Seventh Grade: Plans for 2013/2014

School is underway for my seventh grader (whatever that means when you homeschool), now twelve. As I write, he’s working on math, and once that’s done, he needs to spend time on a project for an online class. Our early start wasn’t my choosing, but since his online classes started last week and he does better when occupied, here we are.

Math (mean, median, and mode today) picks up where we left off in the Spring. Rabbit trails, anxiety, and a textbook switch means he’s still a few chapters short of finishing Singapore’s Discovering Mathematics 7B (Common Core edition).This seriesweaves algebra, geometry, trigonometry, and miscellaneous math topics across four years of texts, meaning that we’re likely trapped in this series of four books until we see our way to the other side. That’s fine, Singapore has served us well for many years, and we’re both happy while he’s learning.

Biology is our science this semester, and I’m thrilled. I’ve spent weeks reworking the high school level biology course I used for his brother and a friend when they were technically in  seventh grade. (Syllabus here.) Centered around Exploring the Way Life Works (Hoagland) and Biology: Concepts and Connections (Campbell), this is a rigorous study with plenty of labs, reading, and writing, as well as explicit teaching of note taking skills.We have two weeks before our first class, and I can’t wait.

Much of my twelve year old’s learning is online this semester. He’s taking two classes from Online G3, an impressively taught source of real-time classes for younger learners ready for big ideas and dialogue. He’ll take Current Events, where a portion of each session is in the hands of a student who takes fifteen minutes to present on an event he or she finds interesting. (My younger son is taking on Common Core and presents next week. That should be interesting.) Also from G3, he’s studying Shakespeare’s Comedies, a high school level literature course using Lightening Literature’s text by the same name. For second semester, he’s hoping to take Shakespeare’s Tragedies and perhaps British Literature. My children couldn’t be more different.

New this year is Latin. We played with Latin in the spring, using Linney’s Getting Started with Latin, which provided a gentle introduction to the language. He’s enrolled in Lone Pine Classical School’s Latin 100, an intense course requiring strong study skills. What he does not have now he’ll hopefully develop along the way without too much drama or trauma for either one of us. He’s also plotting his language learning course, debating the benefits of four years of one language then two of another versus two years each of three different language. That’s my child. Planning years ahead when there is absolutely no need.

NaNoWriMo (National Novel Writing Month — write a novel in a month) will keep him busy come November, although he’s not decided on a word count goal. He’s participated two other years, with a published book coming out of his first experience. While I love his dedication to the project and accompanying word goal (25,000 this year, he says), it does take a good-sized chunk out of each day. Our only flexible point this semester is math, so we’ll likely take a break from that for November. He’s not complaining.

Social skills are my hidden agenda for him. Asperger’s doesn’t go away with age, and he’s struggling more again as he approaches his teens. There is more to miss, more subtext, and more to feel anxious about. We’ve not had an easy time, and I’ll admit that homeschooling has buffered us from not just the perils he’d face at school but  also made me a bit complacent about his lagging social skills. He has good friends who accept him as is. I’m grateful. But he needs some assistance in the everyday sorts of relations: small talk, meeting new people, even emailing a friend. So we’ll be hitting these harder at home and enrolling in a live class for homeschooling  middle-schoolers, Jury Trial. He adores the topic, and I’m glad to have him try some of those skills in a live classroom. We’ll see how it goes.

His extracurriculars remain the same: fencing with Salle d’Etroit  and piano with a private instructor. He makes slow but steady process in both. Neither come naturally to him, and I’m some mix of pleased and surprised that he’s not daunted by that. As he says, he’s not sure where his body is in space. He simply can’t feel it, and both endeavors are far easier for those who have access to that internal wisdom. I hold my breath when he struggles over and over with each, hoping he’ll stick with it despite the struggles. That can be hard for gifted folks. When so much comes so easily, persevering in what doesn’t (fencing, piano, social skills), takes a good deal of sense of self outside of one’s natural intelligence. I admire his persistence.

Reading through our plans, I realize my role is gradually shifting from teacher to facilitator. This didn’t happen with my older son until tenth grade, when he started dual enrollment courses and a few online classes. I can’t say I mind, since my younger definitely does well learning online, and the options for that mode of learning expand by the day, but it does remind me that we are closer to the end of our homeschooling journey, which started nine and a half years back, than the beginning. As I somewhat reluctantly look at our schedules and the waning days of August, I find that a bit of a relief.


Nearing The Half: Curriculum Keepers and Changes

We’re closing in on the end of the semester. My older has finals for two of his courses in two weeks, with the rest of the term ending in three. While we caught a breath at Thanksgiving break, it was not the idyllic week of rest I envisioned. How could it be, with classes going through Tuesday night, past when company arrived? The following five days were a flurry of cooking and eating followed by a few too-short days of respite from a semester that started at the end of July.

Yes, I’m tired. Tired, with a to-do list that grows by the minute, urgency growing on numerous items. I’m longing for more evenings where no one needs to go anywhere and just a few weekends where, “What do you have for homework?” doesn’t escape my lips. Fortunately, a break is coming, and the second semester is set. Here’s what we’ll be doing for Winter 2012

A.D. (15)

Classes at a local university are going well — astonishingly well, given my doubt three months back. My son doesn’t seem as surprised, but he is pleased. Despite a few hiccups and a resulting rapid revision of study habits, he’s pulling good grades in both his Sign Language class (our answer to a foreign language, and the first of four semesters) and Calculus I. He’ll move on to the next in both come January, with more of the series the following semester. I do like predictability and pattern.

He’ll add a third college-level class, PC Troubleshooting and Repair, come January. After building his own computer with a neighbor and fiddling with it endlessly on his own, he’s itching to know more about the innards of those machines. Now, I get antsy at the suggestion of even opening the case of any computer, sure that my mere presence will frighten the workings of the thing into an eternal black screen of death. I’m limited outside the box as well, having a few quick fixes at my fingertips but quickly phoning a more capable friend (or more recently my son) when something goes awry on the screen. While this isn’t a class with credits likely to transfer to a university some day, it could lead to the ability to perform some helpful work around this house and the homes of others. I’m enthused, as is he.

Personal Finance (Dave Ramsey), taken with a handful of friends, continues until early spring. Initially, he was certain this course had nothing to offer him, a sure sign to me that he very much did need some financial education. A few months in, he’s enjoying himself and appreciating the information. (Since I’ve not been watching the lectures, I can’t give a full review of the curriculum. Ramsey is entertaining to watch although overly optimistic about saving rates and investment returns. Watch this series with a post-2007 reality check from a well-grounded adult.)

Piano continues, albeit with a new instructor. I’ve shared our piano woes here before (Piano Lessons), and we’ve learned a good deal about the importance of chemistry between music teacher and student as well as the necessity of teens to set their own musical course. I’m optimistic, as is he. (A full post on music education will follow).

Physics, taught by me to my son and his friend, continues as well. We’ve finished our tour of mechanics and have moved on to sound. Next semester takes us to light, magnetism, electronics, fluids, heat, and quantum physics. I have quite a bit to learn. Our original goal was the SAT Physics Subject Test, but I’ve not looked at where we are on that road in some time. Add that to my very long list.

Ironic as it may be, I’m farming out writing instruction to a tutor. It seems teaching writing to one’s own teen isn’t always effective or desirable. Now, as a source of some of my income, I rely on that fact, but it took me until now to act on it at home. So my older is looking forward to ten assignments spread over 20 weeks, all lead by someone who is Not Mom. I’m smiling, too.

A.B. (11 years old)

My younger son will enter his fifth semester with Online G3, lead by the brave and nearly saintly Jamie Smith. With an assortment of gifted kids in the 8 (or younger) to 13 (or older) age group, he’ll take three classes. Magic Lens/Word Within the Word 2B continues his trip through Michael Clay Thompson’s books by the same name. Aside from adding weekly vocabulary quizzes and reviewing the new stems and words with him, he’s independent in this class. American Literature will round out his Language Arts study, carrying him through Huck Finn, Uncle Tom’s Cabin, Red Badge of Courage, and Call of the Wild. The accompanying text is from Lightening Literature, a series with which we’re familiar. Finally, he’ll take Government. He’s been prepping for months, if one considers his immersion into the election and regular (guided) watching of The West Wing. Jamie, beware.

Math will continue as before, with the goal of finishing Discovering Mathematics 1A and 1B (or 7A and 7B, as the new editions are labelled). Well, unless we’re distracted by other math. An interest of trigonometry will return us to Challenge Math after our current chapter in Discovering Mathematics. I’m in favor of side roads on this journey.

Physical Science (CPO Middle School series) continues, and we’re adding a third young person to our studies come January. Overall, the book is serving us well, and we’re progressing through at a reasonable rate with rather impressive retention. I’ll review this more thoroughly a bit later.

New to the schedule will be Latin with The Pericles Group. This is Latin via video game  (practomime), and he’s enthused. I’m interested to see how much he actually learns. It’s recommended for ages 12 and up and requires a good amount motivation and initiative to be worthwhile, says the creator and Latin teacher. My younger son doesn’t lack either, so I’m betting he’ll be fine. When we know more, I’ll report it here.

His Coursera World History class is winding down, and he’s done a fine job keeping up with 750-word essays, challenging readings, and over two hours of lectures a week. We’ve just started a Coursera class on argumentation, and while I’m not sure we’ll take all the quizzes or make it through all the assignments (which walk right through the two weeks when  I don’t want to discuss homework), so far the lectures are interesting and even amusing. The wisdom of placing a naturally argumentative child and his mother into an argumentation class is not open for debate.

Piano and fencing round out his schedule. He’s happy with his piano teacher of the last four years, and he steadily progresses.  He’s also quite satisfied with his with his fencing coach and venue, feeling accepted and challenged. He’s started to enter local tournaments, fencing foil at the  under 12 level. He loves it, and he’s gradually gaining skill.

Those are the plans. We’ll see what really happens. My older son thrives on the greater challenge and demands from his college-level coursework. My younger continues to do well whether I’m in charge or someone else is, although his schedule is heavy on outside courses this semester. Everyone, myself included, is learning. And perhaps just as important, everyone is feeling successful and happy. Sounds like a fine start to second semester.

Review: Discovering Mathematics (Singapore Math, Secondary Level)

Note: Since beginning Discovering Mathematics, Singapore Math has released a new edition, Discovering Mathematics Common Core. The order of lessons vary a bit, and new topics have been included. At this writing, only a few levels are available. We tried the new ones, and they are fine, but as they’ve been slow to release, we’re still working through the earlier series. The differences are slight, with changes in order and a few additions being the bulk of what varies from the old to the new. 

Providing a challenging mathematics education was one of the key reasons we started homeschooling. Deeply disappointed by the depth of the math provided by two schools, my older son, then seven, assumed he was the problem.

“I don’t think I’ve very smart, Mom,” he told me.

“Why not?” I inquired.

“Because they don’t give me anything hard to do,” came his sad reply.

Math (and science) were his loves at age 4 and 5 in Montessori and while at home. He was appropriately challenged in the first at school and free to explore the second at home. First grade ended all that, where math became repetition of previously mastered lessons. Second grade, at our local gifted and talented public school, it was nonexistent  which was because, we were informed, he knew all the material for that year already.

So once home, math took a starring role. Singapore Math quickly became our preferred curriculum (reviewed here) for the elementary sequence. Even doing the Challenging Word Problem books, we burned through it quickly. Almost 10, my older insisted on Algebra, so we started the standard sequence, happily making our way through a fine text, Jacobs’ Algebra. (reviewed here).

When my younger finished 6B, I wondered if there was another way. We vamped for much of last year, working through a variety of books while choosing our next course of action. After much consideration, we decided to stay with Singapore, specifically, their Discovering Mathematics series. This four-year series is designed to cover some prealgebra, algebra (I and II), geometry, and a smattering of other topics, like probability and counting. Unlike most American programs, these topics are interwoven throughout the years, with chapters on algebra followed by chapters on geometry with a side trip to data handling. It’s challenging, with plenty of problems, tests with answers, and teacher’s support books if needed.

But I hesitated. Accustomed to the four-year math sequence I’d known as a child and that my older son had followed, I was hesitant to commit to a different path. What if we didn’t like it after a year? What then? (Answer: Start a traditional Algebra program and compact or test out of what has already been covered. Ditto the next year with Geometry.) I presented my younger son, then 10, with the options. Singapore, Jacobs, or Art of Problem Solving? He looked at samples of all online and liked the familiarity of the Singapore. Thus, we reached a decision.

We’ve not been disappointed. We started Discovering Mathematics 1A soon after it arrived and found that while it certainly felt like the Singapore Math we’d enjoyed the previous years, it was a step up in challenge and pace. He’s enjoying it, but we don’t whip through the pages as we did at the elementary level. Concepts aren’t broken down in such small parts, and even the sample problems (Try This!) are fairly challenging. Fortunately, this increase in challenge has resulted in an increase of effort. As a result, he’s feeling rather accomplished while learning large amounts.

At the minimum, the user will need to purchase two textbooks for the year. These paperbacks are affordable and reusable, in keeping with Singapore Math’s reputation for affordability.   Each of the four levels requires two textbooks, each generally over 200 pages long. The year is broken up into 11 to 17 chapters, roughly evenly divided between the two books. (The fourth level is shorter, with a significant proportion of 4B dedicated to review tests, similar to the elementary level 6B.)

The chapters are broken up into shorter sections, some amenable to a single lesson or day of work, others requiring multiple days, given the depth of the lessons. Each section ends with problems in four categories: Basic Practice (the easiest problems), Further Practice (definitely a bit more work), Maths@Work (word problems just as challenging as the aptly named Challenging Word Problems of the elementary series), and Brainworks (sometimes too hard for Mom but worth trying if no one is crying). The so-called Revision Exercise (test) at the end of each chapter is at the level of the Further Practice and Maths@Work level. Aside from the Brainworks problems, all the answers for the problems are in the back of the book. If you desire worked solutions (and so far, I’m good without), there are Teacher’s Guides available, which include other teaching assistance, activities, and a breakdown of lessons and timing.

An additional workbook is available for each level, providing some extra practice as well as more problems at the more challenging level. Unlike the traditional workbook, these don’t provide a place to do the problems, making them more of a reusable problem bank. I assign some of these at the end of each chapter, before the revision (test). The number I assign depends on how well he’s handling the material — some sections just require more practice than others. Generally, these workbook problems are more challenging than the textbook ones. They are broken down into sections called Basic Practice, Further Practice (both a bit more involved than the same-named section in the text, it seems), Challenging Practice (and it generally lives up to its name), and Enrichment (excellent problems that we don’t get to most of the time). As with the text, answers are in the back, but solutions require the Teacher’s Edition of the workbook. I’d strongly suggest the workbook to supplement all learners, with the Teacher’s Edition on the shelf if a parent is a bit math wary and wants guidance on the trickier problems.

The strengths of the elementary level of Singapore Math continue at the secondary level. The pace is swift, which is excellent for the mathematically talented child but could be overwhelming for others. The problems in the text at the secondary level are far more challenging that what is in the workbooks for the elementary level, but on par with the Challenging Word Problems books. (I’ve not used the Intensive Practice books at the elementary level, which are designed to increase the challenge at their respective levels.) The depth we’ve encountered thus far is also impressive. Math is not taught via algorithm but by deep understanding, which, in my opinion, is by far the superior method. It is applied, not simply in one-step word problems, but across the sciences and into the work world. Math lives in these books, with all its complexity and beauty there for the learning.

The downside to the Discovering Mathematics series? If one isn’t math-comfortable, these could be a challenge to teach. That said, for the math-uncomfortable, these are an excellent way to build a new relationship with math. I know that throughout teaching even the elementary level of Singapore Math to my boys, this math-comfortable mom moved from number capable to number savvy. I’ve said before that I believe that math is best taught rather than learned solo. Discussion is part of the process, and many times, I’ve had a child teach me and correct me, thus delighting the child and enlightening me. (For more on thoughts about strong mathematics programs, read my post, Math Matters.)

We’re early in our exploration of this four-level series, and I’ll post again as we move through the program. I’m hoping we continue to enjoy Discovering Mathematics over the next several years, allowing us continuity with a strong mathematics educational program.

As always, I only review what we’ve used, and I never accept compensation of materials or money for my reviews. 

Math Matters: A Response to “Is Algebra Necessary?”

Math has taken another hit. This time, it’s from Andrew Hacker, emeritus professor of political science at Queens College, City of New York, whose piece “Is Algebra Necessary?” appeared in the July 28, 2012, New York Times Opinion section. His premise is that since so many kids and adults find math hard, it just shouldn’t be required. Or at least, they shouldn’t be subjected to the algebra, geometry, more algebra, calculus sequence that had been the US math sequence for so long.

Here’s Hacker’s initial thesis: “Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower.” His support rests on statistics of high school dropout rates (75% of ninth graders complete high school) and the role he sees algebra playing in that rate. I have no doubt algebra is a serious stumbling block for many students.  Does this mean we should toss it out and teach calculating the Consumer Price Index instead, as Hacker suggests? No, although some shift in how we educate our children in math is definitely in order.

First, let’s clarify our terms. Arithmetic is what you were taught before algebra, at least in most schools and certainly what you experienced in grade school if you’re now in your 40s. Addition, subtraction, multiplication, and division (including that long kind Hacker says is essential). Fractions, decimals, and percents appear, with a nod to generally single-step word problems for application. Arithmetic is number-crunching. It can be taught with algorithms and tricks or deep conceptual understanding, although it’s too often taught the former way rather than the latter.

Arithmetic is not mathematics. Math is problem solving and reasoning, relying less on rules and more on understanding the way numbers and geometry works. Math uses those skills in arithmetic to problem-solve and reason, but not all arithmetic needs to be in place before math is taught. In fact, the best arithmetic teaching puts math at its heart.

It’s been said that arithmetic is to math as spelling is to writing. You’d not mistake a great speller for a fine writer, and while a fine writer should produce a product with conventional spelling, one must not wait to spell all the words one could ever want to use in order to start writing. We teach our kids to write before they can spell well, allowing both to develop together.  The same relationship can and should exist between arithmetic and math.

Math matters. Like it or not, some degree of math comfort and skill is mandatory for full participation in today’s world. A sound mathematical education opens doors into the STEM jobs that increase in number by the day. A good understanding of numbers makes economics, politics, and social science more accessible.  It allows people to understand credit, mortgages, taxes, and savings.  If we drop our current math requirements in high school, shifting them to simply consumer math, as it was called in my high school years, we vastly under-prepare our children for the options ahead.

Hacker agrees that math matters.

Quantitative literacy clearly is useful in weighing all manner of public policies, from the Affordable Care Act, to the costs and benefits of environmental regulation, to the impact of climate change. Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship. What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey. (Hacker)

But then he backpedals, wondering why we subject our “potential poets and philosophers” to the traditional math sequence rather than nurturing their talents. My answer is because we really don’t know at 14 what path many kids will choose. We need to prepare them for more options that whatever their fancy of the week may be. I agree with Hacker’s assessment that today’s math path is likely outdated. I’d prefer to see more integrated math, weaving algebra and geometry together and focusing on applications across the disciplines.

What Hacker fails to address is the why behind the algebra fear and failure at the high school a college level. Early elementary math matters, whether at home or at school. Math (or actually arithmetic) taught as rote memorization with no deeper applications is like teaching spelling without writing, scales without true music, or love via self-help manual rather than personal experience. It deadens math. Kids aren’t born fearing and hating math. Aversions to math are learned, often from those teaching them math. Hacker spreads this sense of math as too hard in his final paragraph: “This of math as a huge boulder we make everyone pull, without assessing what all this pain achieves.”

What if, from the start, we taught our children to look at math with wonder. What if we nixed the “drill and kill” and senseless algorithms in favor of teaching actual math. I picked Singapore Math for a reason (reviewed here). It teaches math along with the arithmetic. The whys of the processes are right there, and the word problems (especially those from the Challenging Word Problem series) demand complex problem solving. There’s no waiting until algebra to think in math fluently. It starts in the first books. Singapore isn’t alone in this process. The arithmetic my sons learned at age 4 and 5 in Montessori was rooted in deep understanding of how the numbers work. Heavily manipulative-based and backed my a masterful teacher, they learned WHY regrouping works for subtraction and what is truly going on in long multiplication problems. (Note: Manipulatives are not the key here. The key is excellent instruction about the concepts paired with judicious use of manipulatives, followed by transitioning to abstract work without those hands-on items.)

Curriculum matters. What matters more is teachers (parents of homeschoolers, that’s you or whomever to entrust your children to for their math education). The best curriculum in the world won’t teach mathematical thinking if the educator is uncomfortable with the subject matter. Hacker’s treatise focuses on high school mathematics education, but he’s focusing on the wrong end. Those math teachers went into teaching to teach math, a subject they likely deeply appreciate and understand. But what about our elementary kids, at home or at school? While I know there are exceptions, I sense the comfort level with math (not arithmetic by algorithm) isn’t high for many elementary teachers, and I know it’s not present for many parents. (That’s why Saxon sells so well. It’s easy to use, highly scripted, and able to be turned over entirely to the kids early. And it’s arithmetic. Not math.)

So what to do? If you’re a homeschooling parent, find a curriculum that supports deep mathematical thinking. If you kids are young, rejoice. You can easily learn along with them. Singapore Math and Mammoth Math are fine elementary programs. Art of Problem Solving offers excellent texts for the set ready for pre-algebra and beyond, and Singapore has an integrated math progression for the post-elementary level. Too intimidating? Consider adding in supplemental math into your existing arithmetic program (see list below). Anything that demonstrates the wonder of math over the tedium works toward supporting young learners of math.

Hacker makes a few good points. Teaching more practical mathematics in high school makes sense. Not everyone will choose a path that requires calculus, and that’s fine. But rerouting the mathematical train before algebra is begun seems foolhardy and shortsighted. At 14, the age many American children face algebra (and I’d argue that’s way too late for math to truly begin), we don’t allow kids to drive, vote, sign a contract, or work most jobs. I’d add to that list we shouldn’t allow them to limit their career options by opting out of algebra either. Instead we should be making math meaningful during the elementary years rather than simply teaching rote arithmetic skills while bemoaning how hard math is. As parents and teachers, we can emphasize the utility of math and encourage deeper mathematical thinking skills, both by curriculum choice and in supplementary reading and discussion. We should not abandon algebra nor the rest of higher math. Rather we should provide proper support from the start to make that math not only possible to do but delightful to explore.

More reading on mathematics education:

Supplementary resources for all ages:

Review: Algebra Survival Guide

I recently posted a list of options for math beyond Singapore 6B. My younger, 10, finished that milestone a few months back, and I gave him some choice of what to pursue next. He selected The Algebra Survival Guide and The Algebra Survival Guide Workbook, understanding that they would not be a substitute for a full Algebra class but rather serve as an introduction. He agreed to that condition, so we began about two months ago. He was thrilled. I was satisfied. That’s about as good as it gets around here.

The Algebra Survival Guide, by Josh Rappaport, contains 12 chapters of largely pre-algebra topics. Broken down into bite-sized morsels, Rappaport explores mathematical properties, negative numbers, orders of operation, absolute value, exponents, radicals, and factoring. All those subjects are taught with variables and real numbers, but the real “algebra” part of the book doesn’t begin until halfway through the book, when he addresses factoring polynomials before moving on to canceling, equations, coordinate planes, and finally (though briefly) word problems.

For the most part, the Algebra Survival Guide breaks up those first concepts into page-long mini-lessons. Generally, the pages go beyond the “how to do this” and introduce why a property or process works. I like this. While there are times where memorization is a must, I’d rather math be deeply understood and utterly reproducible by one’s own mind and hand. Understanding how math works allows a person to do this. It’s a bit early to see if this understanding will stick,and he’s moderately mathematically intuitive, so I don’t know how much to attribute to the methods in the book, but I can say with certainty that this book does more than introduce rules to memorize.

Ironically, the book is also rule-heavy. In the process of breaking topics down into rather small parts, the author creates more rules than I recall from teaching my older son the same material in Jacobs’ Algebra.  In the section on negative numbers, these rules became burdensome, so we simply skipped those sections and moved on, after assuring he could do the problems themselves. The rules were actually a barrier to his intuition, so away they went. For a child struggling, these might be helpful and support understanding, but for my son, they got in the way.

What’s missing is the why of algebra. Until the final chapter on word problems, there is not a single example or explanation as to why anyone would bother moving all these numbers and variable around.  We stopped using the book near the end of the factoring section. I’d been growing restless with the teaching of technique in a vacuum, but he was progressing well and learning a good deal of the pre-algebra that Singapore Elementary Mathematics lacked (and saves for the secondary levels). Midway through a lesson on factoring polynomials, he asked the question: “Why would I do this?” With all the book had taught, there had not yet been one equation to solve, one word problem to ponder, or even one substitution of a number for a variable to consider. The “why” was missing.

I went to a bookshelf and pulled out Jacobs’ Algebra and searched for the section on factoring polynomials. We read through an example about a human cannonball’s trajectory. We talked for a while, and I realized that we needed to move back to math with context. He agreed readily, and we returned the Algebra Survival Guide to the shelf. Later that day, we ordered the first set of Singapore’s Discovering Mathematics series, per his request. He’s a creature of habit, and Singapore worked well for him. It’s worth a try.

I’m not sorry we spent the two months on the Algebra Survival Guide. It provided instruction on number of algebra and pre-algebra techniques with clear examples. It is designed not to be a full Algebra course but rather a support. It would serve quite well in this role. The text alone provides scant opportunity to practice the skills taught. Each one page lesson ends with four or five problems to solve, with the answers upside down just and inch or two away. Therefore, we used the Algebra Survival Guide Workbook for supplemental practice. For each page in the text book, the workbook offers ten to thirty problems for further practice. This was more than plenty, given the small bites in which the material was taught, but when we needed it, more problems were available. The workbook problems are rather cramped onto the page, with short lines for answers and no room for working solutions. This shortcoming was becoming more of an issue as he progressed through the book, and it does nothing encourage the student to show one’s work.   However, the book pairing was quite successful for what I desired as well – it served to introduce some topics missing from his knowledge bank in a palatable, gentle way. Mission accomplished.

On the positive side, the Algebra Survival Guide and workbook are easy understand, occasionally humorous, and fairly painless in their presentation of pre-algebra and the mechanics of working equations. They do incorporate the logic behind the mathematical concepts they introduce. They’re also inexpensive, with only the $10 workbook being consumable.

The chief drawback is the lack of context for learning algebra. Word problems make up the last chapter, but the approach is formulaic and is likely to do little to support a working understanding of algebra or help the user appreciate the skill they’ve learned much less an enjoyment for the beauty of mathematics.  Additionally, my 42-year-old eyes (which do not yet require reading glasses) found the font less than easy to read, especially the portions of small, fine print that explain why the various rules work. My son found my challenge amusing while I was just annoyed.

Would I use it again? Probably not. My son made great gains over these past two months, the largest being that he became comfortable with the idea of algebra. As I survey the other choices on our shelves and await the start of the secondary Singapore series, I know there are better choices out there — choices that support serious mathematical study while maintaining a humorous side. Ah, well. We have plenty of time to explore those materials while taking the next steps that Singapore has to offer.

Review: Jacobs Elementary Algebra

I wrote recently about options for math after Singapore 6B that we’ve tried or at least considered. While some of those resources found their way into my older son’s schedule while he was finishing Singapore, he felt strongly about immediately moving on to  “real” algebra. He was nine and sick of arithmetic. He was also fascinated with the algebra I used to solve some of the more perplexing parts of Challenging Word Problems 6, Singapore’s last book in their honestly named supplement series. When I couldn’t make those bar diagrams work, I’d resort to methods more familiar to me. He wanted in on those methods.

After a moderate amount of research and consideration, I went with an old-standby, Elementary Algebra by Harold R. Jacobs (ISBN 0-7167-1047-1). Written in 1979, this black-and-white text is written with humor and interest without the distracting color splashes and sidebars that grace more modern textbooks. Perhaps those brighter, busier features and are a draw for some learners, but for my son (with ADHD), the less chaos on the page, the better. The cartoon at the start of most lessons held up well over those decades and grabbed my distractable child onto the page while giving us both a chuckle. A bit of a laugh is a fine way to start a math lesson.

There’s plenty of substance after that laugh. In seventeen chapters with four to nine lessons each, Jacobs takes a learner directly into the use of variables while teaching order of operations, graphing, exponents, radicals, and other pre-algebra topics not covered in Singapore’s first six books. For a mathematically geared child, this seamlessly integrates those missed topics into algebra, obviating the need for a separate pre-algebra course. For my older son who is highly mathematically intuitive, this was fine.

In Elementary Algebra, Jacobs does far more than teach the procedural goings-on of algebra. He explains why it works. This is not a text of algorithms to memorize and practice, practice, practice. Rather this is a book that encourages deeper understanding of the math it contains and that connects math to the greater world.  This creates a rather lengthy book, and my son did take a year and a half to move through it. At then end, however, he had a fine grasp of algebra and could easily relate and apply it to other studies.

The structure of the book makes for easy teaching, and the supplemental teacher’s guide (A Teacher’s Guide to Elementary Algebra  ISBN 0-7167-1075-7) provides additional ideas for teaching if that’s desired. This is, however, not a scripted program. For the parent whose algebra is more than a bit rusty, this text could be a challenge. Or, perhaps, it could be an opportunity to polish those rusty skills and dress them up with deeper understanding. Even if one doesn’t require the additional teaching tips in the guide, this book contains the answers to three of the four sets of problems in each chapter. (One set has its answers in the back of the textbook.) For this, it was worth its price several times over.

Each lesson takes a mathematical idea and develops it in two or three pages of text, diagrams, and examples. I’m a believer in interactive math lessons, since I think there’s much to be learned from discussion about mathematics. My son and I would sit together, with me reading the chapter aloud and discussing examples along the way, generally with scrap paper or a white board by our sides. Each lesson concludes with four problem sets: one review, two sections to practice the ideas from the current lesson, and a fourth presenting a challenging problem or two often with a historical bent or mathematical twist.  We generally omitted the review and did the second set (first set of practice problems) together. He’d then do the third set (second set of practice problems) and fourth set (challenge problems) on his own. The following day, we’d review his mistakes and move on to the next lesson.

Each chapter ends with two sets of review problems, of which I’d assign one. One review could be used for a test, but we used tests from the accompanying Test Masters for Elementary Algebra (ISBN 0-7167-1077-3), which offers four tests for each chapter, additional exercises on a host of topics, four multiple-choice midterms and two multiple-choice final exams. We’d have been fine without this supplement, but this was in my more obsessive “afraid we’ll miss something” homeschooling days. It’s definitely an optional supplement.

Algebra was more than a math class for my son. It was a jump in organization, textbook use, and test taking. Up until algebra, he’d done most of his mathematical work in his head. Dysgraphia and impatience with process had led to me scribing most of his work until this point, and while I’d modeled showing work, algebra was the first time I insisted he show his work every time. It was a painful first many months. The math came easily. Writing down steps did not. A second challenge presented when working through problem sets. Writing answers on paper while referring to a page in a book proved difficult. Often the writing issues, visual tracking work, and organized step-writing proved more challenging than the math. Test taking was also new to him. I don’t test my boys much — generally I can tell what they know and what they don’t. Test taking increased his accuracy and gave him a reason to show his work, since even a wrong answer with a clear and largely correct trail could earn partial credit.

Jacobs’ Elementary Algebra prepared my older well for the math that followed: Algebra II, Geometry, Trigonometry, and Precalculus flowed fairly easily from the lessons learned in that first algebra text. I enjoyed teaching from it, and he enjoyed learning from it. My understanding of some concepts deepened along the way. While it’s hardly the only algebra choice for the homeschooling family, Jacobs’ Elementary Algebra is a strong text based on sound pedagogy that prepares mathematical thinkers well for higher math.

Planning Time: What’s Happening for the Younger (age 10)

After an email request for an update to my “What We Say We’re Doing” page, I decided it was indeed time to figure out what the heck we’re doing come fall.  I have plenty kicking around in my head, but that’s only the start of the real work.  Planning for my 10-year-old is the easier of the two jobs this year, so I’ll start with him.

Math:  Last year, more independent mathematical work was one of my goals.  My younger still has a fair amount of panic about getting problems wrong, so generally he checks in with me after each problem.  This drives me nuts, honestly, and while he’s sometimes willing to forgo that pattern when he’s feeling super-confident, he has a long way to go.  We slowed math down last year when his panic at the word “math” began to mount.  He’s mathematically talented, and I really struggle with his aversion to something he does so well.  We added some of Theoni Pappas‘ work for fun, and Penrose the Cat is a hit.  Anything with a cat is a hit, but I have yet to find the all-cat math curriculum. We’ll continue with Pappas and similar material as we finish up Singapore 6B and Singapore Challenging Word Problems 6, a project that shouldn’t take long.  Upon his request, we’ll work through Pre-Algebra I and II from Life of Fred. (He saw a friend’s copy and thought it looked okay.)I didn’t bother with pre-algebra with my older, heading straight to Jacob’s Algebra after Singapore 6, but this child needs confidence despite his obvious talent, and I hope time and some diversions into other aspects of math provides that.

Science:  We’re all on to Earth Science this year, using CPO Middle School Earth Science for my younger.  It’s an inquiry-based curriculum, which means that questioning comes before vocabulary and scientific thinking trumps rote comprehension questions.  I’m a fan of the inquiry method and excited to try this well-reviewed curriculum.  It’s not designed for homeschoolers, and I’ll try to keep track of changes we make and materials we need so others might benefit later.  We have a bit of Middle School Chemistry to finish still, but hopefully we’ll finish that up this summer.

History:  After a highly successful semester with Online G3‘s History of US 2B (1899 to the present), my younger’s eager to take the rest of her offerings.  First semester, he’ll take the corresponding 1A course, covering the first three books of the History of US series by Joy Hakim.  He’s likely to pick up another in the series come spring.  History is in Headmistress’ Guinevere’s hands. Whew.

Language Arts:  My younger devoured two levels of Michael Clay Thompson’s Grammar and Vocabulary books, so this year he hits the big leagues with Word Within the Word I and Magic Lens I.  As did his brother, he’ll do these with Online G3, but while I left his brother does his own devices and kept my nose (mostly) out of the class, I’ll keep tighter reign on my younger son.  We’ll read the books together, and I plan on more outside work on the vocabulary for him.  I probably should have done the latter with his older brother last year, but it just didn’t happen.  We’re only half-way through Paragraph Town’s 20 lessons, meaning the book has been read but that other activities are left to be done.  At the end of last school year, typing skills sharp from Online G3 classes, he started a blog (Bertram’s Blog).  He’s abandoned it so far this summer, but it’s built his confidence as a writer.  Hopefully, we’ll move into Essay Voyage as the year progresses.  For the fall, he’ll take Lightening Literature 7, again with Online G3.  Can you tell we adore Headmistress Guinevere and her classes?

The Rest:  As a family, we’re trying Rosetta Stone Spanish I in hopes of providing all of us with some exposure to the language before someone takes Spanish in a classroom (likely my older son, who needs two years of it before college).  Karate continues to be our main source of PE, and we may be up for our black belts in March.  Piano study for my younger also continues.  Spelling with Steck-Vaughn materials was a wild success.  Who knew we just needed a traditional old workbook approach for that subject?  He’ll move onto the 5th level this year, and he’s delighted.  Handwriting issues have hit and hit hard. A year and a half of cursive via Handwriting Without Tears has produced many tears and no usable cursive.  His older brother fared no better, so, like his older brother did, we’ll move him back to print and finish out Handwriting Without Tears Can-Do Print.  His printing is far better than his older brother’s who has some serious dysgraphia issues, but it is still a work in progress.  Thankfully, both boys type quite well.

Of course, these plans are all subject to change, but this is one year for one child that I feel I’m looking at plans that could really work. As always, suggestions and “been there, done that” stories are welcome.





Review: Singapore Math

We’re curriculum dabblers.  We’ve been through more language arts curriculum than I care to admit, although after five years of trying and rejecting numerous lines of materials, we’re happily settled with Michael Clay Thompson’s materials.  Science has seen a similar path, although I’ve yet to find the MCT equivalent for homeschool secular science studies.   Foreign language study, critical thinking, and spelling meet similar fates.  Try them, like them for a while, and leave them behind.  Through it all, though, Singapore Primary Math remained in use.  I’ve used the texts, workbooks, and Challenging Word Problem books for all the primary levels with at least one child.

My younger son, now nine, will start level 5B this fall and should complete the elementary series by May 2011. It’s been his primary math text from the start, but his inital grounding in mathematical thought came from exposure to a rather math oriented mom and big brother supplemented with fantastic instruction in a Montessori classroom at ages 4 and 5.  His number sense is quite strong, so our pace is brisk.  We skip sections that contain material he understands, since, like many gifted children, he has no tolerance of repetition.  Often these sections are continuations of a previous topic.  Place value, for example, starts many of the books, with a new place taught every few books.  For many gifted children, this concept is learned early and completely due to curiosity and an ability and desire to see the whole picture at once. 

Singapore moves fairly quickly compare to Saxon and other commonly used homeschool math programs, which makes it a good match for many gifted mathematical learners.  If more practice is needed, there are supplementary books to provide this.   I’ve supplemented with the aptly named Challenging Word Problems, and these are the highlight of the Singapore series for us.  These multi-step word problems require planning and advanced mathematical understanding, two skills I value.  I’ll admit I’m sometimes stumped on how to solve a problem without using algebra in levels 5 and 6 of the Challenging Word Problem series, but at least then my kids get to see a bit of what’s to come (and they love it when Mom is stumped and they’re not).  My boys are resistant to writing down their steps, and since the steps to these more advanced problems are multiple, they’ve learned (albeit with whining) that they’re better off writing a few things down so they don’t lose their steps.  Modeling this process is no problem:  there’s no way my 40-year-old brain can hold four or five steps to a problem without a major slip.  When their writing skills/willingness aren’t up to the task, I scribe for them.  It works for us.

Singapore is not a scripted curriculum, and that’s fine with me, but I know some parents like more guidance with math lessons.  Singapore offers  Home Instructor guides for the 1A through 3B and teacher guides for levels 4 through 6, and while I’ve heard positive reviews of these from a few parents, I can’t speak about them through personal experience.   The textbook’s examples are clear and easy to teach from, and while manipulative exercises are part of only a few fraction and geometry lessons in the series, base ten blocks, fraction cubes or strips, a clock with movable hand, and counters could be easily incorporated for the earlier books and would be helpful with many children. 

Singapore Math is known for teaching true mathematical thinking, not rote adherence to formulas and rules.  A child following the elementary sequence through level 6 has a strong base in not just basic arithmetic but in the workings of mathematics.  This, in my opinion, should be a goal for any math education.  For my older son, this led to a smooth move from Singapore 6B to Jacobs Elementary Algebra , a sound and interesting Algebra I course.  As I’ve mentioned in previous posts (and ruminated on regularly), I’m not sure if this will be the route my younger takes.  I’m aware of so many more options that were unfamiliar to me four years ago:  Life of Fred, Thinkwell, and Art of Problem Solving, to name just the top contenders for our after-Singapore Primary Math experience. 

Finally, cost and ease of placement matter to homeschooling parents choosing math curriculum.  At a cost of $36 for a full level (levels A and B) of the text and workbook (and the gifted kid may need more than this for a year — mine do), it’s one of the least expensive math options around.  Adding Challenging Word Problems or another supplement adds less than $10 (the other supplements are similarly priced, and a single book of the supplements corresponds with both halves of the text and workbook for a level).  Teacher guides, if desired, add a bit more, but they’re likely to hold their resale value.  The Singapore website offers free printable placement tests online as well, which mirror the content of their books quite accurately. 

I’m a huge Singapore fan.  It teaches comlicated mathematical thinking from the start, is affordable and easy to use, and prepares kids for Algebra I.  Plus, my kids like it.  Now that’s a series we can stick with.

I’ve received no free products or payment from Singapore math or a distributer of any of the above mentioned programs.

The Math Can

Summertime.  It brings longer days, campfires, real tomatoes, and raspberries fresh from the bush.  It also brings stinky feet, mosquito bites, wasps, and skinned knees.  And somewhere between these extremes, summertime at our house brings The Math Can.  Say it in a deep voice, somewhat drawing out the second and third words.  There you go. 

The Math Can (deep and drawn out, remember?) is something of institution in our house.  It’s simply a large can filled with math problems of the type studied in the preceding school year.  Word problems and other problems from Singapore Primary Math and occasionally other sources are copied, cut into individual or groups of problems, folded into quarters, and placed in the can.  The victim, ahem, I mean eager child, picks a given number of pieces of paper a week, tapes them into a notebook, and does the problems.  My youngest is the chosen math can man this year, with 10 pieces of paper a week assigned. He can do the ten whenever he wants, Monday through Friday, but they must be done.

The Math Can is a somewhat gimmicky math review mechanism.  It’s simple but highly effective.  The random nature of the draw adds an element of mystery, albeit small, but it assures a varied assortment of problems to review and eliminates the complaint that, “Mom picked all hard/long/easy/boring ones this time”.  The element of chance plays again on the number of problems on a single piece of paper.  My younger and I have reviewed the rules many times:  10 pieces of paper each week, regardless of how many problems are on a piece of paper.  Despite not starting an offical Math Can week yet, he’s already lobbying for 10 problems instead.  Good luck, kiddo.

Come on, reach in. No peeking allowed. No returning problems you don't like to the can.

Last year, I didn’t bother with The Math Can.  My older no longer needs the reinforcement.  We used it occasionally when summer broke up his year with Jacobs’ Elementary Algebra, but there was no need after that point.  My quite mathematically talented younger son, however, found himself stymied last September by problems he breezed through just a few months earlier in May.  We’d stopped our school year just after long division and multiplication and division of decimals, and I had a feeling he’d drop those skills without reinforcement.  However, our summer homeschooling plans were lost in the shuffle and emotion of my divorce, however, and The Math Can sat empty.

I wish it hadn’t, and so did my younger, come last fall.  He was irritated with himself for forgetting some basic arithmetic skills, and, for him, irritation at self is expressed as anger at those loving family members in his midst.  While it only took a few lessons to recall each skill, it took much longer for him to find his confidence in math again.  Let’s just say that he’s on board with The Math Can this year. 

The Math Can.  It’s somewhere between sprinklers, lemonade, and making snapdragons talk and poison ivy, ants in the house, and heat rash.  It may not be the favorite part of summer for my kids, but it’s ours and it’s staying.

It’s your turn.  What do you do to keep skills sharp over the summer?