Part 1 (Basic Overview: Classical Education and Mathematics) Part 2 (Day 1 Notes: Cosmos!)
Fibonacci
In the West, the Fibonacci sequence first appears in the book Liber Abaci (1202) by Leonardo of Pisa, known as Fibonacci. Fibonacci considers the growth of an idealized (biologically unrealistic) rabbit population, assuming that:
A newly born pair of rabbits, one male, one female, are put in a field; rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits; rabbits never die and a mating pair always produces one new pair (one male, one female) every month from the second month on. How many pairs will there be in one year?
(The photo above is an example of how we went about looking at the problem.)
At the end of the first month, they mate, but there is still only 1 pair.
At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field.
At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field.
At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs.
At the end of the nth month, the number of pairs of rabbits is equal to the number of new pairs (which is the number of pairs in month n − 2) plus the number of pairs alive last month (n − 1). This is the nth Fibonacci number.
The Fibonacci sequence is named after Leonardo Fibonacci. His 1202 book Liber Abaci introduced the sequence to Western European mathematics. It is a number pattern found in nature—such as in branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of artichoke, an uncurling fern and the arrangement of a pine cone—even galaxies and the curing of waves. It also has many practical applications—the Fibonacci sequence is also the foundation of how apparel is sized (called "grading"), and it’s used in knitting. There is so much more to say about it, but for now I’ll just tell you that the sequence starts with the numbers 0 and 1. Then every subsequent number is the sum of the previous two numbers. So you have 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on.
Blockhead: The Life of Fibonacci is a beautiful (and entertaining) picture book introduction to the life of Fibonacci for elementary students.
“It is a blueprint that describes how living things such as flowers grow in an orderly, harmonious way. The numbers even pop up in works of human imagination—buildings, music, art, and poetry.” Blockhead: The Life of Fibonacci
The Fibonacci sequence is related to the “golden ratio,” or phi. Take any two neighboring Fibonacci numbers. Divide the larger by the smaller and you get roughly 1.618. (Phi is an irrational number, which means that it is a non-terminating, non-repeating decimal, 1.6180339887….) (Phi shows up in art and architecture, body proportions, the heart, DNA, spiral in snail shells, etc…)
In no way can I replicate the richness and depth of the conversations (I am immensely thankful for all of the participation of attendees!) and atmosphere from the two practicums where I spoke, but I pray that—whether you attended the Eugene or Albany (Oregon) practicums, attended a CC practicum in another city, or were unable to attend—these abbreviated notes are helpful or inspiring. (I am sharing my personal speaking notes, so they will not necessarily correspond with other practicums.)
In all my reading (in the spirit of copiousness) leading up to the practicum, I continually came across the word cosmos. I had a general idea of what cosmos meant, but as I personally have been on a “words matter” focus lately, I decided to look up the definition.
A cosmos is an orderly or harmonious system. The word derives from the Greek term κόσμος (kosmos), meaning literally "order" or "ornament" and metaphorically "world,” and is diametrically opposed to the concept of chaos.
While we’re at it, let’s look up the definition of ornament: (Merriam-Webster) 2a. something that lends grace or beauty 3: one whose virtues or graces add luster to a place or society
Order + Beauty (literally) = World (metaphorically)
(We’re really starting at the very beginning, here.)
Genesis 1:1-2 In the beginning God created the heavens and the earth. Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters.
Formless. And what did God do? Created form: separated light and darkness, waters and sky, land and seas.
Empty. And once the form established, he filled the place with beauty: plants, stars, birds, sea creatures, animals, man.
Genesis 2:1 Thus the heavens and the earth were completed in all their vast array.
(Words matter!)
Array: verb (used with object): 1. to place in proper or desired order 2. to clothe with garments, especially of an ornamental kind; dress up; deck out.
And, as Leigh Bortins says, that’s how you teach everything to everybody. Figure out what the form is, and then you have all the content in the world to make it creative, beautiful!
Sentence forms Latin ending forms Math formulas The structure of story
You can put in whatever content you wish once you know the form. The content is what makes it unique and interesting.
This includes the form of classical education.
Day 1: Focus on Grammar
Grammar is the first art or tool of the trivium. This is the stage of input. Grammar is not just the study of the structure of language, it is defined as the “science of vocabulary” (Leigh Bortins, The Core: Teaching Your Child the Foundations of Classical Education, page 48). The student (of any age) must first internalize (by exposure and mastery) the vocabulary, definitions, facts, stories, ideas, names, dates, and rules of a subject or skill.
“No matter what your children’s strengths and weaknesses are, or their likes and dislikes, or their gifts and talents—their brains want to gather, sort, and store, and retrieve information.” (The Core, page 52)
“It is not surprising that, for the Greek mind, the Muses—of epic, history, astronomy, music, dance, tragedy, comedy, lyric poetry, and sacred poetry—should be daughters of Memory.” (Anthony Esolen, Ten Ways to Destroy the Imagination of Your Child, page 9)
“One simple and immutable fact about the human brain is that you can’t get something out of it that isn’t there to start with. Supernatural inspiration notwithstanding, human beings in general—and children in particular—really can’t produce... thoughts or concepts that they haven’t first experienced and stored. In other words, we cannot think a thought we don’t have to begin with. Even the most unique, creative, and extraordinary ideas can only exist as a combination and permutation of previously learned bits of information.” (Andrew Pudewa, 1 Myth, 2 Truths)
“There are times when memorization is out of favor in education. Some might say that “rote memorization” is not appropriate as a teaching strategy. “Rote memorization,” however, is loaded language, biased against the discipline and effort required to learn things permanently. There is nothing wrong with challenge. We must remember that the alternative to remembering is forgetting, and when we teach something as important as grammar, that will be needed for one’s entire life, the ban on memorization makes little sense. There are areas of knowledge that should be memorized, and in the past, there was a better term for it: to learn by heart.” (Michael Clay Thompson)
“But more than that, we would desire to bring children into the garden of created being, and thought, and expression. Caldecott reminds us that for the medieval schoolmen, as for Plato, education was essentially musical, an education in the cosmos or lovely order that surrounds us and bears us up. Thus when we teach our youngest children by means of rhymes and songs, we do so not merely because rhymes and songs are actually effective mnemonic devices. We do so because we wish to form their souls by memory: we wish to bring them up as rememberers, as persons, born, as Caldecott points out, in certain localities, among certain people, who bear a certain history, and who claim our love and loyalty.” (Anthony Esolen, author of Ten Ways to Destroy the Imagination of Your Child, in the Foreword from Beauty in the Word: Rethinking the Foundations of Education by Stratford Caldecott)
Mathematics
“The sheer amount of information available in every discipline is far too great to be mastered by one person even in a lifetime. The purpose of an education is not merely to communicate information, let alone current scientific opinion, nor to train future workers and managers. It is to teach the ability to think, discriminate, speak, and write, and, along with this, the ability to perceive the inner, connecting principles, the intrinsic relations, the logoi, of creation, which the ancient Christian Pythagorean tradition...understood in terms of number and cosmic harmony.” (Stratford Caldecott, Beauty for Truth's Sake: On the Re-enchantment of Education, page 28)
Michael S. Schneider writes, “Numbers are a map of the beautiful order of the universe, the plan by which the divine Architect transformed undifferentiated Chaos into orderly Cosmos.” (Beauty for Truth’s Sake, page 54)
God spoke in words (His very name “I AM” is a subject and a predicate, the form of language, Exodus 3:14), but he also spoke in math.
“Mathematics is the language of science, but it is also the hidden structure behind art…, and its basis is the invisible Logos of God.” (Beauty for Truth’s Sake, page 30)
Galileo Galilei (1564-1642) said, "The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth."
“The laws of nature are but the mathematical thoughts of God.” ~Euclid
(Words matter!) The word mathematics comes from the Greek μάθημα (máthēma), which, in the ancient Greek language, means "that which is learnt", "what one gets to know," hence also "study" and "science", and in modern Greek just "lesson."
From Merriam-Webster, the definition of MATHEMATICS: the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations. (Whew!!)
Another source defined math as the study of relationships using numbers.
Mathematics is the abstract study of quantity, structure, space, change, and many other topics. It has no generally accepted definition.
Let’s talk about a brief history of math.
Why?
“An integrated curriculum must teach subjects, and it must teach the right subjects, even mathematics and the hard sciences, within the history of ideas, which is the history of our culture. Every subject has a history, a drama, and by imaginatively engaging with these stories we become part of the tradition.” (Beauty for Truth’s Sake, page 28)
Up until c. 500 B.C. mathematics was indeed the study of number. During the period of Egyptian and Babylonian mathematics, it consisted almost solely of utilitarian arithmetic or counting.
500 B.C. to 300 A.D., the era of Greek mathematics was primarily concerned with measurement and geometry—number and shape. Not just utilitarian, mathematics was regarded as an intellectual pursuit having both aesthetic (beauty!) and religious elements. From the Greeks we have Euclid’s Elements.
In the middle of the seventeenth century, Newton and Leibniz independently invented calculus—essentially the study of motion and change—making it possible to study physics and the motion of planets, among other things. So mathematics became the study of number, shape, motion, change, and space.
In the year 1900, all the world’s mathematical knowledge would have fit into about 80 books. Today it would take maybe 100,000 volumes to contain all known mathematics.
As you can imagine, many quite new branches of mathematics have sprung up.
[Mark Twain said “We could use up two Eternities in learning all that is to be learned about our own world and the thousands of nations that have arisen and flourished and vanished from it. Mathematics alone would occupy me eight million years.”]
Many mathematicians agree that mathematics can be considered the science of patterns. Mathematicians examine abstract patterns using symbolic notation—mathematical language.
The History of Counting is a fantastic picture book introduction to the history of counting across cultures.
The quadrivium consists of arithmetic (pure number), geometry (number in space), music (number in time), and astronomy (number in space and time) (Beauty for Truth’s Sake, page 24)). Our focus is arithmetic.
There are only are 3 (three!) basic things to learn in arithmetic…everything else is just more complex combinations of these three categories:
Numbers (8), operations (6), and laws (4). That’s it!
This is our FORM!
Math in a nutshell: “There are digits, you do things with them, and they follow laws.” Leigh Bortins
So let’s begin with the definitions. You cannot have a conversation about something if you don’t have words to use—not “thingy”! Kids soak up vocabulary. If they can say Tyrannosaurus Rex, they can say denominator. It’s adults who are intimidated!
A Number is the IDEA that I have three of something.
A Numeral is the SYMBOL used to express the idea. (For example, we use the heart symbol to express the idea of love.)
We are talking about real numbers today. Real numbers can be written as a fraction (as opposed to irrational #s which do not have a ratio—cannot be written as a fraction—such as pi).
Natural Numbers are the counting numbers. They are positive and exclude 0. 1, 2, 3, 4, 5… and so on.
Whole Numbers are the counting numbers and 0. 0, 1, 2, 3, 4… This is easy to remember if you look at the word Wh0le and think of the o as a 0.
Integers are the whole numbers and their opposites (including 0). …-4, -3, -2, -1, 0, 1, 2, 3, 4…
A number located in between integers on the number line is called a Decimal. Add a decimal point and add numbers to the right to indicate a decimal. This is part of our base 10 system. A natural number can be expressed as a decimal by adding .0
Fractions. A fraction is a number in the form of a over b. the line represents division. A fraction is simply an integer or decimal number, prior to completing the division. The top number is called the numerator. The bottom number is called the denominator. Also called a ratio. (A fraction may also be defined as a ratio of numbers, where a ratio is just the division relationship a/b.)
A proper fraction has a value less than one (the numerator is less than the denominator).
An improper fraction has a value greater than one (the numerator is greater than the denominator) such as 6/1 or six divided by 1 equals 6.
Mixed numbers include an integer and a ratio. Could 6 be expressed as a mixed number in different ways? Yes. The integer of a mixed number will be a 0 if the value is less than one.
Percent. % symbols mean the number was multiplied by 100, so divide by 100 to return to a non-percent number.
Scientific Notation is used when working with very large or very small numbers and is a very specific form. In scientific notation a number is rewritten as a value between 1 and (less than) 10 (a digit in the one’s place) expressed as a decimal, multiplied by a factor of 10.
10 to a positive power means that you move the decimal that many places to the right (used for large numbers). 10 to a negative power means that you move the decimal that many places to the left (used for small numbers).
Anything to the 0 power = 1, so the number three expressed in scientific notation would be 3.0 x 10 to the 0 power or 10^0.
Why? Here is one example of why it works:
I challenge you to express a number in as many different ways as possible. This is a fun activity to do with kids. The boys and I filled a page with symbols expressing the value of the number six, including Roman numerals, percent, tally marks, stick figure people, fraction “pies,” dots on a die, and various numerical expressions (numbers and operations).
“When I was a boy, we had to memorize the multiplication tables in the second grade, up to 12 x 12 = 144. Let’s set aside the fact that it takes a deal of intelligence and some ingenuity to accomplish that task. Forget that you would have to learn that anything multiplied by 5 ends in 5 or 0, alternately. Forget that if you were sharp you’d see that odd times odd is odd, and everything else is even. Forget the patterns showing up among the 2s, 4s, and 8s. Forget the nice progression in the 9s, with the tens digit gaining one and the ones digit dropping it: 09, 18, 27, and so forth. What that memorization did was to free you up to become comfortable with numbers themselves, and with the structure of arithmetic. Once you had done that, you could play with numbers creatively, long before you’d ever suspected the existence of algebra or calculus, with their toboggan curves and their infinite series and their radio waves, their transcendental numbers and the mysterious i, the square root of -1, whose existence we must leave to philosophers to determine.” (Anthony Esolen, Ten Ways to Destroy the Imagination of Your Child, page 20)
And another interesting dive into the meaning of words:
“In English, integrity is a word related to a number of other familiar ones. It is built from the root word, integer. Now, as most of us learned in early math, an integer is a whole number, as in 1,2,3,3- that is, whole numbers as opposed to fractions. They are whole or complete numbers, not parts of a whole.”
In·teg·ri·ty 1. Steadfast adherence to a strict moral or ethical code. 2. The state of being unimpaired; soundness. 3. The quality or condition of being whole or undivided; completeness.
[Middle English integrite, from Old French, from Latin integrits, soundness, from integer, whole, complete]
“In relating the word integrity to our lives, it describes an uncompromised character, an unjaded soul, an unsullied heart, an undivided mind. It requires the maintenance of our hearts in entirety before the Lord. David said: "Unite my heart to fear Your name." Those words say, "God, draw the strands of my heart so firmly tight and in such reverence before Your throne, that I will be kept wholly and entirely aligned with You."
This is the first post in a series containing various information from my CC Parent Practicum speaking notes for those interested. If you attended the practicum and have questions or requests for specific information, please leave me a message in the comments or email me at heidi (at) poetsgarden (dot) com.
Classical, Christian Education
A good introduction to the form of Classical Education:
Leigh Bortins and Andrew Kern discussing the seven liberal arts with a focus on the quadrivium (arithmetic, geometry, music, and astronomy). Phenomenal.
Mathematics
The best article I have read about the mathematics within the framework of classical education (don’t miss this one!):
“The study of mathematics should instill in students an ever-increasing sense of wonder and awe at the profound way in which the world displays order, pattern, and relation. Mathematics is studied not because it is first useful and then beautiful, but because it reveals the beautiful order inherent in the cosmos.” (from The Education Plan of St. Jerome Classical School, Hyattsville, MD)
And
“The mathematics curriculum in a classical education will seek to promote the understanding of order and harmony in the universe. Mathematics, as a language, reveals this order and harmony, yet it should also be lifted from this concrete foundation and brought into the world of the abstract. The study of mathematics will engage this endeavor by training students in the context in which the discovery of its concepts arose as well as the reasoning which provides its structure. Although the study of mathematics has fallen well short of this purpose in modern times, its implementation will deepen a classical education.”
How to Teach Math Classically by Bill Carey:
Bill Carey on Math as A Humanities Subject (If you have the time, watch this video. The quality isn’t great, but the content is excellent!) This video was recorded before a group of high school students at a classical school and would be a fun one to share with your own students!
“[The universe] cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language.”
~ Galileo Galilei, 17th century professor of mathematics
“The world is God’s epistle written to mankind…It was written in mathematical letters.”
In 1955 Albert Einstein was asked to summarize his philosophy of physics at a lecture at Moscow University. In block letters he wrote on the blackboard:
“Physical laws should have mathematical beauty.”
And a quote from Beauty for Truth's Sake: On the Re-enchantment of Education by Stratford Caldecott, a deeply inspirational book that takes a look at the quadrivium (‘arithmetic being pure number, geometry number in space, music number in time, and astronomy number in both space and time’) and how God reveals Himself through these disciplines:
“Kepler’s breakthrough came because he introduced a “why?” question where the astronomers of his day didn’t see the need for one. He sought physical causes for heavenly motions. And that was not because he believed less in God as the cause of everything, but because he had more respect for the physical world as God’s creation and as the image of God’s mind. It was the first step toward Newton’s cosmos, in which the same universal laws (such as gravity) governed both the earth and the heavens.”
How did I miss those big ideas when I was in school? Oh, I think my schools subscribed to the philosophy that math = worksheets.
The problem, in our homeschool, though, is how to translate these big ideas into the systematic teaching of math skills—especially for a parent-teacher who understands (basic) math intuitively, but who finds teaching math (to a son for whom math does not come intuitively) tedious (and the cause of many emotional breakdowns, for both mother and son).
::For the sake of sanity and an intact parent-child relationship, we have employed Teaching Textbooks. This program is a God-send. The voice of an infinitely patient math tutor talks the student through each lesson with interactive problems on the computer. The lectures can be watched multiple times, or reviewed at any time.
The student then proceeds through a few practice problems and a series of graded problems for each lesson. Little “buddies” encourage the student as they progress through the lesson. Hints are often available, but the student can choose whether to listen to them (“Remember, if you are finding the difference, you will need to subtract.”). The student can choose to watch the problem being solved after he has entered an answer so that he can see where he went wrong (or right). The student gets immediate feedback. The student can often try a second time to solve the problem if he gets it wrong.
The student can view his grade book at any time to see what lessons or quizzes he has completed as well as his scores. The parent can view (or print) the student’s grade book at any time with a password-protected account. There a parent can also see exactly which problems were missed, how many tries a student took, and whether solutions were viewed. The parent can change the score for individual problems (for instance, if they go over the problem orally with the student) or delete scores so that a student can re-do problems or lessons.
TT is a spiral program—the skills are constantly reviewed. The first few levels have timed math fact drills in the form of a game show quiz. We purchase the workbook/textbook to go with the computer program so that we have a backup in case we need to work on math away from home, if a child would rather do the work on paper and then enter the problems, or if we have a computer malfunction.
TT ensures, for us, that systematic math instruction happens daily. We don’t have a specific schedule. Each of the boys works at his appropriate level and speed regardless of listed grade level. That means that one of my boys works on grade level, the other two boys work 1-3 levels ahead. I have had the boys complete just the quizzes until their grade drops below 90%, and then I have them do the lessons as well. If they score less than 90% on a lesson, I delete the scores for all of the missed problems and have them redo the problems. A parent could also sit with a student and teach the lesson from the workbook/textbook or monitor work as the student progresses through each lesson.
We also continue with TT during the summer to retain math skills. It might not happen quite as often, and we may take week-long breaks here and there. Continuing with math over the summer means that we either complete more than one level each year and/or supplement with other math programs for review and various styles of instruction and approach.
:: To complement our basic math program, the boys memorize basic math facts through Classical Conversations. The skip counting songs (1-15, squares, and cubes) were revolutionary for my son who does not easily memorize basic math facts. All three of my boys find multiplication a breeze. They also memorize basic conversions and measurements (teaspoons to tablespoons, liquid equivalents, linear equivalents), geometry formulas (area of rectangles, squares, triangles, and circles and circumference of a circle), and four basic mathematical laws (associative, commutative, distributive, and identity).
Levi also plays math games with his CC Essentials class each Monday.
:: To add in more challenging conceptual math instruction, Beast Academy has been a good choice. Unfortunately, only level 3 is available at the moment, but all of the boys have enjoyed reading through the full color comic-style teaching guide. They will be adding level 4 soon, so we’ll move onto that as soon as it is available. (Beast Academy is published by the makers of Art of Problem Solving, a conceptually challenging math program for older students. I may consider AoPS for Luke or Leif when they hit advanced math.) We use BA informally (surprise!). Luke uses the workbook when he needs a break from TT. All three boys read and re-read the guide for fun.
:: When we need a quick challenge, Balance Math (and other math/logic workbooks from The Critical Thinking Co.) makes kids think in creative ways to solve puzzles. These workbooks are perfect for a Friday or for taking along in the car.
:: I cannot fail to mention Life of Fred. Life of Fred is tops on my list for “spaghetti education” from a master who is passionate and imaginative in his approach to the subject. Stanley F. Schmidt, Ph.D. dedicates his books “Ad Majorem Dei Gloriam” (to the greater glory of God) in the tradition of J.S. Bach, and his books are like symphonies, albeit much more amusing. The Life of Fred books may not appeal to straight-forward, sequential, give-me-the-facts-and-let-me-do-it, worksheet-loving, no-nonsense kids (or parents). But for kids who love stories, ideas, and silliness, these are another God-send.
The author weaves mathematical ideas and problems into “real” life events, introduces students to very big concepts in a light-hearted you-will-love-this-when-you-get-to-calculus sort-of way, and has no qualms about discussing anything under the sun such as butterflies, Kansas, Christina Rossetti, fine art, healthy eating habits, the inventor of the first paper straw, constellations and the star Betelgeuse, English grammar (including the proper use of lay and lie), book signings, the German word for toenail, the definition of syncope (fainting), a campus newspaper, when to use single and double quotation marks, the definition of naissance and how it relates to Renaissance, the first letter of the Hebrew alphabet, classic literature (Moby Dick, Don Quixote), the history of pizza, Virgil’s Aeneid, and how to set the table—all in the second book in the Elementary series. Seriously.
We have all ten of the elementary books as well as Decimals & Percents and Fractions (the intermediate books are on my purchase list for this next year), and I can tell you they are among the most oft-read books at our house. They stand up to a great deal of wear and tear. Leif rarely goes a day without pouring over one or two or three. They delight and entertain. They show students that math is a joy.
:: The ipad has become a great learning tool at our house. We have a few favorite math apps.Sushi Monster Math is great for addition and multiplication facts. Chicken Coop Fractions is another good one. Dragon Box is a fantastic intuitive game that teaches algebraic concepts in a creative and non-math sort of way.
:: Levi and Luke like to do IXL Math on the computer. Kahn Academy is a phenomenal free online resource for all subjects, but the math instruction videos are particularly excellent. I’m certain we will be using them even more as the boys progress to more advanced concepts and skills.
:: The boys have watched the MathTacular videos over and over again. They are a little bit cheesy, but the boys love Justin. Throughout the series, he introduces all basic math concepts and skills from Kindergarten up through 9th grade.
:: And then we have books and more books. Many are history-related. Just spreading the feast, people.
Many of our science and math books overlap (such as The Story of Science series, which is excellent at communicating the joy and wonder of math, science, and history), so I’ll have more to share when I get to science…
For a variety of reasons, parents may wish for a rigorous core curriculum that is time-efficient and straightforward to implement. Possibly the integration of subjects (and exposure to more content material) will occur in travel, field-trips, child-led interests, wide-spread reading, and/or various hands-on activities. I personally believe it is wise to have a specific plan and method for the teaching of core skills, but the introduction to content can happen in many ways, particularly in the grammar stage.
Following are my top core skill curricula picks for elementary students:
:: Handwriting Without Tears—This is a solid handwriting program that works particularly well for children who struggle with handwriting. I’ve used Handwriting Without Tears for all three of my boys with great success. The workbooks make HWT easy to implement. The program begins with pre-writing instruction (my boys loved the wooden shapes and chalkboard) and goes through cursive instruction in late elementary.
:: All About Reading/ All About Spelling—I have a love-affair with All About Spelling (so much so that I signed up to be an affiliate). It is more teacher-intensive than some other spelling programs, but I believe so strongly in a solid grounding in phonics as well as the multi-sensory, mastery-based approach approach of AAS that it is my top recommendation. We are heading into level four, and I have nothing but praise for this program. All About Spelling instruction includes the memorization of phonograms and spelling rules as well as dictation of phrases and sentences and writing exercises. While there are many components to the program, the teacher’s manual is well-organized, clear, lightly scripted, and extremely easy to use—just open and go. A parent needs no additional instruction in the All About Spelling method. Lessons take just 15-20 minutes daily and can be customized for each child’s needs. There are seven levels to complete spelling instruction in the middle grades; the final level includes Latin and Greek roots.
I’ve approached reading instruction in various ways with my boys. If I feel the need to use a phonics program for Lola beyond my basic recommendations for the LeapFrog Letter and Word Factory DVDs and the incremental phonics readers by Nora Gaydos, I will be purchasing All About Reading. All About Spelling, however, may be all the formal phonics instruction needed. We’ll play it by ear.
::First Language Lessons for the Well-Trained Mind—Written by Jessie Wise, co-author of The Well-Trained Mind, First Language Lessons is a comprehensive yet gentle introduction to language arts for the elementary student. The program is simple to use and open-and-go. It is fully scripted for the parent who appreciates the hand-holding but can be easily customized for the parent who wishes to have a more natural dialogue with the student. First Language Lessons includes copywork (and later dictation), narration, memory work (in both English grammar and poetry selections), English grammar instruction, and picture study. The lessons are quite short and include a great deal of repetition for reinforcement and review (which can be easily skipped for the child who quickly grasps the memory work). Four levels are available for elementary students.
::The Complete Writer: Writing with Ease—Susan Wise Bauer makes writing instruction accessible for both parent and student. Bauer provides excerpts from excellent literature and non-fiction selections for narration and dictation material. The textbook gives a broad scope and sequence and how-to for grades 1-4, but the workbooks are invaluable for the time and effort they save the parent. Each workbook is a stand-alone program with parent instruction, literature passages, and workbook pages for the student. The overall text is great for understanding the big picture, but it is certainly not mandatory. My boys have loved the literature passages. Some are selections from books we have already read, and many selections have caused my boys to request the book for free-reading. Some parents may prefer to plan to schedule the books as read-alouds or assigned reading, rather than simply reading excerpts and moving on.
Parents using First Language Lessons for early elementary may find Writing With Ease to be redundant (particularly if doing the dictation with All About Spelling as well), but I would highly recommend the workbooks for upper elementary. The series continues in the middle grades with The Complete Writer: Writing With Skill.
::Teaching Textbooks Math—I adore Teaching Textbooks. Yes, I do. A complete (math 3 up to pre-calculus) computer-based math program. Independent. No paper. No mess. An infinitely patient math tutor. Silly little ‘buddies’ that give instant feedback. Interactive lessons. Automatically graded lessons. Opportunities for students to watch missed math problems worked through step-by-step. Math drills in the form of a game show. A grade book available for the student to see their progress and grades. A password-protected grade book where parents can see their student’s progress, including grades, which problems were missed, how many tries the student used (many problems have two tries available), and whether the student viewed the solution after missing a problem. AND a parent can change or delete scores so that a student can re-do a lesson or specific problems. No other math program is as easy to implement as Teaching Textbooks.
Teaching Textbooks begins with Math 3, but the first level begins with the basics of addition. Many 2nd graders should be able to work their way through Math 3 and continue to work a level ‘ahead’ of their grade level. I haven’t had enough experience with early elementary math instruction to give a seasoned recommendation. I used RightStart Math early on with Levi, and I think it is an excellent foundation in math instruction, but it is teacher intensive and has many different parts and pieces to organize and keep track of. Singapore Math works well for many families and is somewhat easier to implement.
Core content curricula:
:: The Story of the World: History for the Classical Child—Susan Wise Bauer has written an incredible, accessible world history series for elementary students. We are on our second round through the four volumes, and my boys adore them. They are written in an engaging narrative form, perfect for reading aloud. The books are also available on CD, which allows children to listen to the stories in the car or during quiet time. The corresponding activity guides are well-worth the investment. They include comprehension questions, sample narrations, book lists, a large range of activities, map work, and coloring pages.
:: Christian Kids Explore Science—This science series includes Biology, Earth and Space, Chemistry, and Physics. It is a basic, systematic introduction to science for elementary students, obviously from a Christian perspective. Written by a homeschooling mom, it is realistic in its scope and sequence as well as the implementation. It has narrative style lessons, vocabulary words and definitions in the margins, review questions at the end of each lesson, and coordinating hands-on activities (with more simple alternatives for younger children). Each unit also has wrap-up review questions. The appendix offers coloring pages, additional resource lists (books, science kits, biographies and list of notable scientists to research), and answer keys.
For a more professional, colorful, exciting, and non-faith-based (but faith-friendly) science curriculum that extends through the middle grades and into high school, I am very pleased with Real Science 4 Kids. Each program (Biology, Chemistry, Physics, and Astronomy) contains just ten chapters, so the books would work well either as short unit studies one per year or all four books as a two-year survey of science (one per semester). (Level 1 Geology is scheduled to be released in December.)
And More:
::Prima Latina—The study of Latin may sound intimidating, but Memoria Press materials make it a simple task. The program is easy to teach using the teacher’s manual and the CD, but the lessons are also available on DVD. Prima Latina is perfect for 2nd-4th grade students. Students can progress to Latina Christiana and then First Form Latin. Why study Latin? Read what Cheryl Lowe has to say here and here.
::Telling God's Story—I have greatly appreciated this Bible curriculum focused on Jesus: who he was, what he did, and what he taught. Each year, the books have 36 short lessons covering stories Jesus told, miracles Jesus did, teachings of Jesus, the Sermon on the Mount, Jesus’ early life, Jesus’ disciples, opposition to Jesus, and the end of Jesus’ life as well as three supplemental lessons on the crucifixion. The lessons contain background information for the parent, retellings of the Biblical passages, context information for the student, and life applications. The lessons are short and designed with elementary students in mind, but they are not childish and would be informative for and enjoyed by a larger range of ages. Highly recommended.
My boys and I have also read and re-read The Children's Illustrated Bible. I want my children to have a grasp of the chronological narrative of the Bible as the true story of the world, and this is a perfect introduction. It has beautiful, realistic colored-pencil drawings, background historical and cultural information, and many other visual elements including pictures of geographical areas, maps, artwork, artifacts, animals, people, and architecture. You can read more reviews here, but be sure to get the earlier, larger edition.
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This is a solid line-up of curricula, but it could all be scheduled in about 4 hours of concentrated lessons daily (less for early elementary, and possibly just 4 days weekly), leaving a good portion of time to be spent in other ways according to the needs of a student or the family.
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I would highly recommend adding the Classical Conversations Foundations program for 1st - 6th grade students. (The program starts as early as age 4.) One could either use CC Foundations as a ‘spine’ for history and science (using only the CC history and science cards, history and science encyclopedias, and possibly related picture books and DVDs at home during the week for context) OR use The Story of the World and Real Science 4 Kids programs, as well. The Latin and grammar memory work could serve as reinforcement for the core curricula, or a parent could choose to wait until 4th grade (or above for Latin) to add in formal lessons.
For 4th grade - 6th grade students, I would highly recommend the Classical Conversations Essentials program, which could replace all language arts curricula.
I wrote extensively about the Classical Conversations programs at this link here.
Was that simple? Or overwhelming? Let me know if you have any questions!
Next Up:
Mt. Hope Academy Curricula ~ History (The Tie That Binds)
:: From Beauty for Truth's Sake: On the Re-enchantment of Education by Stratford Caldecott (much more where this came from, but that will have to be a post in itself…):
No wonder students come to a college education expecting nothing more than a set of paper qualifications that will enable them to earn a decent salary. The idea that they might be there to grow as human beings, to be inducted into an ancient culture, to become somehow more than they are already, is alien to them. They expect instant answers, but they have no deep questions...The process of education requires us to become open, receptive, curious, and humble in the face of what we do not know. The world is a fabric woven of mysteries, and a mystery is a provocation to our humanity that cannot be dissolved by googling a few more bits of information.
:: Why Homeschooling is a Boon to a Liberal Society @ The Atlantic:
There is value in the public education system. Lots of intelligent, informed people have helped to shape its curriculum and norms. Consider their model with an open mind, and depart from it only after taking their claims seriously. And if you reach an informed conclusion that a different model is better, if that is your strong conviction, go out and be the change you want to see in the world. It may happen that you're right or wrong, but society as a whole requires people who challenge the prevailing system if it is to identify the few who can offer new insights.
Many of our popular stories are of individuals faced with the call to leadership and their struggle to accept that responsibility. It is our nature to seek and need leaders. What we often fail to see is that true leadership is, fundamentally, about service and sacrifice, not about position, power, or even education. In other words, true leaders are something other than mere figureheads or those giving commands. One does not need to command armies to be a leader, but one cannot be a leader without first being a servant.
From the apprenticeship: 5 faculties the successful teacher cultivates: 1. Attentive perception 2. Recollection (the ability to go into your mind and get what you are looking for) 3. Contemplation (the ability to compare) 4. Re-presentation (depends on skills cultivated without which a person cannot re-present the truth) 5. Imagination (that which fulfills the skills learned).
Good teachers possess a capacity for connectedness. They are able to weave a complex web of connections among themselves, their subjects, and their students so that students can learn to weave a world for themselves. The methods used by these weavers vary widely: Socratic dialogues, laboratory experiments, collaborative problem solving, creative chaos. The connections made by good teachers are not in their methods but in their hearts -- meaning heart in its ancient sense, as the place where intellect and emotion and spirit and will converge in the human self.
:: This is an excellent video of Andrew Kern (of CiRCE Institute) speaking on teaching literature. Some of my favorite take-aways:
‘Every single story by its nature is a morality tale. It is about someone who does something to overcome a problem. And the moral of the story is always contained in the ultimate final decision that the character makes to overcome that problem. So the question that opens up any story, whether it be a fable or James Joyce or Homer or whatever, the question to explore is, “Should he have done that?”’
Play with the frog, don’t pin it to the table.
Five topics of literature discussion:
What is that? What do you mean by that? What kind of thing is that? Topic of definition. How is that similar? How is different? Topic of comparison. What was happening at the time? (Topic of context?) Is it probable? Is it possible? (If it’s not possible, should he try anyway?) Topic of relations. Cause and effect. Topic of authority. Witnesses and judges. (First-hand accounts and experts.)
Two threats to homeschooling: moralizing and anxiety. Make homeschooling winsome not fearsome.
Teach from a state of rest.
:: Boy, howdy. That’s a challenge. But it brings to mind another quote from Beauty for Truth’s Sake (just this one last quote until I can do a full review post):
As we have seen, the “Liberal” Arts are precisely not “Servile” Arts that can be justified in terms of their immediate practical purpose. “The ‘liberality’ or ‘freedom’ of the Liberal Arts consist in their not being disposable for purposes, that they do not need to be legitimated by a social function, by being ‘work.’” …At the heart of any culture worthy of the name is not work but leisure, schole in Greek, a word that lies at the root of the English word “school.” At its highest, leisure is contemplation. It is an activity that is its own justification, the pure expression of what it is to be human. It is what we do. The “purpose” of the quadrivium was to prepare us to contemplate God in an ordered fashion, to take delight in the source of all truth, beauty, and goodness…"
:: Speaking again of Beauty for Truth’s Sake, did you listen to the conversation between Leigh Bortins and Andrew Kern that I linked last month? That interview left me hungry for more and ultimately led me to purchase the book by Stratford Caldecott, which was a delicious feast. My book is underlined and marked throughout. Both relate to the quadrivium: arithmetic (pure number), geometry (number in space), music (number in time), and astronomy (number in both space and time (or motion)), and then how those subjects reflect the nature of God. I don’t want to give away any more of the book as I will be reviewing it in a post of its own, but I did want to share a link to a second conversation between Leigh Bortins and James D. Nickel, author of Mathematics: Is God Silent? which addresses many of the same concepts.
:: Following the rabbit trail of the beauty of mathematics (there are three humorous, quirky videos in the series):
:: Okay, just for laughs, one more link @ The Risk of Education:
I know the links and quotes are a great deal to digest, and I’m not sure if anyone is interested in taking advantage of them, but it is handy to have a record of the information here for my own reference.
Classical Conversations (Cycle 3) Weeks 17-19 (One morning each week; includes social time and public speaking.) Faith: CC Memorizing John 1:1-7 (in Latin and English) The Children’s Illustrated Bible (reading together) Telling God's Story (Luke: weekly hymns on piano)
Math: Teaching Textbooks The Critical Thinking Co. math workbooks Khan Academy videos and practice Math-Whizz (online math) CC weekly memory work (skip counting/formulas/laws)
Science: Christian Kids Explore Chemistry (Read lessons 7-12 with oral review) CC weekly science memory work (chemistry) CC weekly science projects and experiments Borax crystals
P.E.: Swim Team practices (Levi), Swim Lessons (Luke and Leif)
Fine Arts: CC weekly famous artists and art projects Monthly Fine Arts Study (O’Keeffe, Holst, William Carlos Williams) A River of Words: The Story of William Carlos Williams by Jen Bryant William Carlos Williams (documentary video on YouTube) Georgia Rises: A Day in the Life of Georgia O’Keeffe by Kathryn Lasky My Name is Georgia: A Portrait by Jeanette Winter Georgia O’Keefffe: The “Wideness and Wonder” of Her World by Beverly Gherman (117 pp, Levi-IR) Great Women Artists: Georgia O’Keeffe (DVD)
Geography: CC U.S. geography (states, capitals, mountains, rivers, lakes, features, and more) Geography games (capitals, states, landscapes) Place the State online game Map drawing and 'blobbing' continents (CC) The Scrambled States of America by Laurie Keller
History/Literature/Historical Fiction: The Story of the World: Early Modern Times(chapters 29-37) CC weekly history memory work (American history) The Usborne Encyclopedia of World History(select pages, Luke) The Kingfisher History Encyclopedia(select pages, Levi) DK Children's Encyclopedia of American History (select pages) The American Story: 100 True Tales from American History by Jennifer Armstrong (Oliver Twist, North & South, DVDs, historical fiction, industrial revolution in England) Midnight Is a Place by Joan Aiken (historical fiction, industrial revolution in England, 287 pp, Levi-IR) The Bobbin Girl by Emily Arnold McCully (based on memoirs of a real mill girl of the 1830s) The Trailblazing Life of Daniel Boone: How Early Americans Took to the Road by Cheryl Harness Naya Nuki, Shoshoni Girl Who Ran by Kenneth Thomasma (Sacajawea, 175 pp, Levi-IR) Sacagawea and the Bravest Deed by Stephen Krensky Meriwether Lewis and William Clark: Explorers of the Louisiana Purchase by Richard Kozar How We Crossed the West: The Adventures of Lewis & Clark by Rosalyn Schanzer Lewis and Clark (In Their Own Words) by George Sullivan A Picture Book of Lewis and Clark by David A. Adler Sacajawea: The Journey West (Drawing America) by Elaine Raphael and Don Bolognese Lewis and Clark for Kids by Janis Herbert America: The Story of Us (Westward, Netflix Instant Streaming) Lewis and Clark: The Journey of the Corps of Discovery (Ken Burns, Netflix Instant Streaming) Mary Jemison, Indian Captive by Jeanne Lemonnier Gardner (historical account, 126 pp, Levi-IR) Tecumseh: Shooting Star of the Shawnee by Dwight Jon Zimmerman (117 pp, Levi-IR) Little House by Boston Bay (The Charlotte Years) by Melissa Wiley (historical fiction, 1814, 135 pp, Levi-IR) On Tide Mill Lane (The Charlotte Years) by Melissa Wiley (historical fiction, 258 pp, Levi-IR) Washington City is Burning by Harriette Gillem Robinet (historical fiction, War of 1812, 147 pp, Levi-IR) By the Dawn’s Early Light: The Story of the Star-Spangled Banner by Steven Kroll The Star-Spangled Banner illustrated by Peter Spier The Star-Spangled Secret by K.M. Kimball (historical fiction, War of 1812, 234 pp, Levi-IR) The Battle for St. Michaels by Emily Arnold McCully (War of 1812) Sisters of Scituate Light by Stephen Krensky (War of 1812) Napoleon: The Story of the Little Corporal by Robert Burleigh The Importance of Napoleon Bonaparte by Bob Carroll Simon Bolivar: The Liberator by Frank de Varona On the Pampas by Maria Cristina Brusca (Argentina) My Mama’s Little Ranch on the Pampas by Maria Cristina Brusca (Argentina) Gauchada by C. Drew Lamm (Argentina) Argentina, Peru, and Venezuela (Countries Around the World DVDs) Dragons in the Waters by Madeleine L’Engle (fiction w/references to Simon Bolivar and Venezuela, 326 pp, Levi-IR) African-Americans in the Thirteen Colonies by Deborah Kent Amos Fortune: Free Man by Elizabeth Yates (historical account, 181 pp, Levi-IR) Sojourner Truth (In Their Own Words) by Peter and Connie Roop (120 pp, Luke-IR) Sojourner Truth: Ain’t I a Woman? by Patricia C. McKissack (164 pp, Levi-IR) Words Set Me Free: The Story of Young Frederick Douglass by Lesa Cline-Ransome A Picture of Freedom: The Diary of Clotee, a Slave Girl by Patricia C. McKissack (Dear America, historical fiction, Levi-IR) Amistad: The Story of a Slave Ship by Patricia C. McKissack Amistad: A Long Road to Freedom by Walter Dean Myers A Voice of Her Own: The Story of Phillis Wheatley, Slave Poet by Kathryn Lasky Revolutionary Poet: A Story about Phillis Wheatley by Maryann N. Weidt The Underground Railroad by Raymond Bial Big Jabe by Jerdine Nolen The Talking Eggs by Robert D. San Souci Sweet Clara and the Freedom Quilt by Deborah Hopkinson The Talking Eggs (DVD, Rabbit Ears Storybook Collection) Amazing Grace (DVD) Shaka: King of the Zulus by Diane Stanley and Peter Vennema Ashanti to Zulu: African Traditions by Margaret Musgrove Saba: Under the Hyena’s Foot by Jane Kurtz (historical fiction, Ethiopia-1846, 207 pp, Levi-IR) Literature Study: Book Detectives (literary analysis book club) Oliver Twist (DVD) The Hound of the Baskervilles by Sir Arthur Conan Doyle (Levi-IR) The Extraordinary Cases of Sherlock Holmes by Sir Arthur Conan Doyle (Levi-IR) The Great Adventures of Sherlock Holmes by Sir Arthur Conan Doyle (Levi-IR) The Adventures of Sherlock Holmes (Classic Starts) Retold from the Sir Arthur Conan Doyle original (Luke-IR)
Levi’s Free Reading: The Door in the Hedge by Robin McKinley The Medusa Plot by Gordon Korman (The 39 Clues, Cahills vs. Vespers, book 1) A King’s Ransom by Jude Watson (The 39 Clues, Cahills vs. Vespers, book 2) Lots of easy books and re-reads (and historical fiction, listed above)
Luke’s Free Reading: Ralph S. Mouse by Beverly Cleary Mouse and the Motorcycle Runaway Ralph Lots of Diary of a Wimpy Kid series Henry and the Clubhouse by Beverly Cleary Lots of re-reads
Leif’s Free Reading: Homer Price by Robert McCloskey! Lots of Magic Tree House and Diary of a Wimpy Kid Flat Stanley books The Magic Finger by Roald Dahl
Life is chaotic. Our ‘routine’ is chaotic. There isn’t enough of me to get it all done. And yet…
I’m having a complete, THIS IS IT moment when it comes to homeschooling. Our subjects, resources, materials, and lessons are synchronizing in the most awesome sort of way.
I shared our 2010-2011 homeschooling plans a few weeks ago, but I’d like to share more (okay, a lot of) details and review a few of my curriculum choices. Sorry about my tendency to go on and on! I’ve divided this into at least two posts so that it isn’t overwhelming.
First of all, Classical Conversations: I could not have guessed how perfect CC would be for us this year. Yes, it was a challenge getting us all there with smiles on Monday mornings (especially being 9 months pregnant, and then having a baby during week 3, and crazy illnesses during the first two months). Yes, my boys had to adjust to being in a class (which may have been more stressful each week for me than it was for them).
BUT, it was positively an anchor for us this year. The boys loved class and were always enthusiastic. Having all three boys learning the same material made review during our week a very unifying experience for them. The boys were very possessive of their individual teachers and classmates, which gave them a bit of autonomy. The relationships we all made are priceless.
The memory work took on a life of its own as it initiated discussions, ‘aha’ moments, and deeper learning. It has also woven its way (sometimes quite unexpectedly) through our lessons and life. Looking at the pages of facts and ideas that we have committed to memory and now have as ‘pegs’ on which to hang further information and ideas, I am astounded. I have experience over and over with the boys that it truly works. When they can relate something they have already learned or memorized, more information sticks easily, and the boys show greater interest. It has also given us all a beautiful sense of achievement.
Secondly, Teaching Textbooks: Math used to be my greatest struggle. I LOVED RightStart Math. I think it gives children an incredible foundation in math. But it is also very time- and teacher-intensive, with lots of little parts and pieces. If it isn’t getting done, it isn’t the right thing. We started working through Singapore workbooks, and then I realized that Teaching Textbooks was available starting with 3rd grade! This has revolutionized and renewed our math studies.
The program is extremely child-friendly. Each lesson has an audio-visual and interactive lecture (which can be viewed as many times as needed), then the child completes a series of problems (both new concepts and review) one at a time. The child may make two attempts at each problem with instant feed-back. Often, the child can click on their little ‘buddy’ for a hint. After answering the problem, the child may click to see the worked solution. (There are sample lessons at the above link.)
There are chapter quizzes and bonus rounds (speed drills) in the form of a ‘game show.’ The program features an online grade book that is accessible to the child. The parent also has access to the grade book. Parents can see exactly how many problems were completed, how many were correct, how many attempts were made, and the percentage score for each lesson. Any scores can be edited or deleted, so that the child may repeat a problem or a lesson if needed. (Parents have a separate password, so a child can only view their scores.)
Math 3 starts out very basic (my boys did more than one lesson a day in the beginning) but increases in difficulty rather quickly. It has been said that the program is not considered a rigorous math program, and that it is lacking in conceptual math. I say, if it gets done daily, if it covers all of the math concepts and skills with constant review, if students respond well to the program, if math is no longer a struggle, if the students are finally understanding math and progressing steadily, then it is a huge success. And it is for us.
Both Luke and Levi started with Math 3 in March. Levi has struggled with math in the past, but he should have no problem completing Math 3 by September and moving on to Math 4. Math comes more easily for Luke, and he, too, has done really well with Math 3. He may plateau at some point, but I suspect he will work at least a grade ahead with TT. I think that is the key for any program. Ignore pre-conceived levels. Make sure your child is working at a level (and pace) at which he or she can comprehend the material, progress, and be challenged.
Because the boys can do their math lessons in a reasonable time frame with complete independence, it is now on the every. day. list (even on the weekends and during summer) along with brushing their teeth, emptying the dishwasher, reading, and piano practice. It’s just a fact of life. This means that the boys will complete more than one level of math in a year. Instead of moving on to the next level in TT, which they may not be ready for academically, we are supplementing with Singapore Math workbooks for a more conceptual, rigorous approach as well as Mathematical Reasoning workbooks from Critical Thinking and Life of Fred after completing TT4.
(The boys have also memorized skip counting up to the 15s, squares, cubes, measurements, formulas, and laws with Classical Conversations. This information repeats every year, so once they have it completely memorized, I may add my own list of math memory work.)
We are currently attempting to learn to play the tin whistle (along with music theory) in our Classical Conversations classes. This is a wonderful way to introduce children to an instrument. Not only is a tin whistle an instrument that is used in orchestras, it has smaller holes than the recorder (making it easier for little fingers), is simple to play, is inexpensive, and takes up very little space.
One of the boys' CC tutors shared this incredible website with video tutorials and sheet music, everything you need to begin playing the tin whistle! No more excuses for not learning an instrument!
Speaking of music theory, Making Music Fun is a treasure-load of free printables. Check out these free music theory worksheets. I love the composer biographies and free sheet music. (We printed out a very simple version of Bach's Musette in D for this month's composer studies.) We also used the It All Adds Up! free rhythm worksheets to switch up our math review for a day or two. (Scroll down to the bottom of the music theory worksheets page.)
Which leads us to math. I've been using math-drills.com for our (free) easy-to-implement math review worksheets the last few weeks. Check out the index at the top of the page. There are over 6000 free printable worksheets (with answer keys!). Nice.
Our next core subject is Mathematics. I chose RightStart Mathafter a long deliberation. There are so many math programs available, and I had no desire to jump around from program to program trying to find the best fit.
The Well-Trained Mind recommends Saxon Math. I chose not to use this program because my niece (very similar in personality to Levi) struggled with Saxon (and math in general). I looked at Horizons Math which would have suited my learning style as a child and teaching style as an adult, but decided against a workbook-style program.
In the end, I chose RightStart Math for its ability to introduce math concepts in a variety of ways (visual, tactile, auditory) with little writing in the beginning stages. (I started Levi with RightStart A when he was four and not yet writing.) In general, I liked the RightStart approach and learning goals, feeling that it would best give Levi (and his brothers) a strong start in math.
The emphasis on groupings of five, both with tally sticks and beads on the abacus is brilliant. The math games make learning fun. The variety of manipulatives is terrific. Lessons are scripted (they tell you exactly what to do and say). Each lesson lists objectives, materials needed, warm-up, and activities. RightStart is teacher-intensive, which is fine with me as Levi does not do math well independently.
Planning is straight-forward. You decided how quickly you want to move through the program, plan a certain number of weekly lessons accordingly, schedule time to do math (plan extra time for catch-up, math games, and review), and spend time at the beginning of each week to look over the lessons and set aside materials that you will need.
Having a copier available is necessary for reproducing worksheets and other patterns, etc. from the spiral-bound lesson book.
Here is where I admit that math is the toughest subject for me to maintain consistency in. We are only half way through Level B (first grade), which technically is right on target for Levi's age, but I had hoped to finish the book by this time.
Math takes complete focus for both Levi and myself, more than any other subject. It also requires that we have the materials out and ready. Both Leif and Luke are incredibly distracting, and Luke begs to do math with us.
Lately, I've been working on making math our priority. My mom has been watching Leif a couple afternoons each week, so that is an incredible help. I also gathered all our supplies into a 'mobile math' bin, so that it is easy to grab and take to the table.
Luke usually sits on my lap and listens in, as well as being my partner in any math games. It is his favorite subject. I desperately need to get out Level A and start at the beginning with him (I want him to have the correct foundation, and he will pick it up quickly), but I will wait until Levi and I have found our math groove. (Any math updates will be posted with the Math label.)
