A Year in the Life: Ambient Math Wins the Race to the Top!
Day 289
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 next series of posts will focus on Grade 4 Common Core 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: INFORMATIONAL TEXT
Integration of Knowledge and Ideas:
CCSS.ELA-LITERACY.RI.4.7
Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, diagrams, time lines, animations, or interactive elements on Web pages) and explain how the information contributes to an understanding of the text in which it appears.
CCSS.ELA-LITERACY.RI.4.8
Explain how an author uses reasons and evidence to support particular points in a text.
CCSS.ELA-LITERACY.RI.4.9
Integrate information from two texts on the same topic in order to write or speak about the subject knowledgeably.
Range of Reading and Level of Text Complexity:
CCSS.ELA-LITERACY.RI.4.10
By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 4-5 text complexity band proficiently, with scaffolding as needed at the high end of the range.
Information. Isn’t this the information age? Or maybe it’s the digital age. In any case, it’s too much, too soon for your fourth grader. It was WB Yeats who said that education should not be the filling of a pail but the lighting of a fire. Pouring too much information into your fourth grader’s head is putting the cart before the horse. Time enough for information processing (like that specified in standard 7) later, after the fires have been lit.
The spirit of standard 7 however, is well met by the Waldorf approach. Stories based in both myth and fact are told and retold in great detail by the students and then processed in many ways: visually, orally, musically, dramatically, and in movement. Processing learning through the arts is most effective at contributing to understanding. As for the web, the Waldorf approach is notorious for delaying computer/media use and exposure for good reason, much of which has been amply documented. (Note that many Silicon Valley families choose low-tech Waldorf for their children.)
Reasons and evidence. Best reserved until reason and logic naturally awaken: later. Information from two texts on the same subject is well covered by the Math By Hand trickster tales from many cultures. A rich, cultural tapestry makes up the curriculum at all grade levels, and the spirit of “compare and contrast” is alive and well with every lesson. So that when formal essay writing happens, there’s a solid foundation upon which to draw.
History and social studies are covered within the local geography lessons, zoology within animal studies, and technical information abounds in the handwork and practical crafts activities. Waldorf students are steeped from the beginning in the high end of each grade level range and beyond, since the restriction of having to read complex texts independently is removed. And fractions! Note how inversion for dividing fractions is illustrated in this delightful page from the Nelson Waldorf School. (Notice the cursive writing, a lost art that’s still being taught in Waldorf!)
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 RI.4 7-10: Not Filling A Pail But Lighting a Fire (#289) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 288
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 next series of posts will focus on Grade 4 Common Core 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: INFORMATIONAL TEXT
Craft and Structure:
CCSS.ELA-LITERACY.RI.4.4
Determine the meaning of general academic and domain-specific words or phrases in a text relevant to a grade 4 topic or subject area.
CCSS.ELA-LITERACY.RI.4.5
Describe the overall structure (e.g., chronology, comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in a text or part of a text.
CCSS.ELA-LITERACY.RI.4.6
Compare and contrast a firsthand and secondhand account of the same event or topic; describe the differences in focus and the information provided.
This begs the question: how much reality is too much reality for your 10 year old? Piaget, Steiner, and many other child development experts cite the years until puberty as pre-logical, pre-reason. If the tools of logic and reason are not yet accessible, why burden 10 year olds with information they are not prepared to handle? Norse Mythology is the staple literature for the Waldorf fourth grader, for good reason.
We are living in an age that is all but devoid of myth, so that in effect our daily measure of reality is akin to metal against metal, with nothing to mitigate its harshness. Be that as it may, shouldn’t it behoove us to give our children a measure of what we lack? To provide a respite before growing up that steeps them in the graces of what we once revered?
If indeed, children’s mental and physiological development is as most experts say it is, then we need to put the brakes on too early exposure to inappropriate material. That said, the Waldorf curriculum can nicely meet all of the above standards, in a developmentally appropriate way.
The “meaning of general academic and domain-specific words or phrases in a text relevant to a grade 4 topic or subject area” is well covered with subjects like local geography and zoology. Academics are deepened through the grades while remaining couched in the arts, and in fact are more rigorous and technically advanced than those without an arts-based approach.
The latter two standards are covered by the wonderfully complex and dramatic Norse mythology. All of the elements described in standard 5 are taken in through these stories, though they are not yet abstractly perceived and/or processed. The dialogue among and between the Norse Gods and Goddesses afford many opportunities to discern or compare and contrast firsthand or secondhand accounts of the same event or topic, and/or describe the differences in focus. Here’s an account of Iduna and her apples from waldorftoday.com.
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 RI.4 4-6: Until Reason Awakens, Reality Can Wait (#288) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 287
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 next series of posts will focus on Grade 4 Common Core 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: INFORMATIONAL TEXT
Key Ideas and Details:
CCSS.ELA-LITERACY.RI.4.1
Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.
CCSS.ELA-LITERACY.RI.4.2
Determine the main idea of a text and explain how it is supported by key details; summarize the text.
CCSS.ELA-LITERACY.RI.4.3
Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, including what happened and why, based on specific information in the text.
It’s a radical idea. There are no textbooks to speak of in the Waldorf lower school, and no computers. The students’ informational source is their teacher, who ideally sees them through the grades from first to eighth. The teacher studies the students, giving them what they need individually and as a group. This can be accomplished beautifully in a homeschool setting as well.
All Waldorf lessons are taught in story format since the narrative form is most effective at this age. The teacher is the filter through which the world is brought into the classroom and into students’ hearts and minds. This is essential on two counts: the pictorial or story format is most developmentally appropriate until the age of reason dawns at age 12 or so, and the teacher, standing before the students as a trusted and respected authority figure, is so much more humane and effective than an impersonal text or computer screen could ever be.
For a local geography lesson, the teacher might present anecdotal, historical stories about the neighborhood and/or town. The students hear the story on day 1, retell it on day 2, then summarize and illustrate it in main lesson books that will become their self-created textbooks. For a human and animal lesson, the teacher might convey the main characteristics that make an animal unique and how those might compare to similar characteristics in the human. Here’s a strong, courageous lion from the page chalkboarddrawings.com
These lessons can support great detail as well, such as the animal limbs study below, taken from Kara Johndro’s Pinterest page. I love that the neck of the giraffe is considered a limb! Keep in mind that in the Waldorf classroom, less is more. To borrow a concept from the Common Core, less subject matter is studied at much greater depth.
You can see that all aspects of the above standards are beautifully covered, with heart, grace, and warmth. 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 RI.4 1-3: Should Information @ 10 Be Text or Teacher Based? (#287) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 286
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.
Stories and art provide an excellent framework for your math lessons, along with movement, music, and recitation, frills that budget cuts have eliminated from most classrooms. The ability to add these essentials as an integral part of your school day is one advantage among many to homeschooling. In Grade 4, trickster tales can add fun, enthusiasm, and success to math, every day!
The Math By Hand trickster tales include several about Ijapa the Tortoise, the rascally African trickster. In one tale, he stole many yams from a farmer and then tricked his way out of the crime. The 1089 trick fits nicely with the story and is an excellent way to encourage skills practice. Your fourth grader loves tricks, codes, and patterns, so do include them with your math lessons.
Here’s the 1089 trick: take any 3-digit number, reverse and subtract it, then reverse the answer and add it. The answer will always be 1089! Portions of the story could be written in the indicated spaces, along with several examples of the trick. Then the trick could be extended to skills practice.
The Tlingit tale, Raven and How the Tides Began, tells how Raven tricked the Old Woman of the Sea into moving the tide line so his hungry people could gather food when the tide was out. The tide line and the number line can be happily partnered. The story could be summarized as indicated and the number line drawn in the sand, along with the shells, and then extended to skills practice.
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 launch into Grade 4 Common Core Language Arts standards and their ambient counterparts.
The post Grade 4: Math & Trickster Tales (#286) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 285
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 next series of posts will focus on Grade 4 Common Core 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: LITERATURE
Integration of Knowledge and Ideas:
CCSS.ELA-LITERACY.RL.4.7
Make connections between the text of a story or drama and a visual or oral presentation of the text, identifying where each version reflects specific descriptions and directions in the text.
CCSS.ELA-LITERACY.RL.4.8
(RL.4.8 not applicable to literature)
CCSS.ELA-LITERACY.RL.4.9
Compare and contrast the treatment of similar themes and topics (e.g., opposition of good and evil) and patterns of events (e.g., the quest) in stories, myths, and traditional literature from different cultures.
Beginning in Grade 1, Waldorf students routinely translate texts of classic literature into various forms including visual: all stories are beautifully illustrated and summarized; oral: students retell stories daily, and in great detail; dramatic: the main literature theme is represented in end-of-year-plays produced and performed by students.
Good and evil is a deep and recurring theme in Waldorf Grades 2 and 4, represented in the former by the fables. contrasted with saints’ and heroes’ legends. The Grade 4 focus on Norse mythology and other trickster tales brings the dichotomy of good and evil deeper into the human realm. Math By Hand is an integrated math and language arts curriculum, and features trickster tales from many cultures.
From a Karok Indian tale, Coyote cleverly steals fire from greedy. evil monsters to warm the freezing humans in a nearby village. Savitri, a wise and beautiful Indian princess, uses her wits to defeat Death and bring her betrothed back to life. A travel-weary Swedish itinerant persuades a reluctant villager to feed him (while revealing her hidden generosity) in the tale Nail Soup.
Range of Reading and Level of Text Complexity:
CCSS.ELA-LITERACY.RL.4.10
By the end of the year, read and comprehend literature, including stories, dramas, and poetry, in the grades 4-5 text complexity band proficiently, with scaffolding as needed at the high end of the range.
Waldorf fourth graders are now reading independently, usually at the high end of the range, since they have been exposed to classic literature from the beginning. They absorbed it all, and then learned to read when ripe and ready. Usually no scaffolding is needed, since complex stories, drama, and poetry have all been enjoyed, performed, and learned by heart.
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 RL.4 7-10: Reading (& Appreciating) Literature (#285) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 284
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 entire Grade 1 Language Arts curriculum consists of learning one upper case letter at a time, each one introduced by a relevant fairy tale, and then carefully and reverently drawn next to an illustration that represents the letter, taken from the story. A tale about a wolf (they abound in fairy tale lore!) could illustrate the letter W with the head of the wolf and two paws forming the letter. So it goes for all of the consonants.
The vowels are a different story however. Steiner suggested that the consonants are more earthy, practical, and their sounds are more superficial, formed by the lips, tongue and teeth. The vowels are sounded from a deeper place, the throat, larynx, and even the solar plexus. In the Waldorf first grade, the consonants are covered over several blocks, then at the end of the year the vowels are introduced using body gestures and feelings. Here is an image from Natalia Derbeniova’s Pinterest page.
In the upper right corner, angels (or fairies) bring the vowels down the rainbow bridge to earth. The individual vowels are represented by gestures taken from Eurythmy, Steiner’s method of making speech visible (in which each letter is represented by a gesture). A is a feeling of awe and openness, E is more self protective, I is the feeling of the self as the bridge from spirit to earth, O is encircling and inclusive, and U represents receiving blessings from the spirit world.
If there’s a hesitancy in bringing the “spirit” dimension into your language arts lessons, know that these gestures will resonate with your young children. We have moved too far away from the deeper dimensions in favor of an exclusively materialistic bent, which not only takes its toll on us as adults but does so much more so on the more vulnerable and innocent.
Back to Grade 4! If these deep foundations are laid at the beginning, they will color and carry through all aspects of the language arts: literature, composition, grammar, spelling, and vocabulary. Reverence for a subject goes such a long way toward effectiveness and ultimate success. Then there’s the matter of trust. Much of Common Core, No Child Left Behind, and in fact all standards and testing based approaches, function from a foundation of untrustworthiness. Children cannot be trusted to learn and retain knowledge, as we their teachers cannot be trusted to teach it. Hence the relentless drilling and testing. This, from Life Learning Magazine, says it so well.
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 launch into Grade 4 Common Core Language Arts standards and their ambient counterparts.
The post Vowels, Angels, Reading, & Writing (#284) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 284
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 entire Grade 1 Language Arts curriculum consists of learning one upper case letter at a time, each one introduced by a relevant fairy tale, and then carefully and reverently drawn next to an illustration that represents the letter, taken from the story. A tale about a wolf (they abound in fairy tale lore!) could illustrate the letter W with the head of the wolf and two paws forming the letter. So it goes for all of the consonants.
The vowels are a different story however. Steiner suggested that the consonants are more earthy, practical, and their sounds are more superficial, formed by the lips, tongue and teeth. The vowels are sounded from a deeper place, the throat, larynx, and even the solar plexus. In the Waldorf first grade, the consonants are covered over several blocks, then at the end of the year the vowels are introduced using body gestures and feelings. Here is an image from Natalia Derbeniova’s Pinterest page.
In the upper right corner, angels (or fairies) bring the vowels down the rainbow bridge to earth. The individual vowels are represented by gestures taken from Eurythmy, Steiner’s method of making speech visible (in which each letter is represented by a gesture). A is a feeling of awe and openness, E is more self protective, I is the feeling of the self as the bridge from spirit to earth, O is encircling and inclusive, and U represents receiving blessings from the spirit world.
If there’s a hesitancy in bringing the “spirit” dimension into your language arts lessons, know that these gestures will resonate with your young children. We have moved too far away from the deeper dimensions in favor of an exclusively materialistic bent, which not only takes its toll on us as adults but does so much more so on the more vulnerable and innocent.
Back to Grade 4! If these deep foundations are laid at the beginning, they will color and carry through all aspects of the language arts: literature, composition, grammar, spelling, and vocabulary. Reverence for a subject goes such a long way toward effectiveness and ultimate success. Then there’s the matter of trust. Much of Common Core, No Child Left Behind, and in fact all standards and testing based approaches, function from a foundation of untrustworthiness. Children cannot be trusted to learn and retain knowledge, as we their teachers cannot be trusted to teach it. Hence the relentless drilling and testing. This, from Life Learning Magazine, says it so well.
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 launch into Grade 4 Common Core Language Arts standards and their ambient counterparts.
The post Vowels, Angels, Reading, & Writing (#284) appeared first on Math By Hand.
The post Vowels, Angels, Reading, & Writing (#284) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 283
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 next series of posts will focus on Grade 4 Common Core 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: LITERATURE
Key Ideas and Details:
CCSS.ELA-LITERACY.RL.4.1
Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.
CCSS.ELA-LITERACY.RL.4.2
Determine a theme of a story, drama, or poem from details in the text; summarize the text.
CCSS.ELA-LITERACY.RL.4.3
Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text (e.g., a character’s thoughts, words, or actions).
Authentic, original literature remains the focus in Grade 4. Trickster tales culled from various cultures or Norse Mythology form the backbone of literature this year, although other stories are told in conjunction with local geography, human/animal studies, or even math! Since faculties of reason and logic have not yet fully dawned at this age, the children should not be expected to draw inferences from the text, though each story is taken in and then retold in great (and minute) detail.
Typically in Waldorf, independent reading and writing is begun mid to late Grade 3. In Grade 4, stories are told by the teacher daily, and retold by the children the next day. The teacher still provides images for the students to draw from, as illustrations of the story in main lesson books. These illustrations serve as prompts and/or guides for the children’s written summaries of the story on the facing page, focusing on theme, character, setting, and events. These in-depth summaries will invariably include characters’ thoughts, words, or actions. Here’s an excellent example from the blog, Ducks In the Pond.
Craft and Structure:
CCSS.ELA-LITERACY.RL.4.4
Determine the meaning of words and phrases as they are used in a text, including those that allude to significant characters found in mythology (e.g., Herculean).
CCSS.ELA-LITERACY.RL.4.5
Explain major differences between poems, drama, and prose, and refer to the structural elements of poems (e.g., verse, rhythm, meter) and drama (e.g., casts of characters, settings, descriptions, dialogue, stage directions) when writing or speaking about a text.
CCSS.ELA-LITERACY.RL.4.6
Compare and contrast the point of view from which different stories are narrated, including the difference between first- and third-person narrations.
As always, the Waldorf student acquires a considerable wealth of wisdom and knowledge, all culled from great literature and other, more practical stories. However, all teaching must pass through the filter of childhood at this age. Analytical and conceptual modes need to be trumped by the pictorial and concrete. Although vocabulary is prodigiously built through exposure to great literature (and this is the best, most effective way to build it) it is not directly drilled to any great extent at this point.
A great deal of poetry is learned and recited by heart in Grade 4. Again, the analytical approach must wait. Major differences between poems, drama, and prose are deeply absorbed as are the structural elements of poems by virtue of their memorization and recitation. Casts of characters and settings within the myths and tales told are richly presented, illustrated, and portrayed, verbally and in writing. Script-writing, costuming, set design, and stage direction are extensively taught and learned in the process of producing and performing an end-of-year play.
Compare and contrast is an essay-writing tool that is still a bit too analytical at this age, though the basics of this skill are instinctively and foundationally learned. Narrative point of view, along with the distinction between first and third person narration is deeply taken in, but not yet analyzed as such.
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 RL.4 1-6: Reading (& Appreciating) Literature (#283) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 282
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 fourth 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 or a number line to represent and compare decimals and protractors to measure angles. They use other measurement tools to understand the relative size of units within a system and express measurements given in larger units in terms of smaller units.
6. Attend to precision.
As fourth 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, they use appropriate labels when creating a line plot..
7. Look for and make use of structure.
In fourth grade, mathematically proficient students look closely to discover a pattern or structure. For instance, students use properties of operations to explain calculations (partial products model). They relate representations of counting problems such as tree diagrams and arrays to the multiplication principal of counting. They generate number of shape patterns that follow a given rule.
8. Look for and express regularity in repeated reasoning.
Students in fourth grade should notice repetitive actions in computation to make generalizations. Students use models to explain calculations and understand how algorithms work. They also use models to examine patterns and generate their own algorithms. For example, students use visual fraction models to write equivalent fractions.
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 launch into Grade 4 Common Core Language Arts standards and their ambient counterparts.
The post Grade 4: Common Core Standards for Mathematical Practice 5-8 (#282) appeared first on Math By Hand.
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A Year in the Life: Ambient Math Wins the Race to the Top!
Day 281
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 4 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.
Mathematically proficient students in grade 4 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. Fourth graders 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?” They listen to the strategies of others and will try different approaches. They often will use another method to check their answers.
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 instinctively, much more than we as adults do, with our more empirical mindsets. From this perspective, math in a Waldorf fourth grade takes a back seat to the rich tapestry of ever-expanding subjects 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 many practical examples such as mapping the neighborhood, sketching a cross stitch pattern on graph paper, noting and comparing animal characteristics, etc. Discussing how a problem was solved takes a back seat to the process and the finished product. Besides which, discussion is antithetical at this age, which is a few years shy of being comfortably conversant with logic and reasoning. A fourth grader’s main lesson book drawing of a compass rose, from the blog mud between our toes, is a freehand geometric 8-point construction that takes a back seat to orienting a hand-drawn neighborhood map.
2. Reason abstractly and quantitatively.
Mathematically proficient fourth graders 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. They extend this understanding from whole numbers to their work with fractions and decimals. Students write simple expressions, record calculations with numbers, and represent or round numbers using place value concepts.
A Waldorf fourth 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. Introduce and extend whole number understanding to fractions with the Math By Hand clay plaque, shown below. 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, including estimation and rounding.
3. Construct viable arguments and critique the reasoning of others.
In fourth grade, mathematically proficient students may construct arguments using concrete referents, such as objects, pictures, and drawings. They explain their thinking and make connections between models and equations. 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 fourth grade local geography mapmaking project would be an 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’s questioning as listed above often takes on an artificial tone. If however, the explanation of and responses to thinking occur in a project context, i.e., through the modification of techniques, measurements, and specifications, the resulting teaching and learning is much more effective and successful. For example, a relief map of California could be started on a grid as a scaled up version of a smaller, gridded map. Math practice (and even new concepts) could be embedded in this project.
4. Model with mathematics.
Mathematically proficient fourth grade students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Fourth graders 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. In both the Waldorf and Math By Hand systems, students and teachers alike experience a full spectrum of math expression.
Waldorf handwork is one of the best practical examples of experiencing math principles. For all who practice it regularly, knitting or crocheting 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 enhancing eye hand coordination, by the repetitive and detailed use of the right and left hands. And all children most decidedly thrive on it. Here’s an idea that includes handwork, math, and community: a granny square blanket group project!
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 4: Common Core Standards for Mathematical Practice 1-4 (#281) appeared first on Math By Hand.
The post Grade 4: Common Core Standards for Mathematical Practice 1-4 (#281) appeared first on Math By Hand.
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