical thinking, and not to be expected just yet. At this stage, the child is still absorbing all we can offer from the annals of those who came before us. As teachers/parents we are the keepers, obliged and entrusted with this task.
At the Waldorf Grade 3 level, stories are told by the teacher who really is a “living textbook” in that all the material to be relayed is taken in and then translated to fit the needs of the children before him or her. After sleeping on what they’ve heard, the children recount the story the next day. And yes, all of the guidelines in SL 3.1 B/C are present at this recounting! As for SL 3.1 D, not yet. The 9 year old is still in the absorption phase, not yet able to form reasoned opinions or original ideas.
CCSS.ELA-LITERACY.SL.3.2
Determine the main ideas and supporting details of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.
CCSS.ELA-LITERACY.SL.3.3
Ask and answer questions about information from a speaker, offering appropriate elaboration and detail.
Main ideas and supporting details come from the teacher in pictorial story form and not from a text read aloud or presented in diverse media and formats. As I stated in a Facebook post on the value of various screens in the elementary classroom, oxytocin never has and never will come from a screen, because it is the essence of human presence: the best teaching tool available.
All is faithfully recorded in the children’s main lesson books, after the material is recounted from the teacher’s presentation the day before. From the alphabet in Grade 1, letter by letter, to the structure of the skeletal system or the workings of the human heart in Grade 7, all is beautifully illustrated and documented. Here are two examples from Grade 7 Waldorf main lesson books: the skeletal structure of the hand, from the Four Winds Waldorf School, and the human heart from the blog, In These Hills. As you can see if you visit these two pages, appropriate elaboration and detail is always attended to in the production of all main lesson books.

Presentation of Knowledge and Ideas:
CCSS.ELA-LITERACY.SL.3.4
Report on a topic or text, tell a story, or recount an experience with appropriate facts and relevant, descriptive details, speaking clearly at an understandable pace.
CCSS.ELA-LITERACY.SL.3.5
Create engaging audio recordings of stories or poems that demonstrate fluid reading at an understandable pace; add visual displays when appropriate to emphasize or enhance certain facts or details.
CCSS.ELA-LITERACY.SL.3.6
Speak in complete sentences when appropriate to task and situation in order to provide requested detail or clarification. (See grade 3 Language standards 1 and 3 here for specific expectations.)
Reports on topics are completed every day in main lesson book pages, after the topic has been thoroughly recounted orally, with appropriate facts and relevant descriptive details. All of those details are illustrated beautifully as well. Waldorf students speak most clearly from Kindergarten on, as many classic verses and songs are learned by heart. The teacher’s clarity of speech is emulated in all that’s said, on any topic.
Students create many engaging presentations, from daily recitation to elaborate class plays, though no audio recordings are usually made. Visual displays are consistently created, both for the love of art and to emphasize and enhance certain facts or details. Since the teacher always speaks in clear, complete sentences and all content is conveyed in this way, the student learns by example to do the same.
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 continue to explore ambient counterparts to the CCSS language arts standards.
The post SL 3.1 A-D, SL 3.2-6: Speaking & Listening. All Through Waldorf, K-12! (#235) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 234
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.
I found an excellent article in the Philadelphia Waldorf School’s blog, Loving Learning. In it, Barbara Sokolov beautifully illustrates the practical sensibility of the Waldorf approach to reading in the early grades (from the Spring/Summer 2000 issue of Renewal: A Journal for Waldorf Education). The following excerpts are highlights from the article which can be read here.
“In the primary grades, children continue to work on the outer mechanical aspect of reading. Students spend long periods of time reading simplistic texts that correspond to the level of their decoding abilities. Readers and textbooks contain stories and information written with restricted vocabularies and simple sentence structure. There is little to ignite young imaginations, to evoke wonder, or to stimulate appreciation for the beauty and complexity of language.”
Such is the sad truth of conventional early reader books. If you think of the child as a seed of what s/he will be as an adult, these simplistic stories are insulting and demeaning. How much more uplifting and fitting to offer intact, authentic, unadulterated literature? It’s a leap of faith to see the mighty oak sleeping in the acorn, but this is exactly what we as educators must do, if we would not violate the inherent integrity of the child.
“How unfortunate it is that in the early grades most children are not exposed to rich complex language, simply because such language would not be compatible with their limited decoding skills. Just at the time when their minds are most open to language acquisition they are working with artificially limited vocabularies in school! Of course, vocabulary building is an ongoing process throughout the school years and beyond. But it is much easier for older children to learn new vocabulary if they already have a well-developed sense of language, and a large pool of words and mental images to build upon.”
We must think of this as storing up treasure in the child’s repertoire of language. It is essential throughout to understand what part mental imagery and imagination play in the acquisition of language. Such is the domain of the young child, and we ignore this to their and our peril. As they learned to speak, naturally and seamlessly putting together complex language structures, so will they learn to read. If we let them.
“It is apparent that the growing illiteracy problem in this country is not caused by the lack of technical decoding skills. For most of the children with reading deficiencies, it is a crisis in comprehension, a crisis largely brought about by the early introduction of abstract decoding skills and by ignoring the powerful tools of imagination and artistic activity that are the natural avenues of learning for young school children. Ironically, the only cure put forward by the educational establishment is to work harder and earlier on decoding skills, which only exasperates the problem further.”
Interesting that this was written some fourteen years ago and rings so true for what we are experiencing with the Common Core today. Working harder and earlier on decoding skills is mistaken. As Sir Ken Robinson tells us, what’s needed in education today is not reformation but transformation. Or as Albert Einstein so wisely said, “We can’t solve problems by using the same kind of thinking we used when we created them.”
“Working with a real knowledge of the developing child, Waldorf teachers begin teaching reading by cultivating children’s sense of language and their inner capacities to form mental images. Vivid verbal pictures and the use of rich language are constantly employed in the classroom. Difficult vocabulary and complex sentence structure are not held back in the telling of tales. Children sing and recite a vast treasury of songs and poems that many learn by heart. Children live into the world of imaginative inner pictures, totally unaware that they are developing the most important capacities needed for reading comprehension, for reading with understanding. They learn naturally and joyfully.”
It’s essential to true language arts success that children be “totally unaware that they are developing the most important capacities needed for reading comprehension.” This sort of back door approach is the only way to unlock the deep wellsprings of ability and the innate capacity for wisdom within each child.
“Working with a true knowledge of the human being, a true understanding of the stages of child development, the Waldorf teacher is able to educate children in ways that enable them to blossom forth with joy. As Rudolf Steiner says, “It is indeed so that a true knowledge of man loosens and releases the inner life of soul and brings a smile to the face.”
I found myself smiling as I read this, recognizing once again how Rudolf Steiner touches the nerve of true wisdom with his words. Childhood happens only once, make it count by giving every child the gift of slow, authentic learning. 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 as we continue to explore ambient counterparts to the CCSS language arts standards.

Image from the Philadelphia Waldorf School’s blog, Loving Learning
The post Grade 3: A Reading Revolution, It’s Time! (#234) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 233
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.
Back to the Common Core for Grade 3 English Language Arts Standards. Math By Hand integrates language arts with math, and though the Waldorf curriculum is taught in blocks, none of the subjects are really taught in isolation. Integration is key, and the ambient standards posted here will reflect that. The Common Core language arts standards are listed here in blue, followed by ambient language arts suggestions.
WRITING:
Text Types and Purposes:
CCSS.ELA-LITERACY.W.3.1
Write opinion pieces on topics or texts, supporting a point of view with reasons.
CCSS.ELA-LITERACY.W.3.1.A
Introduce the topic or text they are writing about, state an opinion, and create an organizational structure that lists reasons.
CCSS.ELA-LITERACY.W.3.1.B
Provide reasons that support the opinion.
CCSS.ELA-LITERACY.W.3.1.C
Use linking words and phrases (e.g., because, therefore, since, for example) to connect opinion and reasons.
CCSS.ELA-LITERACY.W.3.1.D
Provide a concluding statement or section.
CCSS.ELA-LITERACY.W.3.2
Write informative/explanatory texts to examine a topic and convey ideas and information clearly.
CCSS.ELA-LITERACY.W.3.2.A
Introduce a topic and group related information together; include illustrations when useful to aiding comprehension.
CCSS.ELA-LITERACY.W.3.2.B
Develop the topic with facts, definitions, and details.
CCSS.ELA-LITERACY.W.3.2.C
Use linking words and phrases (e.g., also, another, and, more, but) to connect ideas within categories of information.
CCSS.ELA-LITERACY.W.3.2.D
Provide a concluding statement or section.
CCSS.ELA-LITERACY.W.3.3
Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.
CCSS.ELA-LITERACY.W.3.3.A
Establish a situation and introduce a narrator and/or characters; organize an event sequence that unfolds naturally.
CCSS.ELA-LITERACY.W.3.3.B
Use dialogue and descriptions of actions, thoughts, and feelings to develop experiences and events or show the response of characters to situations.
CCSS.ELA-LITERACY.W.3.3.C
Use temporal words and phrases to signal event order.
CCSS.ELA-LITERACY.W.3.3.D
Provide a sense of closure.
Creative or original writing does not begin in the Waldorf system until Grade 4. In Grade 3, the mechanics of good writing are still being learned in a pictorial, artful way. As with much else in the Waldorf curriculum, time is devoted to building a solid foundation. The “slow food” (vs fast food) movement favors quality over convenience or expedience. Just so, Waldorf carefully builds capacity before demanding performance.
The standards above reflect a rigorous approach, with clearly defined rubrics for grading student work. One student might be more verbally inclined and therefore better at written self expression. Another student may be brimming with ability and ideas but not yet able to verbalize them, especially in writing. The student with a different developmental time frame then suffers by receiving a failing grade.
Better to wait on the original writing and focus instead on the basics: spelling, parts of speech, punctuation, and the building blocks of composition. There are many creative, colorful, interesting options for teaching these basic elements. Cursive writing is a lost art, one that has proven beneficial to the retention of information and creativity. As stated by the Morain Waldorf School. “Cursive writing is also introduced this year (third grade), which recent studies indicate aids in reading, retention and even idea generation.”
We could say the the overeagerness of the Common Core’s pushing requirements down the grades has gotten us into a pickle. That of discouraging 9 year old “poor writers” from a potential lifetime of true learning, one that grows from the seed to the stem, to the leaf, flower, and fruit. As gardeners we would not expect to find apples on the tree in spring, instead of buds and blossoms. We urgently need to allow the young child to go through the stages that are most conducive to healthy growth and development.

The Waldorf Grade 3 curriculum is still very much in the “input” stage, feeding great literature, poetry, and cultural history into eager minds. Forms of writing: narrative, informational/expository, and persuasive can be introduced in a foundational, nascent way. For example, growing food and later preserving or canning it, while colorfully listing the procedure, with lots of guidance, is an excellent example of informational text.
Back to the aforementioned “pickle,” here is a wonderfully illustrated list for preserving food, from Ms. McLachlan’s third grade class at Four Winds Waldorf School. This list could be copied into the students’ Farming main lesson books after having experienced several of the methods first-hand.

Production and Distribution of Writing:
CCSS.ELA-LITERACY.W.3.4
With guidance and support from adults, produce writing in which the development and organization are appropriate to task and purpose. (Grade-specific expectations for writing types are defined in standards 1-3 above.)
CCSS.ELA-LITERACY.W.3.5
With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. (Editing for conventions should demonstrate command of Language standards 1-3 up to and including grade 3 here.)
CCSS.ELA-LITERACY.W.3.6
With guidance and support from adults, use technology to produce and publish writing (using keyboarding skills) as well as to interact and collaborate with others.
“Guidance” is the key word here, but the Waldorf version differs greatly from the Common Core version. The Waldorf guidance nurtures the child’s consciousness at its appropriate stage by allowing abilities to be grown and fed until ready to blossom and fruit, as opposed to the Common Core version which pushes developmentally inappropriate requirements down to younger and younger ages. The reasoning “earlier is better and more productive” has been proven wrong in many ways but it persists, to great harm all around.
Technology should not be used at all until later. As mentioned above, cursive writing serves many positive purposes. And the rampant introduction of iPads and laptops into schools in lower and lower grades is counter productive to say the least. Oxytocin is produced by human presence, and it does not yet (and will not ever) come off a screen.
Research to Build and Present Knowledge:
CCSS.ELA-LITERACY.W.3.7
Conduct short research projects that build knowledge about a topic.
CCSS.ELA-LITERACY.W.3.8
Recall information from experiences or gather information from print and digital sources; take brief notes on sources and sort evidence into provided categories.
CCSS.ELA-LITERACY.W.3.9
(W.3.9 begins in grade 4)
Research should be experiential only at this age. It should not be a junior version of the high schooler’s or college student’s research. No place yet for gathering information and sorting index cards! Here’s a very experiential research project I conducted with my third grade class. We kept a worm bin from the beginning of the year, supplied with 100 or so worms. All year long, the students went to each classroom at lunchtime with a wheelbarrow, collecting leftovers that were composted into the worm bin. At the end of the year I covered the floor with white paper and we counted the greatly increased numbers of worms. A wriggly affair, but a very real way of scientifically measuring and documenting the worm facts.
Range of Writing:
CCSS.ELA-LITERACY.W.3.10
Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
Later for this, explicitly. For now, gather and store for future harvesting. 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 continue to explore ambient counterparts to the CCSS language arts standards.
The post W 3.1-3 A-D, W 3.4-9: Writing, From Seed to Leaf, Blossom & Fruit (#233) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 232
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.
Re our last post (#231), a partial redo. Not to have implied that the mechanics of reading does not warrant or deserve attention. It does. And late Grade 2 / Grade 3 is a good time to start. A playful/artful approach is preferable however. Just as the 4 Processes were characterized and personalized, the mechanics of reading and writing can (and should) be.
For example, the eight major parts of speech could also be given colors and personalities. Verbs could be red since they’re so active or choleric. Or adjectives might be yellow and sanguine, since there are so many, and they are quite gushy! Figurative stories along with drawings and examples of words dressed up in their respective colors make these concepts more approachable and doable.
Here’s a funny poem about the inconsistencies of the English language:
We’ll begin with a box, and the plural is boxes,
But the plural of ox should be oxen, not oxes.
Then one fowl is a goose, but two are called geese,
Yet the plural of moose should never be meese,
You may find a lone mouse or a whole nest of mice,
But the plural of house is houses, not hice.
If the plural of man is always called men,
Why shouldn’t the plural of pan be called pen?
The cow in the plural may be cows or kine,
But a bow if repeated is never called bine,
And the plural of vow is vows, never vine.
If I speak of a foot and you show me your feet,
And I give you a boot would a pair be called beet?
If one is a tooth, and a whole set are teeth,
Why shouldn’t the plural of booth be called beeth?
If the singular’s this and the plural is these,
Should the plural of kiss ever be nicknamed keese?
Then one may be that and three would be those,
Yet hat in the plural would never be hose,
And the plural of cat is cats, not cose.
We speak of a brother, and also of brethren,
But though we say mother, we never say methren,
Then the masculine pronouns are he, his and him,
But imagine the feminine she, shis and shim,
So the English, I think, you all will agree,
Is the queerest language you ever did see.
To keep all of these variances straight, hands-on memory aids could be made with the help of the children, and stored in bins or baskets for skills practice time. Here’s a good example, used for practicing plurals. from the blog 5th Grade Rocks, 5th Grade Rules.

When teaching in blocks, it’s a good idea to alternate math and language arts skills practices after the main lesson. Start with 20 minutes of lively morning circle activities, settle down into the main lesson for an hour and a half, have snack and outdoor recess, then come back to 20 minutes to a half hour of skills practice. This could be pencil-and-paper, hands-on using manipulatives, or interactive (games, spelling bees, math with movement, etc.)
So do include the basics! But do liven them up with movement, visuals, and whimsy. In closing, here is an excellent blog post from Sarah Baldwin’s Moon Child, Myth Busting: How Reading is Taught in a Waldorf School. And here from the same blog post is “M” for Mountain, can’t you just hear the busy gnomes mining the sparkling jewels and gold inside it?

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 continue to explore ambient counterparts to the CCSS language arts standards.
The post Grade 3: OR, When/If Decoding/Phonics IS Needed/Wanted (#232) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 231
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.
Back to the Common Core for Grade 3 English Language Arts Standards. Math By Hand integrates language arts with math, and though the Waldorf curriculum is taught in blocks, none of the subjects are really taught in isolation. Integration is key, and the ambient standards posted here will reflect that. The Common Core language arts standards are listed here in blue, followed by ambient language arts suggestions.
READING: FOUNDATIONAL SKILLS
Phonics and Word Recognition:
CCSS.ELA-LITERACY.RF.3.3
Know and apply grade-level phonics and word analysis skills in decoding words.
CCSS.ELA-LITERACY.RF.3.3.A
Identify and know the meaning of the most common prefixes and derivational suffixes.
CCSS.ELA-LITERACY.RF.3.3.B
Decode words with common Latin suffixes.
CCSS.ELA-LITERACY.RF.3.3.C
Decode multisyllable words.
CCSS.ELA-LITERACY.RF.3.3.D
Read grade-appropriate irregularly spelled words.
Fluency:
CCSS.ELA-LITERACY.RF.3.4
Read with sufficient accuracy and fluency to support comprehension.
CCSS.ELA-LITERACY.RF.3.4.A
Read grade-level text with purpose and understanding.
CCSS.ELA-LITERACY.RF.3.4.B
Read grade-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings.
CCSS.ELA-LITERACY.RF.3.4.C
Use context to confirm or self-correct word recognition and understanding, rereading as necessary.
Waldorf takes a whole-language approach to reading. Children learn to read through writing. Letters are the first step, as each one is taught in a loving and unhurried way in Grade 1. Sounds are never laboriously attached to letters and syllables. There is no need for decoding when reading seemingly magically happens, usually mid to end of third grade, through exposure to and writing about literature.
When the child is not pressured to read, but simply allowed to experience the joy of the story without that encumbrance, the sheer love of story becomes an irresistible impetus to learn to read for oneself! Here’s an example of lovingly rendered letters “w” and “f” taken from a story about a fisherman, from Catie Johnson’s Chalkboard Drawings in the Waldorf Classroom.

Spelling needs to come from the meaning of words. Again, taking words apart to learn how to spell them is counter-productive. The whole to parts approach really applies to every aspect of Waldorf education. The child perceives ripping things apart in order to more easily teach them, in effect sacrificing integrity to convenience, as an act of violence. Here is a helpful article called Why Some Kids Can’t Spell, and Why Spelling Tests Won’t Help.
Waldorf students are given literature that’s way above grade-level, at all grade levels. Long, complex poems, verses, songs, limericks, tongue twisters and more are learned by heart long before they are independently read. So again, love of the subject comes before technical ability, in fact it really does engender excellence and technical ability far greater than anything learned by rote or in parts could.
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 as we continue to explore ambient counterparts to the CCSS language arts standards.
The post RF 3.3 A-D / RF 3.4 A-C: A Love of Reading Makes Decoding Unnecessary (#231) appeared first on Math By Hand.
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