Review: Getting Started With Latin

We have a language gap around here. I’m not a natural at foreign languages, and my one year of high school French, while not harmful to my GPA, hardly enamored me with the work involved in learning them. My older son’s learning challenges made learning a foreign language close to impossible. We tried home-based and online-based programs for Latin and Spanish, but we had no success. He’s moved on to American Sign Language courses at the university, a kinesthetic language that works well with his strengths and avoids his weakness, such as rote memory and attention to spelling.

So as my younger son approaches middle school age, I’ve panicked a bit. I don’t have the brain space to deeply learn a foreign language with him: general awareness is my only hope. My French was never terribly useful, and nearly 30 years later is nearly nonexistant. My younger had mentioned learning German, but I knew no way at this point of his life to make that successful and could provide no assistance. So I gently mentioned Latin. He’s a fan of Michael Clay Thompson, with his stem-based vocabulary, and he’s a master at grammar and memorization, and he appreciated my concerns about finding an appropriate setting for him to learn German. So Latin it was.

Getting Started with Latin (Beginning Latin for Homeschoolers and Self-Taught Students of Any Age), by William E. Linney has been our starting place. Linney approaches Latin gradually and, over 132 single page lessons, introduces the learner to basic Latin grammar. It’s not a full year of Latin, but it’s a fine grounding.  I’m using this book with my younger son, now eleven, who will start formal Latin study with Karen Karpinnen through Lone Pine Classical School, an online school based in Colorado dedicated to high school level Latin study for homeschoolers. Our purpose is to build comfort with the language, especially the ideas of declension rather than sentence order driving meaning and gender in language.

With only one new idea per lesson, this is a gentle approach to a complicated language. Linney covers the first and second declension, two conjugations of present tense verbs, the concept of gender, and a handful of adverbs, adjectives, prepositions, and conjunctions. The vocabulary is relatively small – farmers, sailors, beasts, and women build, sail, swim, and plow in a variety of combinations, but this decreased vocabulary allows the learner to focus on learning the grammar itself rather than on memorizing voluminous vocabulary lists. I’m decent at the former but not so strong in the latter, and with almost no study, I’m keeping up with the poets who carry writing tablets (but never desire to swim to the island) and the farmer’s stories, told often to the girls. That’s miraculous.

It may not be the most scintillating material to translate, but this sound beginner’s text is entirely nonthreatening, an essential feature for this foreign language-phobic mom. It’s also easy to teach. A motivated student could move through the 132 lessons solo, translating from Latin to English the 10 sentences at the end of each lesson, but we’re doing this together, sitting on the couch and reviewing the lessons together. He does keep a notebook of vocabulary, with each noun written in its ten forms and each verb conjugated (first person). While we’ve not been chanting the conjugations and declensions together, he’s figured out that that step helps and does it on his own. (Did I mention he’s my self-motivated and highly driven child?)  If we’re stuck, the answers are in the back of the book, but so far, we’re rarely stuck.

The lessons are never longer than a single page, and the black-and-white pages with plenty of white space keep attention from drifting while making it easy to see the lesson at hand and only that lesson. Some lessons are reminders about English grammar, which we skip, since five levels of Michael Clay Thompson have given him firm grounding in that area. A learner who was less certain about subjects, direct objects, indirect objects, possession, and English verb conjugations might want to spend more time on those sections, although I’d not advise starting Latin without those ideas firmly in place in one’s native tongue. In addition to the 132 lessons are 18 notes about commonly used Latin phrases, such as ad hoc, summa cum laude, and caveat emptor. It’s a nice addition, reminding the user that Latin is in use today, beyond its role in naming genus and species and providing many of roots of English words.

Linney’s website provides files for pronunciation, both classical and ecclesiastical. Occasionally, pronunciation is covered in the book itself, but the website contains far more. We’ve not been using that resource regularly, I’ll admit, but it was initially helpful. We’re also not exactly speaking Latin to each other (what with the poet, sailors, and beasts not much applies to our daily life), but I have had my son compose sentences in Latin, which he also translates. It’s up to me to figure out if he’s correct, and this is only possibly because I’m learning along with him.  Like I said, I’m keeping up, a testament to how clear this book is.  I’m not giving tests, but given the material is cumulative, I can tell from his translation during lessons how he’s doing. If testing is desired, Linney recommends taking sentences from past lessons for translation or having the student translate from the recordings on the website.

We’re working through three lessons four days a week, a pace determined by our start date and desire to be done by mid-May.  We complete more chapters if one is an idea alone with no translations or an English grammar language, with the limit being three chapters requiring translation. Any fewer and I doubt we’d immerse enough to learn much. More and we’d likely retain less. My son then puts new vocabulary into his notebook and, if needed, later reviews that vocabulary.

At  twenty dollars for a nonconsumable text that is easy to use and effective in teaching Latin basics, Getting Started with Latin is one of the best homeschooling bargains around. My only complaint is that it is his only Latin text. Linney has a series of audio lectures based on The First Year of Latin, an 1902 text by Gunnison and Harley covering, at this writing, half the text. That’s a far less user-friendly text, however, and lectures have been slow to come out. But it is a free offering and, if reviews are any indication, well done. I’ll know better how well prepared my young son is for formal Latin study come fall when he starts high school level instruction. But given the breadth of material covered so cleanly and clearly and the rate of retention my son and I have demonstrated, I’m betting it’s done what I needed it to do.

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 levels 7A and 7B are available, with 8A and 8B to be released at the end of 2012. The others should follow soon, I’ve been told. Yes, movement between the old and new programs are doable, and a switch from  the old level 1 to the new level 8 works well, I’m told by their forum guru. Worrier that I am, I have 7B and 1A just to be certain we won’t miss anything. In all regards, including, rigor, the new books are quite similar to the old, with additions and a bit of rearranging being the main differences. 

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. 

Experience/Review: Coursera

We’ve wading into new territory this semester. We’re hardly alone. With over 75,000 learners from around the globe and spanning many decades, my younger son is exploring connections in world history. My older is finishing a science fiction and fantasy literature course while starting a class in beginning Python programming. We’ve sampled just a touch of what this mode of learning offers. At this writing, Coursera lists 198 MOOCs (Massive Open Online Courses), ranging from neuroscience to economics to physics. The preponderance of courses are in mathematics, computers, and science, with a smattering of business and liberal arts offerings making up the rest. All are free and, as the name suggests, all have massive attendance.

Unlike many previous free offerings from universities, these aren’t self-paced, self- evaluated classes. These run at the pace of a college course, albeit generally shorter. Coursera’s offerings run from three to twelve weeks in length with start times scattered throughout the calendar, so just about any time during the year, a class is beginning. While the format differs somewhat for each course, the basic set-up is the same. About two hours of lectures are released weekly, each broken up into shorter segments. Sometimes, an informal quiz falls at the end of the lecture, allowing the learner to check on his or her knowledge. Assessments vary, with objective quizzes dotting the schedules of some and peer-graded papers dominating in others. Some even have final exams.  All have deadlines.

I love that last part.

There is the potential for an interactive experience in Coursera. There are discussion forums for each class, with separate lists for a variety of topics. In part, these are designed to foster conversation about the material or address questions students have. My older has participated a bit, and while I’ve had my younger son check in on them, he has no interest in participating. Meet-up groups are also listed, with people gathering live in small communities to discuss class material. We’ve not explored this option yet, keeping discussion at home for now. These courses would be fine material for a group of homeschoolers to explore together, possibly meeting to discuss assignments or the lectures. If the courses we’ve experienced are any indication, there would be no need to add more material to what’s offered. These are time-intensive offerings — full courses unto themselves, but a live setting for discussion would make the experience richer.

Make no mistake. These courses are not geared toward the under-18 audience. While that’s not likely to matter for most of the classes, my older son’s Fantasy and Science Fiction literature class had numerous (appropriate) references to sex and sexual symbolism. As a previous English major, I wasn’t surprised by these. As a mom, I took them as a learning opportunity about literary analysis. My son survived, although he stuck to choosing essay topics about other literary elements. I’d have been less sanguine about my younger son, 11 years, had he been in the course, but between the reading list and the nature of literary analysis courses, I knew better than to enroll him.  The history course he’s taken has made brief references to the spread of sexually transmitted infections by sailors leaving the Americas and to rape within the context of historical events, both appropriate to the topic at hand. Again, my approach has been to use these times to inform and discuss.  History is full of difficult topics, and I expected some challenges; these topics have been manageable for our household, but some families may want to stick to more technical courses that have less likelihood of wandering into these territories.

The experiences of firm deadlines and peer review are perhaps the two most likely to challenge the homeschooling student. While my sons have had a moderate amount of exposure to deadlines for other online classes and real-life classes, they’ve little experience with the perils of missing a deadline, which, for the courses we’ve experienced so far, can mean receiving a zero for an assignment. I’m grateful for this reality check, and as most of us homeschooling parents know, having that reality come from outside of us makes it all the more, well, real. So far, both boys are on target with these dates, and we’ve taken to artificially advancing the time and date due to avoid last-minute rushes or the inevitable technology crash occurring at the wrong moment. My older son has translated this well to his university courses, and I can see healthy habits beginning.

Kids in school today generally have a fair amount of experience with peer review, an experience I was largely spared as a child. Coursera’s version, at least in our experience so far, relies on a rubric (a scale of 1 to 3, in our experience) with accompanying comments from the student readers. For one class, if you did not submit your reviews, you received no grade on your writing, thus impacting your final grade. My older son found these doing reviews and grading difficult initially. With no experience writing literary analysis, he had little to on which to base his judgement of others work. Initially, we worked together. But in a few weeks, he took on the task himself, seeking me out if there was a theme in an essay that didn’t make sense to him (often due to lack of his experience and knowledge, not due to a fellow student’s lack of clarity). His grades each week were an average of the responses of four readers, thus blunting the most optimistic and pessimistic reviewers while still allowing him to see what everyone’s ratings and comments.

Reviewing the work of others, he found, strengthened his own writing. He saw that grammatical errors and poorly proofread work were laborious to read. I’d told him that for years, but it all became obvious when reading four other essays a week for ten weeks. He learned economy of words, since he had only 320 words with which to express himself. As a sometimes wordy writer, this was invaluable. Both through the process of reviewing others and being reviewed, he found his writing improve. We were both delighted.

While we’ve only sampled a bit of what Coursera has to offer, I can say I’m impressed by the quality of the lectures, the intentionality of the assignments, and the organization of the courses themselves. Like a live course, some professors will appeal to some learners more than others. Some classes will be more demanding than others. Some assignments are clearer than others. Overall, there is plenty here for homeschoolers working at the high school level and beyond to appreciate. There is plenty to challenge young, bright learners who either aren’t ready for the college classroom (my younger son) or want a more convenient  affordable way to access college-level content.

Here are a few additional considerations for those considering Coursera for the homeschooled student:

• Read course descriptions carefully. Some classes are clearly for beginners while others, despite benign titles, are designed for those with far more experience.
• Pay attention to the time requirement mentioned and the syllabus (if available) before signing up. Sure, gifted learners may require less time to master material, but the hours of lecture, readings, and assignments add up.
• Consider having your child just sit in for the lectures if that’s more appropriate for your learner. No one comes after you if you don’t do the work, and for some students, just the lectures may be what they’re after. The work however, is what differentiates these classes from Teaching Company classes.
• Be prepared to support the younger learner, especially at the start of a class. For the child newer to online learning at a rapid pace, organizational assistance may be in order. For peer review work, some advising and supervision initially can ensure that the critique heading out is respectful and useful to the reader.

MOOCs are part of the future of higher education. Udacity and edX also offer similar experiences with a focus on math, computers, and the sciences. More opportunities for university-level learning for no or minimal cost can benefit a range of learners, including the homeschooled student ready for higher-level studies. While I’d not want all my children’s content to come through the internet, it’s a fine way to bring high-quality content home.

Composition Choices: Michael Clay Thompson

Previously, I’ve reviewed MCT’s first three levels of language arts materials (General, Grammar and Poetics, Vocabulary and Composition)  and the first composition book for the fourth level (Advanced Academic Writing I). While the grammar, vocabulary, and poetics books at each level work well together, the corresponding composition books tend to be beyond the reach of many young, gifted kids. As I’ve begun to tutor young writers, discussing what level of MCT composition is appropriate has come up more than once. Here are some thoughts on making a selection. 

Michael Clay Thompson breathes life into language arts instruction. With six levels of materials covering grammar, vocabulary, composition, poetics, and literature, he seamlessly integrates those elements of the English language in a manner that assumes his readers are intelligent, active learners. These are not workbooks for self-study — they are texts best explored with a teacher or guide. While the composition books could be used without the rest of the books in the corresponding level, the learner would need a strong grasp of grammar to truly take advantage of what they have to offer and an understanding of MCT’s four-level approach to grammar. (Take home message — if you’re using a composition book, purchase that level of grammar or higher to use with it.)

All his books within a level are integrated, each rooted heavily in the corresponding grammar book and somewhat less on the vocabulary book.  For many young gifted learners this presents a dilemma — what a level child is able to manage in grammar, vocabulary and poetics reaches a level or often more above what works for composition for the child. Therefore, it’s not uncommon for a child to be ready for the fourth level of grammar and vocabulary but still be working on the second level of composition. No need to worry, however, as that difference works quite well.

Sentence Island: This is a fine start for the beginning young writer. While the content is applicable to writers of all levels, it has a young feel, which would likely be off-putting to the upper elementary or older learner (over age 10, perhaps, depending on the child). This book teaches writing beyond the sentence and demands understanding of the grammar taught in the corresponding level. For my younger son, it was too demanding (unless I scribed for him) until he was about nine, at which point, he was finishing the Voyage (third) level of everything else. This worked well for my (then) reluctant writer, and I was glad we waited. (Only the Teacher Manual is necessary when using this at home.)

Paragraph Town: The second writing book of the MCT series takes the writer through the story of two ducks, Fishmeal and Queequack, as Fishmeal seeks knowledge about the paragraph. The story nature of the book makes it better suited for younger users, but the material is so worthwhile, I’d encourage the reluctant but somewhat older writer to read through the story and work through the exercises (which are fine for any age). Even experienced writers can benefit from the thorough treatment of the paragraph in this fine text. There’s quite a bit here. Resist the urge to fly through, and take time to assure the lessons are absorbed and sufficient practice occurs. (Again, only the Teacher Manual is necessary for home use.)

Essay Voyage: This text makes a big leap from Paragraph Town in style and content. Gone is the story form of teaching. Instead, MCT breaks essay writing tasks into ten chapters, covering such topics as structure, formality,  content, conclusion, and even correct citations and use of quotations. Each element of writing is clearly taught, complete with examples. Most chapters offer a list of options including research and reflections on readings. Gradually, essays are included in the options, and by the end, essays with quotations are expected. It’s a steep set of expectations that, if met, would lead to developing quite strong writing skills that certainly would prepare a learner for high school and exceed what many can do before heading to college.

The essay examples range from the lighthearted to the quite difficult, including a selection from the Federalist Papers and the Narrative of Frederick Douglass, just to name two. This represents a challenge when using the book with a younger learner who just may not related to the content of the essays for examination. For the younger child, moving directly from Paragraph Town, with its more gentle approach and easy reading material, to Essay Voyage may not be advisable. If in doubt, wait, working longer with the earlier book or supplementing with other materials. (As with the other books at this level, only the TM is necessary.)
Advanced Academic Writing I: The fourth book (reviewed here) continues where the third left off, using literature as a starting point for writing with quotations and, new to this level, paraphrasing with citations. While sound in content, the tone is harsh. Yes, writers should be held to high standards in form and content, but this volume is a bit punishing for my taste, at least on the grading front. in my opinion, his focus on grading interferes with the material taught. One could certainly soften that approach and ignore the rubric MCT presents, but a large portion of the book is based on meeting this demands.
This is not a tome for the younger gifted writer, and it is a leap beyond the previous level, Essay Voyage. The first assignment requires writing about literature,  a difficult task for any writer (and the gifted child may be at this fourth level at 10 or even earlier). While there is fine writing advice given here, I’ve chosen other paths to teaching this level of composition. (This book is best used with both the student text and TM. MCT offers a second and third level of Advanced Academic Writing, which I’ve yet to explore.)

Michael Clay Thompson offers a fine introduction to essay writing, starting at the level of the sentence. The young writer will likely need a slower progression through the writing portion of the MCT books, and the guide above may help one find the right pace to start. Remember, MCT’s composition books are targeted toward academic essays and papers, not fiction or other genre. While I’m of the thought that teaching this more formal writing should be the first priority when teaching children to write, there is value in adding other creative components to a writing curriculum, especially for children craving that sort of writing outlet. Whatever type of writing a learner prefers, however, the material taught in his first three composition books will form a solid base of writing skills that would serve writers of any genre.

As with all my reviews, I’ve received no compensation in materials or otherwise for this review. 

Review: Advanced Academic Writing, Volume I (Michael Clay Thompson)

I’m committed to raising strong writers. For parts of my boys’ lives, they’ve been committed to not writing. I managed to cultivate enough patience accommodate this reluctance, scribing until they could type well and exposing them to plenty of fine writing along the way. We tried a few writing programs, but they largely felt formulaic and focused heavily on creative writing, which did not please my older son, who eventually broke through the writing wall with an online course.

A year or so later, we started using Michael Clay Thompson’s Language Arts materials from Royal Fireworks Press. (I’ve reviewed the Elementary resources here:  MCT Overview, Grammar and Poetics, Vocabulary and Composition ) Both my sons moved quickly and happily through the grammar and vocabulary books. Given their writing reluctance, we always lagged behind on the writing portion of the series, generally working a level behind on the writing end of the curriculum. This is a common solution for many using the series with younger children. The output required for the writing books far outpaces what many young children can manage, so many families just adjust accordingly.

Advanced Academic Writing, Volume 1 (AAW 1) is the first of the MCT writing Middle/Secondary writing series. It’s a serious tome designed to teach a learner how to write an MLA-style academic essay or research paper. It’s designed to be used with Magic Lens 1 (grammar) and Word Within a Word 1(vocabulary), which are also far more serious and demanding books than their predecessors. Like with the elementary series, I’ve found that while that at this level, the grammar and vocabulary books are accessible to my kids, the writing program is a giant leap above them. Admittedly, I’m using the books early for my younger (WWW 1 and ML 1 for 5th grade), and the asynchrony of gifted children often results in a delay on the product end of the learning equation. But even as we approach the second level of the secondary grammar and vocabulary, I know he’s not nearly ready for Advanced Academic Writing I.

Like Essay Voyage, the third writing text in the elementary trio, AAW 1 focuses on formal diction and prose and third-person writing. Advanced Academic Writing continues where Essay Voyage, the last volume of the elementary series, leaves off. While the other portions of the MCT language arts curriculum have a spiral element built-in, allowing a learner to enter at about any level, the writing portion is far more linear.  While a high school student could begin the rest of the middle/secondary series and be able to work through the series successfully, AAW 1 relies heavily on the material from  Essay Voyage, where the principles of a well-crafted essay are explicitly taught. This isn’t a problem if a student is well-schooled in writing an academic essay, but many students simply aren’t.

Advanced Academic Writing 1 begins with a fifty-odd page writing guide that briefly covers the mechanics of writing an academic essay or short research paper. After covering standard proofreading marks, MLA rules regarding form and style, and quotations, Thompson gives an example of a paper fitting his criteria with a few proofreading marks thrown in as examples. The paper is heavy on long quotes for it’s three page length, but it’s point is to illustrate form, formality, and adherence to the thesis. The samples in the book are all short, as are the assignments. Thompson is looking for perfecting each part of smaller works — learning correct form. I agree with the philosophy of several shorter assignments with the aim of learning the form. It’s a more efficient and less overwhelming way to learn the intricate process of academic writing. (When I co-taught a research paper class, this point was driven home to me. We assigned a paper three to four times the length MCT suggests, and the students were rather overwhelmed. Lesson learned.)

The guide continues with word usage and punctuation guides along with a few examples of papers with errors. These lists are concise and easy to use, limited to a few pages each and accessible for the grammar-savvy user. What follows is less concise: nearly twenty pages of what he calls “core-element grading.” It’s at this where I disagree with MCT. His grading method starts with correct use of the English language, then moves to MLA format, correct essay structure, and, finally, the meaningfulness of the idea itself. In short, if the first item isn’t present (proper English) the paper can receive a grade no higher than a D with mastery (in order) of the following elements to achieve a C, B, or A. In short, a paper with an excellent thesis that is well-supported with excellent command of the English language can receive no more than a C if MLA formatting is incorrect. Form before function, I suppose.

Don’t get me wrong. I’m a stickler about form and proper use of the English language. But I can’t agree with putting the quality and support of the thesis last. Kids develop their writing ability unevenly, and this one penalizes those who lag on the details but excel in content. Certainly the whole grading system could be dismissed. As homeschoolers, we regularly dismiss what does not fit our needs. However, the focus on errors in the first three categories continues throughout the book, and while the examples are helpful, I’d rather see far more focus on creating effective essays.

Four assignments make up the second half of the book, each with word lists from Word Within the Word 1, hints about word choice, a sentence from 4Practice 1, a sample paper with a few pages of comments (positive and negative) addressing the elements listed above, and, for two of the assignments, a writing lesson (organization and outlining; proper citation). Finally, the assignment is given. Thompson is painstakingly clear regarding expectations for each paper, although he leaves plenty of room for choice on the subject of each essay. His assignments each have a specific purpose, which he makes clear as well. Students are asked to write each of the following:

• An interpretation of fiction using a single source
• An essay citing multiple sources
• An essay on a revolutionary character
• An essay on an abstract concept

These choices leave plenty of room for a student to follow an interest or for a parent or teacher to shape into an assignment that intersects with other material being taught.

So how much did we use Advanced Academic Writing, Volume 1? Not much. The first few sections intimidated my older son, who was a ninth grader by age and still very reluctant to write. He can write quite well but tends to panic easily. The tone of this book was panic-inducing for him, and I quickly set it aside. He has written two fine research papers since then, both using many of the concepts Thompson teaches but with less demanding assignments. My younger is an astonishingly fine writer at ten would be unable to handle many of the assignments now. Interpretation of fiction is a task that flummoxes many an older teen, and his other assignments simply aren’t yet accessible to him. So for now, I rely on Essay Voyage and, for the most part, my own writing knowledge. It’s likely the homeschooler in me, but I’m far more intent on keeping writing from being hated and focusing on continuous improvement than letter-grading my kids’ work. I can see where this book would be a fine addition to an honors-level high school class, but it’s not for the reluctant writer or most younger children ready for the content he provides for grammar and vocabulary at this level.

So for now, Advanced Academic Writing, Volume 1, will continue to sit on my shelf. It may be a fine match for my younger son a few years from now. He’s a strong writer, and he’s less likely to be intimidated by the tone and content of this book. My older, however, needs a gentler, kinder path to mastering academic writing. What that is, I don’t quite know, but I’ll share our journey here when I work that out.

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.

What Do We Do After Singapore Math 6B?

What’s a parent to do after a child finishes Singapore Math 6B? After even the Challenging Word Problems 6 supplement? I’ve googled that question, asked other homeschooling moms on forums, and pondered it with friends each time a child neared that mathematical cliff.  There is, of course, no perfect answer. If your child is mathematically talented and young, delaying the algebra, geometry, algebra II, precalculus, calculus chain should at least be explored. (The Art of Problem Solving folks explain why rather well.) My older decided to start that chain immediately just before turning ten (albeit taking it at a slower pace), and he’s been largely happy with that choice. My younger son, ten,  more recently began life after Singapore 6B, so his path is still in its evolution.

So here are some possibilities. I’ve divided them up depending on whether we’ve made use of them at the pre-algebra/algebra level or not. Some are linked to my reviews while others remain on my ever-growing list of curriculum to review here.  Hopefully, the lists will provide some options for the child that gets to that point several years before his or her teens as well as for kids who reach it later. If you have more ideas, add them (with any links) to the comments section.

What We’ve Done

• Jacobs’ Elementary Algebra: When my older son was done with Singapore 6B at nine years old, he wanted to go right into algebra. Honestly, I didn’t know of any other path to offer, although his insistence was strong enough that I’d likely not have swayed him. Harold Jacob writes with humor, which appealed to my older son. Jacob quickly moves through the pre-algebra basics not covered in the Singapore series (negative numbers, exponents, absolute value, order of operations, and various mathematical properties) and onto a sound algebra program. (Review here.)
• Keys to Algebra: My younger used the first of these ten books while working on Singapore 5. The series is a consumable set of low-cost workbooks designed for a student to use alone. They are fairly dry but provide plenty of practice and start with pre-algebra concepts. I’ve known of families who have used these before a deeper study of algebra or along with the last books of Singapore.
• Algebra Survival Guide: This book breaks algebra down into bite-sized components, starting with a fair amount of pre-algebra (properties, exponents, negative numbers, radicals, etc.) Each page presents one concept, and many concepts are briefly proven along the way. For practice, there’s a consumable workbook with answers. While not a full algebra course in my opinion, it certainly does a fine job introducing many concepts that could make a more challenging algebra class more manageable. My younger is enjoying this book now.
• Penrose the Mathematical Cat: Theoni Pappas has a number of books for children and adults that introduce a variety of mathematical ideas that sit well beyond the traditional curriculum. My younger son and I started reading these together during the Singapore books and enjoyed discussions about fractals, mobius strips, infinity and more. These are definitely our antidote to math anxiety and traditional math blues.
• Life of Fred Prealgebra: Life of Fred has a growing body of followers. We’re not part of them. We tried the first book (reviewed here) and found it rather dull and lacking much math. If you’re looking for a light diversion for a few months, this may work for you. It didn’t hold interest here.
• Challenge Math: Edward Zaccaro presents an array of largely pre-algebra topics that are generally accessible before the end of Singapore 6B but could also be enjoyed after completion as a way of strengthening problem solving skills. His 19 chapters explore some pre-algebra basics (fractions, percents, volume, for example), trigonometry, algebra, and even a bit of calculus. With three levels of problems at the end of each chapter, there’s plenty to play with here. He has an algebra-specific title, Real Life Algebra, that sits on my Amazon wish list.
• The Number Devil: Fiction meets math in this playful trip through math topics that won’t be found in most math books. The author plays with combinatorics, fractals, Fibonacci numbers, roots and exponents, and more. A few folks on the web have created study guides and lesson plans for this book, which go a long way to flesh out this rather content-heavy book. Again, it could be appreciated before finishing Singapore 6B.
• Calculus By and For Young People: Here’s another book that takes meaty, real mathematical concepts and presents them in accessible ways for kids. While the author cites that kids as young as 7 could use it, it’s likely to be best appreciated with kids with a good understanding of fractions and decimals. It contains plenty of hands-on work with excellent explanations.
• Descartes Cove: Distributed by Johns Hopkins Center for Talented Youth, these six CDs make a quest out of math problems. The math is quite obvious and the pace is slow — it’s not a high-speed video game sort of experience. It’s aimed for middle schoolers and covers some algebra, geometry, measurement, probability, and more. The math demands higher-order thinking skills, putting it in a different league than the fast-twitch math fact games designed for the younger set. My older enjoyed this when he reached the last levels of Singapore.

What We’ve Not Done — Yet

• More Singapore Math: Two options exist for families that want to carry the Singapore experience through Algebra II. Both mix geometry, algebra, and other topics throughout four levels covering four years of math. I’ve held back, not wanting to commit to a program that makes moving to another more traditional program more logistically challenging. Both programs are said to be quite challenging. It’s still on the list of possible next steps.
• Art of Problem Solving: This publisher is known for rigor and deep thinking and is aimed at those that not only excel at mathematics (mine do) but really love it (mine don’t). Their pre-algebra book would be a fine place to start the series, which largely covers ground that Singapore 6 does not. Online classes (for a fee) and online problems (for free) could complement the text, although these books stand alone quite well. It’s still on my short list as well. My older tried the online Introduction to Probability and Counting course and was overwhelmed and discouraged. Like I said, it’s best for those students who love math, have ability, and really want to work hard.
• Thinkwell: This company offers a host of math courses from middle school to college. Instruction is via video, and problems can be done and graded online. Dr. Burger is an engaging instructor who adds enough humor to make the lecture interesting. My older son used Thinkwell for College Algebra (before they offered Algebra II) and found it appealing. However, for the child who needs a live human for instruction (and my older son does), this may not be the best choice.
• ALEKS: ALEKS is another online learning system. Unlike Thinkwell, it contains no lectures. Like Thinkwell, it generates and grades problems.  My older son used this for some of precalculus, but it has courses at the pre-algebra and beginning algebra level. Here’s my full review, but in summary, I recommend ALEKS as a supplement rather than a full curriculum.
• Khan Academy: This amazing free educational resource is a repository of chalkboard-style videos about math, science, economics, history, and more that’s growing by month. For many of the K-12 levels of math, practice problems follow lessons. We’ve used this for some cosmology, history, math, and chemistry over the years, largely as a supplement to other curriculum. He may not appeal to kids who need pizzaz to pay attention, but his methodical, clear presentation makes for fine watching for more patient viewers. Tracking  a student’s watching and practicing progress is available. My younger son has watched largely non-math topics, while my older son has worked through much of the precalculus lectures. Like ALEKS and Thinkwell, we’ve not used this for the pre-algebra or algebra level.

I’m sure I’ve left many post-Singapore 6B avenues left unexplored. If you have paths you’ve taken and would be willing to share, please add them to the comment section. Links to the sources are appreciated. It seems my next step is to review the resources we’ve used. That’s a bit larger job than I imagined when I set to making this list, which grew far longer than I imagined. I best get started.

Review: Life of Fred Pre-algebra

I’ve never taught Pre-algebra.  I’ve taught Algebra.  I’ve taught all the math that comes before it, at least what Singapore Math comes before Algebra.  But Pre-algebra?

I had no need, until this year.  My younger is a hair away from the end of Singapore 6B and doing just fine, but for an assortment of reasons that deserve their own post, I’d like to delay a full, rigorous Algebra program.  He’s fairly mathematically talented but not terribly interested, and since we’re not in a race, I thought we’d take the scenic path to the Big Four (Algebra, Geometry, Trig/Pre-calculus, and Calculus). He also has the Algebra jitters, and I’d like to see him more confident before launching into one of my favorite classes.

So after considering a variety of choices and hearing so many accolades for Stanley Schmidt’s Life of Fred series, I secured copies of Life of Fred Pre-algebra I and II.  My ten-year old was thrilled.  We’d snuggled on the couch enjoying The Adventures of Penrose, the Mathematical Cat by Theoni Pappas, and he was certain more math on the couch with Mom and Fred would be equally delightful.  So we settled into the first volume.

Life of Fred is math told in story form.  Each chapter at this level is a few pages of story/biology or economics/math followed by about three to ten problems and questions in the section “Your Turn to Play.”  Answers immediately follow the questions, and we found covering them with an index card kept one from taking in the answers while working the problems.  After seven or eight chapters, a set of five tests of sorts (“The Bridge”) appears.  According to the book, the student should continue to attempt these ten-question tests until mastering one with an 80%.  Then the student can move on to the next section.  Looking back for assistance on all of the tests is encouraged.  At the end of the book, are five “Final Bridge” exams, with twenty-one questions each.

All the books tell the story of Fred.  Fred is a five-year-old mathematical genius who teaches at KITTENS University and sleeps under his desk.  In Pre-algebra I, the story revolves around gardening (in Fred’s office) and a scandalous, swindling shopping mall owner.  The story is interspersed with brief descriptions of sets, volumes of various solids, the five kingdoms of living thing, a smattering of genetics, a bit of algebraic equations, and more.  Evolution in not on the topic list (and the author points that out in the introduction).  Far more biology surfaces in this book than math, although most of the problems to work are mathematical.

No risk that I’ll give away the ending of Pre-algebra I.  We lost interest midway through. Actually, I lost interest in Chapter 3, but my son hung in until the halfway point.  The science is sound, if rather scattered and incomplete. The story was far from compelling, at least to the two of us.  I’ve heard from those who’ve used Fred for the preceding Fractions and Decimals books that those earlier volumes are far more focused and interesting.  And while I’ve read on message boards that some families manage to make Life of Fred their entire math curriculum, for many folks it seems to be a supplement.  If my son had enjoyed it, I suppose we’d have stuck with it as supplement, a way to vamp a bit before Algebra — The Real Thing.

But he didn’t enjoy it, so we stopped.  Perhaps our problem stemmed from not having used prior volumes of Fred. Not that I felt we were missing parts of the story, but the scattershot of math and biology often left me explaining details the author omitted.  I understood that issue when set theory tripped him up (none of that in the elementary Singapore) — that was some of why I decided to try the series.  Sets, a bit of probability, and those sorts of odds and ends are what we need.  Unfortunately, there was precious little of that math — or any math — to be found in Pre-Algebra 1.  The biology was sound, but it’s largely vocabulary (solipsism, proprioceptors, hexaploid, pleotropic genes) amongst interesting biological facts, not ground-up biology that will provide a strong base for future studies.

Yes, I was disappointed.  I was disappointed four years back when my older tried Life of Fred Advanced Algebra.  I can’t recall all the details of that break-up with that piece of curriculum, but I do know my older son’s learning style did not jibe with the series either.  Perhaps it’s just us.  Life of Fred is designed to be self-taught, and we just don’t do that with math.  I have two mathematically talented kids, but they like interaction with a human for math.  I like it that way.  Math deserves conversation. Certainly one could do that with Life of Fred, but it is definitely a sit-and-read kind of series, not a work-at-the-white-board one.

Life of Fred offers books for an ever-expanding range of ages, now starting with early elementary math and reaching to Calculus and Linear Algebra.  Obviously Schmidt is doing something right with this unique approach to math.  But it’s not for us.  We’ll continue to take our time at this point of my younger son’s math education, but instead of Fred we’ll reach for Zaccaro’s Challenge Math (and later Real-Life Algebra), more from Theoni Pappas, and other diversions yet to be discovered.

Early Review: CPO Middle School Earth Science

This is our Earth Science year.  I’ve never formally studied Earth Science (the honors sequence in my high school bypassed it in favor of two years of biology), although my older son was intensely interested in astronomy, meteorology, and natural disasters throughout his younger years.  My younger son had no such previous interest, so this year we set to filling that hole in his education.  He and I are using CPO Middle School Earth Science and, five chapters in, enjoying the tour of our planet. (We had Chemistry to finish for the first two months.  Some day I will finish my science and history plans in a school year.)

CPO Science offers secular courses in Earth, Physical, and Life sciences at the middle school level and physical science (with or without some earth science) at the high school level.