math Archives - Page 2 of 5 - Dr. Marie-Claire Moreau

Jun 17 2013

Chemistry and Calculus: 5 solutions for teaching tougher classes

Parents often wonder about teaching “tough classes” in homeschool, like the ones many students take during the high school years. Topics like chemistry and calculus can make moms and dads nervous if they have never mastered these subjects themselves. And even if they have, they may feel rusty or out-of-date.

There is also the matter of time, since these classes can be rather time-consuming. Particularly in larger families and in homes where both parents work outside the house, it isn’t always possible to be primary teacher and hand-holder during every one of the tougher classes in high school. Besides, by the time students reach this age, lots of parents don’t want to, either.

Every parent has probably had this question at one time or another. I recently heard from a mom who said, “I want my daughter to get the best education she can but I don’t think that would be the case if I tried teaching her these courses.”

Luckily, when homeschooling, this is not a problem. Nobody knows everything. It’s OK. Modern homeschoolers have many choices when learning the tougher subjects.

These include:

Partnering with other parents who possess the skills or expertise you lack, and group the students to learn the subjects together. You teach (or supervise) the classes you can, then ask other parents to teach the ones you cannot.
Joining a homeschool co-op where these subjects are offered at the level your child needs. If no co-op exists, starting one isn’t difficult, either. In fact, starting one that offers exactly the topics your student needs to learn can be the perfect solution.
Enrolling the student part-time at a local college, adult center, technical school or high school . Most communities offer courses in many subject areas for around the same price as a good textbook and answer key, or an online course.
Purchasing curriculum products for high school credit. Courses exist for most anything a student might want to learn, from web design to playing the piano. Most include detailed lesson plans and resources, too, therefore students can usually work entirely on their own.
Inquiring with a local support group or phoning a homeschool volunteer will often uncover other options that may not be as obvious. Connecting with other people is sometimes the only way to find out about people in the group or in the community who offer tutoring services, mentoring programs or might be willing to teach a subject to local school children who have an interest.

Don’t fear the high school years, as there are many solutions for teaching “tough” subjects. After helping to connect students to the world of available resources, parents may sit back and watch the learning take place, often without needing to be involved with delivering the difficult subjects at all.

Earning credit for life skills

Advance high school credit

Lab science

College-prep homeschooling

High school math (series)

Mar 16 2013

High School Math: Learning and earning credit with greater ease

In a previous post, you read how success in high school math plays into the process of college admissions. The facts were pretty clear: high schoolers need math to get into college, and high school math includes algebra and beyond. Most high schoolers, that is, meaning those following a traditional curriculum path, who are seeking traditional college admissions. Case closed.

But, wait a minute. Do kids without math ever get into college? Aren’t there colleges that don’t care about math? And what about unschoolers — don’t they attend college, too?

In this post, you’ll hear about exceptions. You’ll learn 2 different ways to receive credit for math experience — not the number of math courses completed — practices which may appeal to readers taking a different path toward achieving math understanding. Links are also included at the end of this post; these may be of particular interest to unschooled students and others looking for a non-traditional way to learn math in high school.

Demonstrating competency using examinations

While it is true that most colleges require 3 or 4 credits of high school math, students may attempt to demonstrate competency without having credits on the transcript. Subject examinations offered through The College Board are one way to demonstrate math competency in college with or without ever taking a formal math class in high school. Students should begin by inquiring at the college of their choice as to whether subject exams can be used to document math proficiency. Sometimes, taking one or both math exams provides all the evidence a college needs to insure the student understands algebra through precalculus or trigonometry and the student may be considered on that basis alone. Note that not every college accepts subject exams, and even those that do may not consent to using results in this way. It is up to students to find out, or find other colleges that will.

Students without traditional math preparation may also inquire as to whether the colleges of their choice accept CLEP examinations through The College Board. Though not all colleges accept the CLEP either, those that do may allow credit for tests passed in one or both of the math exams presently available through CLEP. In some cases, these tests provide a way for self-taught math students to demonstrate what they already know. Even better, students who pass CLEP exams earn college credits, too, and never have to take the class in college, either.

Find a college that de-emphasizes math

Choosing a college is hard enough. Finding a college willing to accept a student with little or no math experience can be even harder. But colleges like these do exist, assuming students find one they like. A thorough college search may uncover colleges that do not require the SAT and schools that admit anyone who applies. There are tuition-free colleges and colleges that aren’t really colleges at all. Students may also search for colleges that emphasize math scores less than others, admitting students who score in the lowest percentile on math exams. These searches can be performed using college guides available in most bookstores and using free online search engines, too. The best insurance, however, comes from speaking directly to college admissions officers and staff who are familiar with non-traditional and/or homeschool applicants to see if the student stands any chance of gaining entrance.

Demonstrating competency using portfolios

What if a graduate “gets” math, but just demonstrates it differently than other high school graduates? That is where a student portfolio comes in. Just like a resume or a biography, a student portfolio reflects the unique experiences and characteristics of the student it represents. If a student can demonstrate an understanding of mathematical ideas, whether practically or conceptually, colleges may be persuaded to take a look. Careful portfolio preparation could make the difference between a student who lands a personal interview at a college and one who does not. Portfolios may include anything that paints a complete picture of the student and his or her understanding of the mathematical world, up to and including the level expected by college admissions departments. With alternatives to traditional classroom schooling growing in number every year, many colleges are becoming more able and willing to discern information and evaluate students based on mastery and not just coursework alone.

Just learn the math!

With all that said, there is still so much to be said for just learning the math. Today’s high schoolers have so many options for learning math with ease that it seems silly to deny a student the chance at success if they want it.

Courses on computer, video and DVD are plentiful and may be just the ticket for students who are unable to learn from books alone. Courses like Math U See and Teaching Textbooks are just two examples of products that many families have found extraordinarily helpful for teaching math at home.

Math tutors are found in every community and the good ones have no difficulty teaching high school math and preparing students for college admissions exams. Parents who feel they lack the ability to teach math themselves or help with student homework may hire a tutor for sessions once or twice each week until the student feels comfortable completing the work alone.

Test centers and online seminars all over the country offer math practice and test preparatory courses. Study materials are available online and at bookstores all across the country, too. Many students successfully study for the SAT and other exams simply by taking practice exams from previous years. Others use test materials to key in on the kinds of questions they need to study, or hone in on subjects they need to study a little bit more.

Adult education programs are well-known for offering remedial math courses and math for those who have been out of school for a while. These courses may sometimes be used for high school credit and often provide transcript documentation, too.

Don’t forget the many private schools and curriculum suppliers who offer free homework help and online tools, either. Homeschoolers may join these programs in 9th grade and stick with them, or can jump in during 11th or 12th when studying for math exams becomes more of a focus.

Not every student may be a math whiz or enjoy math, either. But no student needs to fail with the number of resources available today. Changing ones attitude about math and finding just the right combination of tools can prepare a student just enough to gain admission and pursue a dream. Leave no stone unturned when it comes to finding what works best.

Internet articles for continued reading:

Math (a collection of articles compiled by HEM Magazine)

Zen & the art of unschooling math (Life Learning Magazine)

Unschooling and math (Sandra Dodd)

Unschooling Math (from Growing Without Schooling)

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Mar 16 2013

High School Math: What is really needed for college admissions — and why?

Do college-bound homeschoolers really need algebra in high school? And if they do, can anyone explain why? Parents and students ask this all the time. Humorous infographics have even begun circulating suggesting that many years may pass before most people ever need to use algebra at all.

To parents who worry about teaching algebra and calculus at home, and to students who don’t like the subject at all, these are critical questions. What if high schoolers cannot succeed in the high school math courses that everyone says they’re supposed to take? What really happens to high schoolers who don’t have the math skills required for college admissions? Can they still get in? Or, should these students seek certificate options and hope to land careers in areas that do not involve math at all?

This is a touchy subject for some people, but an important one. Those who understand algebra sometimes dismiss it as whining or laziness on the part of the students who struggle. Those who are the ones struggling wonder whey they must demonstrate proficiency in something they’ll probably never be able to understand at all. Though future STEM careers necessarily require math, surely there are many career paths that require little or no math at all — ever. So, why is is fair to require the same courses of all students, even those who plan to pursue non-math options in college anyhow?

These are all good points. But, alas, they make little difference when it comes to taking high school math.

The truth is, college-bound students need the math. Public, private, charter schooled students need it. Homeschoolers need it, too. There’s no way around it.

Below is a list of facts about high school mathematics and college admissions. Like them or not, these represent the status of college admissions today. And while homeschooled graduates are easily accepted into colleges, and though colleges occasionally revise their admissions requirements, these math requirements are not likely to change any time soon.

Fact: Most American colleges require applicants to demonstrate success in high school math from algebra on up. These courses include algebra, geometry, precalculus, calculus, and higher.

Fact: Colleges do not make substitutions (for homeschoolers or any other applicants) when it comes to math requirements. Classes like remedial mathematics, consumer math, business math, Accounting, and Finance may be taken in high school as desired and may offer valuable preparation for life. However, mastery in these practical areas — even with extensive documentation to justify transcript credits – will not result in a waiver or substitution for algebra or other higher level math.

Fact: Admissions officers at traditional colleges seeking traditional applicants assume 3-4 years of high school mathematics completion for basic consideration. Different schools have different eligibility requirements for math — for some, it may be a 2.0 or ‘C’ average in math; for others, it may be an ‘A’ or ‘B’. This is one of many requirements that helps determine which student applications make the first cut and which do not. Students who do not present with the number of required classes and the minimum scores are not considered for admission.

Fact: Most colleges today require students to take college entrance exams (SAT, one or more subject exams, or some combination thereof) as part of the application process. What’s more, some colleges (just one of several examples of colleges that do this HERE) may even require more validation of high school math credits from homeschooled applicants.

Fact: The SAT requires a knowledge of algebra and geometry to pass. Even students with superior scores on the english and writing portions will receive lower overall scores once math scores have been added in to the combined total.

Fact: While there are exceptions (a handful of colleges that do not require test scores) colleges have a minimum passing score for the SAT exams. Students who do not take the exams, or who do not present with the minimum passing scores are not considered for admission.

Fact: Though several new college/un-college experiences are being introduced, these are either relatively new or not yet available for widespread use. They have neither gained acceptance by graduate schools nor the confidence of potential employers, either. It will be many years before students graduating from these programs have proven themselves and the public recognizes alternative college experiences as options to traditional college degrees.

Like it or not, for college-bound homeschoolers, high school math is here to stay. Homeschoolers must find ways to prepare themselves for college admissions by taking the required number of math courses in grades 9-12 and succeeding the very best they can.

Chin up, though. An upcoming article will cover ways to prepare homeschoolers for high school math complete with product solutions for teaching it when other methods have failed. Subscribe to the feed and it’ll arrive directly to your Inbox.

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Internet articles for continued reading:

Is Algebra Necessary? (NY Times)

Why learn math? (Scott H. Young)

Examining how mathematics is used in the workplace (Mathematics Association of America)

Photo: Moreau

Jun 16 2012

Choosing a math curriculum

Choosing which math curriculum to use in homeschool is a question for many parents. Like selecting other curriculum products, it can be a big decision — and one that frequently comes with a hefty price tag, too.

But for a variety of reasons, teaching math in homeschool seems to come with an extra set of worries for many families. Among them, the idea that some children are “not good” in math, that some kids are not mathematical or “do not need” math anyway, that some parents aren’t “good with math”, and that many adults report never needing most of what they learned in math anyhow. Do not doubt the influence of these factors when making purchasing decisions, because – consciously or not – every one of these concerns and stereotypes ultimately plays a role in the choice of which math system to adopt for the homeschool.

Even after making the decision, many parents still question if they’ve made the right choice. There isn’t a parent among us who hasn’t wondered if a change is needed somewhere down the road. This is okay — and happens all the time. Changing math systems is a common practice among homeschoolers, in large part because parents have now learned what their students can actually do, and sometimes because they realize their initial instincts were just incorrect, requiring a different format or a different level of preparation altogether.

But there is great news about finding a math curriculum for today’s homeschoolers. Today’s families have so many different options to choose from, there is truly something for everyone. No matter the kind of learner, the curriculum format desired, the math application sought in the future, or the dollars in the budget, modern families will find a math curriculum to match. Better yet, if the first one turns out not to be the best fit, there are dozens more to try the next year!

The marketplace is full of math textbooks, workbooks, worktexts, software, audio and visual math systems, online classes, subscription services and more. We’ve compiled a list here of some of the most popular and the most effective math systems, including those most recommended by parents. But, remember, just because something isn’t on this list doesn’t means it’s not worth a look. As with everything homeschool, what works for one family may not work for another…lesser known products and hidden gems found in smaller bookstores or curriculum sales might be just what a family may be looking for.

A Beka Math

Aleks Math

Horizons from Alpha Omega

Making Math Meaningful

Time4Learning (see sidebar for affiliate links and discounts)

Touch Math

Is it your child or your math curriculum?

What is Spiraling?

A good calculator

Nov 22 2011

Re-framing ideas for greater understanding

“Math is just another name for making something simple sound really, really complicated,” my child said, adding, “Why do they have to take something so easy, and make it sound so hard?” His statement gave me pause. Remembering my own struggles with astronomy and physics, two things I could never particularly “get”, I knew exactly what he meant.

His statement came after I explained a mathematical concept he hadn’t been able to grasp by reading the book alone. I had showed him a way to solve the problem in fewer steps, steps that made a lot more sense to him. I had also re-framed the concept into something he already understood, turning an abstract idea into something real to him. Luckily, mathematical concepts come easy to me. Though I’m not always able to do this for every subject they learn, thankfully I have been able to get all of my kids through their occasional math challenges drawing on my background and my own brain-power alone. So, I drew upon my skill and got him through it. He learned. And I did, too. Again.

I’ve said it before and I’ll say it again…as long as I homeschool my kids, I realize something new about them, and about learning in general, every single day. What I was reminded that day was the importance of re-framing certain ideas into something real for certain children. Undoubtedly, not every child is going to need this. But some do. My kid did. And this is very important to recognize, because by adding the technique to one’s homeschooling toolbox, it may just come in handy at times.

What do I mean by re-framing? Re-framing is looking at an idea in a different way. Imagine removing a painting from its frame. Now imagine removing an idea from its context…

Remember word problems? These are problems, math problems for instance, that are supposed to sound like real-world problems, requiring children to read through a story and decide upon what to do. Word problems ask kids to figure out what kind of math is needed amidst a whole bunch of other information that may or may not even be relevant to the problem.

Re-framing a word problem in math might involve coming up with a different problem that asks the very same thing. It might mean assigning the problem as a math sentence or algebraic equation instead, without any of the words at all. Or it might mean using other math techniques that have already been mastered and solving it a different way, too. Maybe even an easier way. Whatever works for that child.

So, re-framing is removing the question or problem from its context and putting it into a different context, or looking at it from a new perspective, or substituting some of the facts for something kids already understand.

In mathematics, a couple of examples of re-framing might be:

1. When teaching percentages greater than 100 (e.g., 110% or 160%) use sales tax as an example. Most children understand making purchases and having to add sales tax. Instead of problems involving some parts greater than a whole (abstract), ask kids to calculate the total purchase price of something they like (i.e., a video game or pair of boots) instead. Teach that calculating sales tax (the part greater than the whole isn’t enough. Reinforce that sales tax must be added to the retail price of the item (the 100% part) in order to arrive at the total cost.

2. When teaching simple statistics, re-frame problems into real-life things kids can relate to. Instead of looking at coffee-growing or population increases (which do not directly apply to them), ask students to analyze things they know — like allowance received, number of levels beaten in a game, monthly cell phone minutes used, and so on. Ideas like Mean, Median and Mode become very real when involving scenarios they understand. Conjuring up word problems using these ideas can translate into solving the problems in the book much easier later on.

3. When learning the difference between Area and Perimeter, come up with stories illustrating the difference. In our home, I always used examples involving our dogs (digging up every square foot of the yard, or running along the length of the fence). Use any examples that might make sense to your children. Re-frame the problems using different words, different examples, or using some technique they already understand (linear feet measurements, how tall they are, stacking square cubes in a box, or whatever it may be).

Re-framing idea applies to other subjects, too. In writing for example, re-frame ideas so that students can relate. Not every child may understand the purpose of writing a Persuasive Essay. But most will be able to relate to writing an essay in which he or she tries to convince you of something (a later bedtime, decrease in chores, extra cell phone minutes, or having to complete fewer math problems!) or argue their point of view (think teens here). Relating scientific concepts like acids and bases or certain chemical reactions can be re-framed into examples involving baking or cooking, hair coloring, or anything else your kids will understand.

With re-framing, try everything. Be creative. Try different approaches. Think out of the box. Blurt out anything, even if you think it may sound silly or dumb. You never know what your child might pick up on. Ask your spouse or other children, too. Sometimes other people have a unique way of looking at things that can help someone else. Somehow, something will eventually work. Notice when your child’s eyes light up and finally “gets it”. You may be surprised at what it took to convey an idea (and remember what you did for next time)!

The lesson I learned with my child that day was to remember to re-frame mathematical concepts when he needs me to. What you can take away from this story is that re-framing can be useful in many areas of homeschool — and in life, too, by the way. Most parents already know how to do this. How often have you asked your child to pick dirty laundry off the floor or eat his fruits and vegetables? How have you been able to convincingly explain the importance of doing these things? Applying the sames kinds of thinking and logic can help to re-frame school concepts, too. Looking at problems differently – re-framing them in terms kids understand – can work as well in school as it does in life. Every student can understand if something is explained correctly. By re-framing problems, you can help get your child through trouble spots this way.

[Image: Free Digital]