Homeschooling Calculus with Saxon, First Edition

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UPDATE from 2024: My kiddo who used Saxon Calculus, First Edition her junior year of high school achieved a very good CLEP score on calculus. (She used the CLEP booklet to prepare for the CLEP test, and she had a few gaps that she filled in with self-study that we either had not gotten to at the end of the Saxon book or that were weakly covered by the book.) She enrolled in Calculus II as a dual credit at our local university her senior year and is doing excellently thus far. So her calculus journey was paved well using Saxon Calculus, First Edition.

POST: I wrote a post in 2022 regarding homeschooling with Saxon calculus, using the second edition of Saxon Calculus. I wasn’t happy with the progression of that second edition textbook for us. For my next round of teaching homeschool calculus, I changed and used the FIRST edition of Calculus by Saxon and Wang. We have used it this year for calculus. I am very, very satisfied with it. Very glad we changed. Very. It has been smooth.

It is weak on graphing calculator material, so that needs taught if your student has not learned that for another class.

Another minor concern is that because it is the first edition, some typos exist. HOWEVER, I learned this was easily remedied by pulling out the second edition text and solution manual that I’d already invested in. Although the lessons in the first edition and second edition do not match up by problem set number, in general, the lessons have been moved around “en bloc,” keeping the problem set together, just moved.

It has been helpful to have the second edition because it sometimes works out problems in the solution manual better or explains things a bit better than the first edition. So as a supplemental text the second text has been valuable.

BUT the sequence of calculus topics in the first edition is much more conducive to homeschooling by someone like me than the second edition.

Note: I think the second edition is geared for AP takers. We will not take the AP tests. I am not a fan of them. Too “box-like.” However, I have learned that it is a good idea to have your homeschooled students CLEP subjects that you feel they have mastered if they plan to go to college. So I do make sure that we cover everything in our book that is on the CLEP.

That’s just a quick update and blurb on our experience for those seekers out there. Here is that post I wrote before on the first edition:

Homeschooling with Saxon Calculus

And lastly, all in life is well. We are having fun.

Terri F

Do My Kids Ever Ask Me to Go to School?

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3/4/22

Yes, have they! There have been times my kids have asked me to send them to real school. How many times? I don’t know. Definitely depends on which kid. Definitely depends on the age. I’ve noticed the requests the most from about 4th grade to about 9th grade, depending on the person.

This is the time, I feel, when their personalities, the identity they choose is emerging and budding and growing. They want to know. They want to fit in. They don’t want to miss out. They feel like mom is holding them back from the herd. It’s all mom’s fault.

Sometimes it’s easy to divert their arguments about going to school.

For example, my kids wake up on their own morning rhythm to do school. So sometimes pointing out that many kids have to get up each day, every day at 6:00 am to get to school quiets their requests. Also, my kids are done with school when their work is finished. Some days, my kids can finish school early. Pointing out that kids are in school from 8:00 am to 3:20 pm and go home with homework can diminish requests to be sent to school.

Then, other times, it’s not so easy. I’ve done all the right things, like trying to figure out what the daughter feels she is missing, trying to enroll her in activities to fulfill missing gaps (art classes or extra-curricular sports), trying to change up how I teach material. But the requests and accusations keep coming.

And for us, it has never been, “Hey, Mom. The high school here has the most amazing math class. I’ve heard great things about it. Think I could try it?” It has been about people. They want to be with people and have people things, depending on the age: lockers, buses, clubs, a crowd to belong to. And I get it. I like people too. I had these things. I’ve been there.

You’re ruining my life.

I can’t remember if one of my daughters has actually told me, “You’re ruining my life.” I’ve certainly felt the idea steaming off of them at certain times, even if they didn’t voice those words. And I do very, very much take note of their frustrations and work as hard as I can with them to meet their needs socially without sending them to school.

As much as school might allow opportunities for “a group,” it is kind of a strange socialization system to me. All the same ages pushed together. A weird hierarchy. Little autonomy. I just prefer to educate my kids at home and then help find them socialization opportunities in other ways.

Usually, the desire to go to school at our home revolves around nothing academic. I make it very clear that I am confident in the academic fiber of their homeschool. I let them know they can have people over to our house whenever they want. I’ll let them try activities they want.

No matter what I say, there have been two or three times when I finally just had to say this:

“I’m not here to ruin your life. If you think that school is the answer and will give you what you need, I will set up the appointments for us to go meet with them. I will let you go investigate and ask them questions. If you still want to go after interviewing them, then you can go.”

I homeschool because I want my kids to have a great education. I want them to know their family. I want them to have more time to learn diverse topics that they might not have time to learn well if they went to school (Spanish, how to play an instrument, and art). I want to give them the opportunity to explore more of the world through learning.

But if one of my kids really, really thinks that school will fix her problems, and I’ve tried everything, then I have to let her try. But not till after we’ve turned every other rock.

Another reason that I homeschool is so my kids can learn to express themselves under the guidance of a woman who loves them, tries to understand them, and who wants them to learn to communicate their true wants and needs.

If after lots of talking and trying everything else and looking at the heart of matters and also looking into the future of their education with them and their life goals they still want to go meet with the school hierarchy, we will do so.

But I’m graduating one this year, and she stuck our school out!

Terri F

Why Would You Quit?

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2/25/2022

I forget that quitting your career as a medical doctor to homeschool your children intrigues some people. “Why would you go through all that work and then quit?” It was mentioned to me a couple of times this last week, so I thought I might write a little more about this today and in the weeks to come. There was a lot of processing to do to swallow my pride and follow the path I knew I needed to take.

Deciding to stop practicing medicine was a hard, humbling decision, but the decision was already made for me by the fabric of who I am and what drives me.

There is nothing on this Earth more important to me than the integrity and well-being of my family. Every decision I make revolves around the stability, wholeness, and health of our unit.

I don’t care what the world says. Children are given to parents to foster, encourage, instruct, care for, nurture, feed, provide for, learn about, and develop a relationship with. A secure family is truly an amazing, comforting flat stone which your foot rests firmly on when you’re stuck in the mud of the world and can’t see your feet beneath the sludge. You stand on that stone strong and know that you can’t sink because it’s there, holding you steady till you can get out.

I Can Do It

I believe that somewhere says to every mother, “You are the best woman in the world to care for these kids. Can you do it?”

When I was asked, I stepped up boldly, and I said, “I CAN. I will do it. I will take my job seriously. I won’t let anyone down. My life depends on it.”

My life depends on it??!? Yeah. Frankly, I can see into the future. Well, not like that. But I am pretty sure that I’m going to be a pretty worried and frazzled mom for the rest of my life if my kids get into drugs, alcohol, choose a crummy husband, can’t hold a job, suffer from mental illness, can’t handle their finances responsibly, or can’t figure out how to parent their own children positively and responsibly. I want to be a dump and run grandma, not a raising grandma.

When I was in high school, my mom once remarked to me, “One of the most important things you can do is keep your kids off drugs and alcohol.” I observed, after she pointed this out to me, that many of my friends got involved in drugs and alcohol in high school, so I decided the time up to this time and this time itself, must be very, very formative, difficult times for children. (Duh?!) I challenged myself that when I had kids, I would work very hard to help them have the tools that my mom and dad gave to me which steered me away from drugs and alcohol.

From my mom, I learned how to be an emotionally connected and involved mom. From my mom, I also learned that a mom can show enough interest and give enough help in her children’s schooling that they can become lifelong learners and great students. My mom, from a poverty-stricken household of seven kids, only completed high school, but she could do basic math, spelling, and grammar, and she helped me do those things as long as she could, till my academic knowledge surpassed hers.

My mom was the best woman to raise me, and she took that seriously. Now, it’s my turn. And one day, it will, perhaps, be my children’s turn to answer the question, “You are the best woman for this job. Can you do it?”

What’s Inside Your Box?

Good mothering sets my kids up for peace, joy, and happiness. FROM THE INSIDE OUT. NOT THE OUTSIDE IN. There are many, many, many, many, many “boxes” (households/families) in the United States which put up the appearance of happiness. Inside, though, is a pain and hurt that I can’t imagine. I know it. I hear it first-hand. I’ve seen it. Severe verbal abuse and belittlement. Manipulation. Physical abuse. Molestation. Depression. Alcoholism. Drug parties. Denial. Hidden anxiety. Anger. Rage. 

Well, I’m growing long. I quit my career because I know myself well. I had to invest in my family. Even if it meant giving up money, prestige, power, reputation, helping others, and years of hard work. In order for my family to have what I wanted it to have, this is what I needed to do. I want true happiness for people. An inner happiness that can’t be stolen. I want it for me, and so I took it.

My “box” (my home and family) is genuinely happy. Sometimes I hesitate to say it. Like I have something I don’t deserve. Or I have something I shouldn’t tell others about. Or if I say it, it will all crumble away, and I’ll be made a fool. Or people will think I don’t have bumps in the road. Or I’ll be labeled a white woman born into it.

But, yet, if I don’t say it, perhaps it won’t be known that it is possible to have true peace, joy, and fulfillment within families. Perhaps people won’t realize that each decision they make is impactful, that if they didn’t just go around doing it the way it’s done or hiding from the hurt or choosing things which distract from the integrity of their families, that they could have that true peace and calm they are searching for in their families.

Well, anyway. Have a great Friday and weekend. Remember, the world happens, but nobody can steal our inner peace unless we give it away. So if you’re angry or unhappy, you’re giving your peace away. 

Terri F.

 

**Note: The only thing in front of my family is my Faith. I would be wrong if I didn’t mention this because that is how I know to go after the Peace that can’t be stolen.

More on Crumbly Bone Prevention

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My husband saw another adolescent athlete with surgically soft bones. (Back in 2019, I wrote my first post on “crumbly bones.” You can read that post here: Crumbly Bone Alert.) He has to drill holes and put anchors, screws, nails, and pins into bone for what he does, so he sees first-hand whether someone has good bone integrity or not. And increasingly he is seeing normal-appearing, healthy-looking kids with soft bones. Even more distressing is that these kids are high school athletes. They should have strong bones, not soft, flimsy bone.

It’s bad enough when he sees middle-aged women with soft bones, but even more ominous when it’s active kids with no known risk factors. Once, when probed about diet, the mom of one of these youths with weak bones frustratedly replied that her child would only eat two very specific processed, boxed foods. The mom had encouraged other foods to no avail.

Kids Bones are Suffering

“Crumbly bones” are increasing in our kids. In 2003,  a study out of Rochester, Minnesota (USA) looked at the occurrence of forearm fractures in youth and found that boys were 32% more likely to have a fracture when compared to the past 30 years, and girls were 56% more likely (Khosla, 2003). Often-times, these changes of “soft” bone cannot usually be seen with the classic DEXA scan, so it’s not even seen readily with our normal bone density evaluations (Kalkwarf, 2011). And since a broken bone here or there is considered somewhat a normal right of passage for kids, unless the break occurred with exceptionally little incidence, there will be no medical instruction on unhealthy bones and how to take care of the skeletal system with diet and exercise. Doctors and parents aren’t thinking about “crumbly” bones in an otherwise normal, healthy kid.

I guess what I’m trying to say is that this is probably a silent epidemic. That lots of youth probably have poor bone integrity, and we just aren’t catching it.

It’s Not too Late to Start Strengthening Bones at Any Age

But this post isn’t just about kids. Yes, it’s better to play “keep up” with bone integrity than “catch up,” but I have read reports of osteoporosis improvement in elderly patients, either with regard to bone mineral density or with decreased fracture risk (Iwamoto, 2014; Shanb, 2014). There are things you can do now to make bones better.

Today I will touch on vitamin K2, which I mentioned in the first post linked to above.

VITAMIN K2

Bones need vitamin K2 to be healthy. You may also see vitamin K2 referred to as MK-4 (menaquinone-4) or MK-7 (menaquinone-7), the different numbers identify slightly different chemical forms of the same vitamin. (There are even more numbers/forms than this, eg MK-9 or MK-11, which may or may not be important. There are not enough studies yet to know.)

Vitamin K1 and Vitamin K2 Have Different Roles So Don’t Think of Them as the Same

Vitamin K2 should NOT be confused with vitamin K1. (And neither vitamin should be confused with potassium, an important electrolyte whose symbol is a simple “K” on the periodic table.) Vitamin K1 and vitamin K2 are both very, very important, but the expanse of their jobs differ. When you read, you will undoubtedly see vitamin K1 and vitamin K2 lumped together, which is a real travesty. They have different roles and both are needed.

Vitamin K2 Helps Hearts, Blood Vessels, Brains, and Bones

Vitamin K2 is a vitamin which scientists somewhat recently recognized–or at least recognized the significance of. Many American doctors will not even know about it, even though in Japan they have been using high dose vitamin K2 supplementation for osteoporosis treatment for years. (Iwamoto, 2014) Vitamin K2 has profound effects on our blood vessels, brains, bones, immune system [Linneberg (2021) even showed it affected Covid outcomes], and skin.

With regard to bone, Vitamin K2 helps take calcium and put it in bones and teeth. It keeps calcium out of the lining of our blood vessels (think of cardiovascular disease with the calcified plaques blocking blood flow) and tissues and puts it where it belongs.

How Does the Body Get Vitamin K2?

You can get vitamin K2 through different mechanisms. The really confusing thing about vitamin K2 is that its content in foods is unreliable and unpredictable. And some foods might have MK-4, while others have MK-7. And still others might have some of the lesser studies forms of vitamin K2 like MK-9 or MK-10.

Adding to the confusion is that you’ll see some researchers swear by MK-7, while others say MK-4 is fine. It’s often quoted that MK-7, which is found in plant sources of vitamin K2, has a longer half-life and sticks around longer, so it’s better. Others argue that MK-4 is what is present in all animals (so, of course, that’s what we should use), and that it does not stay in the blood because it is “sucked up” by our tissues.

I don’t know. My consensus is to look at the vitamin K2 food list and try to add those foods in. Try to eat more vegetables. And supplement as needed.

Your body gets vitamin K2:

By eating egg yolks, butter, certain cheeses, organ meats, fish eggs, and fermented foods (like sauerkraut or a Japanese food called natto). The problem here is that a food type can have differing levels of vitamin K2 amounts, depending on what an animal is eating or how a cheese is made. So “Brand A” of butter may have less vitamin K2 than “Brand B.” And “Brand A” may have a different vitamin K2 in May than it does in August because the cow is grazing on different grass quality. Vermeer (2018) has a great article with vitamin K2 levels of various foods. Check it out. Chris Masterjohn, PhD, has an extensive page on vitamin K2 and has a spot where you can type in the food to see how much vitamin K2 is in it. Check it out.

By converting excess vitamin K1 to vitamin K2: The human body can convert excess vitamin K1 to vitamin K2. The problem with this is that most humans do not eat enough vegetables and leafy greens to even get enough vitamin K1 for optimal health, so there isn’t much, if any vitamin K1 leftover to turn into vitamin K2. A second confounder is that different people have different processing capabilities, so some people might have “good” genes for vitamin K1 conversion while others do not. A third confounder is that vitamin K1 is best absorbed with fat, and many health-conscious people are low fat.

By your gut bacteria: Your gut bacteria can make vitamin K2. The problem here is the disrupted gut bacterial flora that is very common now, contributed to by antibiotics and poor diets.

By vitamin K2 supplementation: Different formulations can degrade over time, leaving uncertain vitamin K2 levels (Orlando, 2019).

What’s a Person to Do?

So if vitamin K2 is that important, and yet our available sources are that unpredictable, then what’s a person to do? Throw hands up in the air and say, “Life sucks. This is stupid. I can’t do this anymore?” NO! Regularly include the sources you can food-wise. Do what you can! If you can’t eat these things, look at lists and see what you can eat to get K2. If you can’t eat anything, then supplement. Read all about vitamin K2 (the Masterjohn site I linked to above is exceptionally extensive and easy to read).

Eat more egg yolks.

Use butter.

Eat more vitamin K1-rich leafy greens and vegetables. Cook them with butter or olive oil to absorb more vitamin K1 to potentially convert to vitamin2.

Order sushi with salmon roe or some other roe.

Use cheese. Different cheeses have different K2 levels, so check out the lists.

Eat fermented foods like sauerkraut or kimchi.

FInd some vitamin K2-rich foods and eat some daily for your bones. Feed them to your kids for their bones. Every choice. Every day. Adds up.

Terri F

NOTE: Those on warfarin (Coumadin) should not increase their vitamin K2 (including from foods) without a doctor monitoring them closely.

Citations:

Khosla, S., Melton, L. J., Dekutoski, M. B., Achenbach, S. J., Oberg, A. L., & Riggs, B. L. (2003). Incidence of Childhood Distal Forearm Fractures over 30 Years: A Population-Based Study. Journal of the American Medical Association, 290(11), 1479-1485. https://doi.org/10.1001/jama.290.11.1479

Kalkwarf HJ, Laor T, Bean JA. Fracture risk in children with a forearm injury is associated with volumetric bone density and cortical area (by peripheral QCT) and areal bone density (by DXA). Osteoporos Int. 2011;22(2):607-616. doi:10.1007/s00198-010-1333-z

Iwamoto J. Vitamin K₂ therapy for postmenopausal osteoporosis. Nutrients. 2014 May 16;6(5):1971-80. doi: 10.3390/nu6051971. PMID: 24841104; PMCID: PMC4042573.

Shanb AA, Youssef EF. The impact of adding weight-bearing exercise versus nonweight bearing programs to the medical treatment of elderly patients with osteoporosis. J Family Community Med. 2014;21(3):176-181. doi:10.4103/2230-8229.142972

Linneberg A, Kampmann FB, Israelsen SB, Andersen LR, Jørgensen HL, Sandholt H, Jørgensen NR, Thysen SM, Benfield T. The Association of Low Vitamin K Status with Mortality in a Cohort of 138 Hospitalized Patients with COVID-19. Nutrients. 2021; 13(6):1985. https://doi.org/10.3390/nu13061985

Orlando P, Silvestri S, Marcheggiani F, Cirilli I, Tiano L. Menaquinone 7 Stability of Formulations and Its Relationship with Purity Profile. Molecules. 2019;24(5):829. Published 2019 Feb 26. doi:10.3390/molecules24050829

Vermeer C, Raes J, van ‘t Hoofd C, Knapen MHJ, Xanthoulea S. Menaquinone Content of Cheese. Nutrients. 2018;10(4):446. Published 2018 Apr 4. doi:10.3390/nu10040446

Five Tips to Feel Better this Winter (or at Any Time)

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2/11/2022

I’ve done right well this winter, but my motivation started finally freezing this month. And it’s usually too cold for the salt to work. When I was growing up, my mom always told me, “If you’re feeling it, someone else probably is too.” So today I thought I would give us all (me included) a little winter pep talk.

Life and health is mostly a series of many, many small decisions made every day. Here are some good February decisions.

Play feel-good music from a feel-good time in your life.

“The past which is not recoverable in any other way is embedded, as if in amber, in the music, and people can regain a sense of identity. . . ” — Oliver Sacks, Neurologist

Musical memory is powerful. Several years ago I watched a video on Facebook about the power of long-remembered, beloved music on our brains.  A woman named Gladys has severe Alzheimer’s dementia and does not communicate much. She is able to tap along to familiar hymns as a clinician, Naomi Feil, sings. However, when a particular song is sung, Gladys starts singing with Naomi, a real communication breakthrough. (Video)

I suggest listening to music from a happy time to help when life is tough, you need a boost, or just to feel good daily. Research shows that listening to long-known music activates memories about oneself and emotional responses related to those memories. Specifically in one research study, “Exposure to long-known music preferentially activated brain regions including the medial prefrontal cortex, precuneus, anterior insula, basal ganglia, hippocampus, amygdala, and cerebellum relative to recently-heard music. These areas are involved in autobiographical memory and associated emotional responses.” (Thaut et al, 2020)

February is a hard winter month! Play music. Play it strategically! Think of eras you were happy, hopeful, and/or carefree and start dosing yourself up from songs from that time. Add movement and dance to it for even more potential benefits.

I use music apps because when I pick a song, they’re great at picking other songs from the same era. And I keep a little wireless speaker in the kitchen to connect to. Sometimes, I feel too “blah” to pick “happy” music, but I have found that if I can just get the music on, and then start moving it up the “feel-good” ladder, I can work myself up from the melancholy stuff to bright songs which rejuvenate my feeling of hopefulness and joy or even rebellious songs which offer a feeling of empowerment (which one needs for sure in February winter).

Force yourself to seek out comedy which makes you laugh.

Pick up an old Reader’s Digest and find the funny story section. Search your phone for the best stand-up comedy or hilarious bloopers. Think back on your life about scenes which always make you laugh and giggle again!

In order to genuinely laugh, different neurotransmitters HAVE to be made! It’s like a natural anti-depressant! Why not use it? Why not seek it out? You’re probably already paying your cable bill, your phone bill, and your wireless internet bill, so why not take advantage of the comedy you can find on them which can change the chemical imbalance in your brain naturally?

What makes you sincerely laugh? Go find it! I like the site called Dry Bar Comedy to find cleaner language comedy. Here’s some stuff that made me laugh too: 13 Clean, Christian Comedians Who Will Make You Laugh Right Now.

Move. Move. Move.

It’s sub-zero and you don’t even want to leave the house. Do you have stairs? Walk up and down them a set number of times. Do you have a TV or phone? Find the work out stations. Playing music? Dance! Do you have arms? Throw in a push-up today, and try two tomorrow! By the end of the month shoot for five push-ups in a row.

Force yourself to move in an intentional way for strength and cardiovascular reasons. Make it intentional. Why? Because when you start accomplishing your intentions, it feels good, and February blues start leaving!

Give yourself permission to not feel your best, be your best, or do your best.

I’m no good at taking breaks. My idea of taking a break is to unload the dishwasher. Lately, I’ve been going through the motions, not really doing anything well.

I’ve told myself, “It’s winter. Take a break.” So I might sit and read, but I feel guilty about it. So my sitting is never really therapeutic.

In order for a break to be truly effective, one must give oneself permission to really and truly set aside the expectation of themselves that anything else must be done. When I sit, I must stop looking at the kitchen, the toys on the floor, and the kids I’m letting be on technology for me to have a quiet moment.

It’s winter, and that means that physiological changes are taking place in my body which really do not want me to be active. I can’t stop being active, but I can make it permissible to really, truly, honestly rest without guilt.

Look above the horizon.

I try to look at everything in life spiritually. I know from a medical and scientific standpoint, winter is long and hard on both the body and brain. Physical ailments are hard and burdensome on a body and brain. Life’s changes and fights are hard.

But I also know that God has asked me to stop seeing with the eyes given to me in this world and to stop feeling with the physical receptors that have been given to me in this world. I’m to see with spiritual eyes and spiritual receptors, and that means that no matter what happens, God’s peace, love, and acceptance is here. I must somehow search that out even in the cold, even in the physical ailments, even in the angry world. It is natural and human that I am distracted by these worldly negative experiences, but when I can see through them and feel true peace, then I have entered God’s realm for me. It’s the free will of thought that I have been given and that for which I humbly, and falteringly, seek.

Closing

Have a great weekend! Keep making the right choices.

Terri F

Simple Tricks for Meals: Getting Butyrate from Your Diet

4 Replies

2/4/2022

A long time ago I wrote a series on butyrate because I believed it to be very valuable for health. Supposedly decreased cancer, decreased diabetes, decreased obesity, decreased leaky gut, improved brain health, and so much more–and now improved COVID outcomes. My sister sent me an article about it the other day.

I no longer think about butyrate and resistant starch routinely, but I have developed simple habits that add buytrate-producing foods to my family’s diet each day. I wanted to share them with you and remind you to keep at food for health. I don’t know who you are reading this, but I would like you to be healthy and feel good inside and out (emotionally, spiritually, and physically). When a person feels good, they can share that true joy and it survives bumps and potholes in the road.

Simple Tricks to Add Butyrate-Producing Foods to a Diet

Eat a plain green banana.

Freeze some green bananas (I peel them.) and then use them in smoothies.

Use a green banana in banana bread. (I replace one brown banana with a green banana in the recipe. It gives it a very nice texture my kids like.)

Toss some beans onto a salad.

Toss some beans into taco meat.

Eat chili with multi-colored beans.

Eat hummus.

Bake lots of potatoes ahead of time, then eat them reheated or slice them and fry them with onions for fried potatoes.

Baked beans.

Make a big batch of rice, and then use the leftovers for fried rice.

Toss green peas into anything you can: a salad, vegetable soup, fried rice.

Serve green peas as a quick side dish.

Toss nuts onto salads, onto hummus, into fried rice.

Eat a handful of nuts.

Note: Plantains are a wonderful source of butyrate-producing plant matter! You need to be a bit more adventurous to learn to cook them, but they are a real treat we love. Raw oats and corn tortillas are also high, so if you like those and they cause no problems, go for it. My kids tend to eat oats and corn frequently, but I find they’re not pleasing to my body in various ways I try to respect. Whole grain breads are also a rich source, but I hesitate to encourage bread because there are so many additives to it–and it often replaces vegetables and fruits calorically in many people’s diets.

Closing

It’s January, and a VERY hard month for those who live in winter-producing climates. You have to be tenacious and proactive to keep healthy in winter. Move. Reduce sugar. Cut down on breads and grains and comfort foods. Give yourself grace. Give yourself a kick in the butt. But please don’t top trying. Find a path that works for you.

Eat real, whole food as most of your food intake. Please. Please. Please.

Don’t get bogged down in the dogma and the institutions and the fundamentalism and the indoctrination and the propaganda. These things can really confuse you and overwhelm you. Keep it simple. Real, whole food. Take note of your body. Eat real, whole food and see how you do. Adjust foods as necessary.

Don’t forget to add the simple and easy butyrate-producing foods to your diet, which studies suggest will help you out. Decreased cancer. Decreased diabetes. Decreased long-COVID. But keep it simple.

Eat real food to live.

Terri F.

Article my sister sent me:

Long COVID: Gut bacteria may be key

https://www.medicalnewstoday.com/articles/gut-bacteria-may-play-a-role-in-the-development-of-long-covid

Homeschooling with Saxon Calculus

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1/28/2022

Today I write to share my experience for people thinking about homeschooling using Saxon Calculus. I homeschooled my first daughter using Saxon Calculus, Second Edition. I have decided to try using the first edition for subsequent teaching rather than the second edition. I was dissatisfied with the second edition for reasons mentioned below.

My calculus background: I took Saxon Calculus (First Edition) in high school, and I had no problems. Enjoyed it. In college, I have no idea what book I used for Calculus I, but I had no issues whatsoever earning my A.

Calculus Curriculum Terminology (AB? BC? Calculus I? Calculus II?)

When you choose a calculus curriculum for homeschool or high school, it gets a little confusing and you need to know some terminology. This is what I know, which may be corrected if you know more.

The terms “AB” and “BC” are terms made up by the makers of the Advanced Placement (AP) tests. (The makers and sellers of the AP tests are called the College Board.)

The terms Calculus I and Calculus II (and Calculus III) are traditional terms used by colleges. Calculus I usually covers differentials and limits, some basic integration. Calculus II covers more integration techniques, series/sequence. (Calculus III is multi-variate and not single variable.)

If students do AP’s AB calculus, then they get the equivalent of about what is covered in college Calculus I. And if students do AP BC calculus, then they roughly get the equivalent of college Calculus I plus Calculus II.

I wonder why the AP producers did not use the traditional terminology. Does anyone know? (The initial idea of AP may have been sound, but where it has gone today seems wrong for sincere seekers of learning.)

I Picked the Second Edition Saxon

For our first go-round with calculus in our homeschool, I selected Saxon’s Calculus with Trigonometry and Analytic Geometry, Second Edition. My public high school when I was a student used Saxon Calculus, First Edition, which is about equivalent, from what I understand, to college level Calculus I. I chose the Second Edition for my daughter based on all the reviews saying that it was better, more comprehensive, and prepared a student better for the AP exam.

I was taught calculus in high school using Saxon Calculus, First Edition. And I don’t remember that book being as hard as my daughter’s Saxon Calculus, Second Edition book. The second edition has made significant edits to make it correlate with the AP exam, which covers approximately college level Calculus I and Calculus II.

My daughter does not anticipate taking the AP calculus test, nor does she plan to study mathematics (beyond potentially needed prerequisites) in college. I wish sorely I had tracked down the first edition Saxon edition I was trained on for my first daughter. But all the reviews said that the second edition was the way to go. And I was worried that my daughter would be taking classes with kids who had AP classes, so the college calculus class might be geared to the knowledge those kids came to college classes with. So I selected the second edition, which is also much easier to come by than the first edition of the book.

In hindsight, I am now aware that basic college calculus is basic college calculus, and the first edition would have been just fine for our purposes. Although the scope of many college subjects has progressed by 2022, say computer technology or molecular biology, basic Calculus I has not.

Why Choose Saxon Calculus at all?

  1. Information comes in small bite-sized bits rather than tackling complex material all at once.
  2. The explanations are thorough and written with good, understandable prose.
  3. The practice problems are cumulative, really promoting retention.
  4. With mastery of the lessons, you have a good, solid understanding and improved long-term retention.
  5. The page layout is simple and flows. Many new texts have “busy” graphic layouts, not Saxon.

Cons of the Second Edition:

  1. There is too much material in the second edition. There are 148 problem sets. (In the first edition, there are just 117 problem sets.) Also, there are more problems in each problem set in the new edition than the old edition. It actually states that the second edition is to be a three semester class. I guess that’s fine. But since my student isn’t interested in mathematics or other hard-core math related fields and she’s not taking the AP test, she could have done just fine with the first edition’s lesser quantity material, which states is to be covered in two semesters. And then, if by chance after that, she loved calculus, we could have found another text to use for advanced study.
  2. It expects students to have a complex understanding of “arithmetic series,” much deeper than was presented by the Saxon algebra and advanced mathematics texts we used prior to Calculus. (I do not know if perhaps we lack understanding of the needed advanced arithmetic series information because we used older algebra/advanced mathematics editions. Maybe the new Saxon algebra texts cover arithmetic series really well? The old ones teach it at a very basic, introductory level. NOT the level this second edition calculus book demands!) So we had to spend a lot of time learning this to be able to proceed.
  3. Some of the trigonometry equations required were also not presented as thoroughly in prior texts as this book “assumes” its student will have. So you had to go back and learn these.
  4. Not enough supplemental practice problems to do if a student struggles with a particular concept.
  5. When something is not understood, then cross-referencing with other resources is difficult. Why? Because Saxon presents learning in little pieces sporadically as you travel through the lessons. Other resources present it all-out in a discrete unit. Saxon doesn’t always call the new little pieces that are learned along the way by names that will help you cross reference to another text when you get stuck. Make sense?
  6. I guess maybe I just feel like they tried to introduce calculus “theory” and understanding too early in the lesson sequence of the book. I actually kind of enjoyed it because I had some (limited) calculus background, and I was getting to learn exactly what this calculus stuff was “doing!” But my daughter did not like that. She just needed to get comfortable with DOING the work, and then the theory might have sunk in better later in the text. But I feel like the new edition wanted to teach the kids the why early on. If you read about John Saxon’s teaching theory, he didn’t believe in teaching the why and the theory too early in his math books. It can bog down learning. I feel like the book was trying to set the user up for the more complex Calculus II topics (BC), but my user just needed to get comfortable with this new style of math! So again, I suspect I would have been happier with the first edition which doesn’t cover as much Calculus II and setting up of theory for it–then supplementing at the end of we wanted to do more advanced calculus.

Supplemental Resources We Used:

Calculus textbook by Larson and Edwards

On-line tutoring

Khan Academy videos

Calculus for Everyone by Mitch Stokes

Essential Calculus Skills Practice Workbook, Chris McMullen, PhD

CLEP Calculus

Miscellaneous Thoughts

  1. I will use the first edition for my next student, which from experience I feel does a great job with limits, derivatives, and basic integrals without bogging the learner down like the second edition does. My daughters are leaning towards health-related sciences, and they will only need one basic college calculus class. (I went to medical school. My kids are considering that. Some medical schools don’t even require math. Some don’t require calculus. Check the schools you want for prerequisites!) I really do prefer Saxon’s teaching methods, so I want to stick with Saxon. But my students do not need the more advanced topics that the second edition has made revisions to accommodate. The first edition covers basic college calculus preparation quite well without the extra fluff for AP exams. If my daughters wish to proceed to Calculus II one day, the first edition is adequate to help them do well in their Calculus I college class and give them a very strong foundation to move on.
  2. We found an on-line tutor to help us periodically. He was displeased with the sequence of the Saxon second edition book and made no bones about expressing his irritation about it with us. (Kind of stated, “Too much, too early. Why so early? It’ll just depress students.”) I know that there are on-line classes which use the second edition for homeschoolers, and if I used the second edition again, I would use one of those actual classes rather than try to teach it on my own. Those math-minded people would do a better job knowing how to teach any gaps and how to skip unnecessary lessons and problems without interrupting the flow of the cumulative Saxon program. We had to use many extra resources and time as we sifted through this. (I do not consider it wasted time…but my daughter complained a lot…but I think it taught her how to fend for herself in the academic world to get what she needed.)
  3. Another homeschooling family I know used the second edition of Calculus, and their daughter liked it a lot. Different strokes for different folks. That student likes computer programming and math. My daughter does advanced math because I make her and she might need a calculus class in college as a prerequisite for her graduate school plans (and plus I know she can do it).
  4. My daughter has transitioned well to calculus-based physics.
  5. Good luck to you whatever you decide! Have fun with it. If you’re at the this point, your child is about to graduate and move on! This is what you prepared them for! Watch them fly!

Homeschooling Happiness

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January 20, 2022

Are you considering homeschooling?

We still homeschool our four daughters. Our oldest is graduating this May. I am exceptionally satisfied with the resources available to successfully homeschool children. Besides using traditional curriculum, we have tapped the resources and knowledge of friends, family, our local community, and wonderful internet teachers. Because we homeschool, there have been no gaps in instruction due to Covid the last two years.

If you have the time, dedication, and desire, homeschooling your children provides the best opportunity for the best education for your children. It will be tailored to their learning speed, their learning style, the rhythm of the year’s activities, and their learning goals. Our eldest daughter is just one example of what a homeschooled student’s academic and extra-curricular life can look like: fluency in three languages, math work through calculus, science work through physics, proficiency in playing an instrument, solid background in reading, writing, and history, excelling at volleyball and advancing to the State championships, hanging out with friends and family, and following her own interests.

I, like schools, have had 13 years and about 8 hours a day to teach a very special person. A lot can be accomplished in that time, and if you want your child’s learning to be prepared specifically for him or her, go for it. If you are considering homeschooling, I encourage you. If you have any questions, I am happy to share our family’s experience. Homeschooling does not mean you have to do everything as a parent! It means you explore your resources and match them up with the needs of your child’s education.

PS: I have not written for a long time due to helping actively in my children’s activities locally, and also Covid has had me sitting back, watching and figuring out my place in life. But as my daughter approaches graduation, I wanted people out there who may be wondering if homeschooling is a good educational option, to know that it IS a great educational option! I watch my friends’ kids struggle to keep up with all the changes and rules of institutionalized education, especially the last two years, and I am thrilled we started homeschooling and kept at it. I want homeschooling to continue to always be an option in the USA because it has allowed my daughter(s) to have the education that I could only have dreamed of as a teenager. (By the way, I would be remiss to say we homeschooled alone, and I am grateful for every single resource in our community that we have utilized, including public and private school resources. Local and regional cooperation makes homeschooling where I live fantastic.)

Lastly, greetings to old internet acquaintances who may see this. I hope your lives are wonderful. Live locally and develop relationships if you can, beyond controversy. LIVE where you ARE. GIVE where you LIVE. —Terri F

My Preferred Resources to Homeschool

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I always remind myself that many brilliant minds throughout history created and forged many brilliant ideas with simply curiosity and readily available resources. Then, I breathe and smile and determine, if nothing else as a homeschooling family, to focus on the three R’s for my elementary students and the simple resources needed to teach them.

Here is the short version of what I think it takes to homeschool elementary-aged students who can read and write at my house. (Note: I have an 11th grader, 9th grader, 6th grader, and a 1st grader.)

READING: Easy if the library remains open!

I let my kids pick their topics to read. If there’s something I want them to read that they’re not interested in, I will use this as a read aloud and read it to them (poetry, cute science books, fun books on history, etc.).

Being well-read is beyond important, in my mind. Vocabulary. Exploring new experiences. Sticking through to the finish of a book. Heck, even PICKING the book requires lots of decision making! So much learned in simply choosing, reading, and finishing a book. Or listening to a book read aloud. Really helps attention and focus lengthen.)

So…my recommended resource for reading: Student-selected books from the library with supplemental books selected and read aloud periodically by adult. (I usually steer toward poetry, age appropriate history books, age appropriate cultural books, age appropriate science. Just a gamut and not always in any particular order. I HAVE used designed curriculum where the books were shipped to me. Two daughters did not like that. Some books were boring. Some were childish. Some were too advanced. One daughter is so schedule and plan-driven, that she did like it. The others, NO.)

WRITING: Don’t Ruin Them!

Keeping it simple with fun journal prompts, letters, step-wise instructions on how to do something kids know how to do, or writing up summaries of the books being read is a really good idea.

With my first child, I marked her writing up like crazy with suggestions and corrections. Man, was I powerful. BIG mistake. Don’t do it. Just let them write. Let them write. LET THEM WRITE. Let them write.

Sometimes, their writing won’t be long enough; then, I specify the number of words or sentences or paragraphs to get more writing from them. Sometimes they don’t answer a prompt the way you’d want/expect.

One daughter I have is super imaginative and playful. Sometimes, I never know what I’m going to get as a response to a prompt. Which is fun and great, but a little unnerving because I’m like, “This would never fly as an answer to this prompt in school…” Let it go, I tell myself. Work her there eventually. Let her voice shine, and then cultivate it over the next 5-8 years.

(Which is an advantage I have. I KNOW I’m sticking with this homeschooling. I have a long term vision and can slowly move my kids toward the goal. I don’t have to get them writing excellent paragraphs in 4th grade. I can allow their creativity to shine and know that I can work on grammar in 5th, 6th, 7th grade–when they’re more receptive to grammar and more tedious type thought.)

But speaking of grammar…I really like Easy Grammar Daily Grams for simple, concise grammar practice. And then I focus selectively on correcting grammar mistakes in their writing, picking just one topic (maybe capital letters for a couple of weeks or apostrophes for a few weeks), in a kind, less-is-best way to reinforce grammar.

So…my recommended resource for writing: A lined paper notebook (and assigned prompts such as a summary of a book, instructions on something they know how to do, crazy story prompts, serious-to-them prompts, write a poem, etc) and Easy Grammar Daily Grams.

And I didn’t mention HANDwriting. I grab a print/cursive handwriting book that looks fun from Amazon or at a store I’m shopping at. I’ve purchased a few different ones. No preference. But I have them work through this throughout the year. I DO want my kids to learn cursive. It IS important to me.

(Other homeschooling posts I have written detail resources that we use, such as for history or spelling. My homeschooling has relaxed a little throughout the years as I see what is important or not important for each student. However, in general, I still come back to the same resources and incorporate them, I’ve found.)

ARITHMETIC: I only know Saxon Math.

I pretty much stick to the Saxon book and also do lots of timed worksheets for math facts (and lots of flashcards). If I remember right, the curriculum is consumable until about 4th grade; I think there’s a 4th grade book that’s consumable. At Saxon 5/4, it’s not consumable anymore.

We take it as slow as we need to. Or as fast. Usually adjusting to mastery, although sometimes continuing on in elementary school even if a specific topic doesn’t seem to be understood (such as reading a clock). In elementary school, I’ve noticed sometimes kids have HUGE developmental leaps that come in spurts, not incrementally!!!

At the Saxon 5/4 book, it’s like the “big kids” math book. They’ll need to learn how to fold their paper (WHO KNEW!!?? Kids have to be taught to fold papers!!!! 🙂 ), where to write the lesson and date, and how to number down a page and copy math problems to lined paper. That was quite a lot to learn for mine. Much harder than the math. Ha.

So…my resources for math: Saxon Math at appropriate level with extra emphasis on math facts using flashcards.

SUMMARY: I focused on the three R’s.

YES. I had tons of other stuff that I wanted to do and add in: history, art, poetry, spelling, Spanish, music, etc.

But when life was stressful (I’ll speak in past tense as I remember back to the first two children), THIS is what we did (the three R’s) each day. Then, they’d often go off on their own and do art work. Or sewing. Or running and jumping outside. Or practicing their music. Or making their own snack. All the while learning and maturing.

If you can have things to keep you accountable to other subjects, like specific music lessons or a Spanish tutor come once a week, great. Do it. But not necessary.

So…my last recommended resources to keep in house: Find a way to MAKE ACCESSIBLE AND ABLE TO BE USED FREELY WITHOUT YOU AND FEAR OF STAINS/ETC: Paints, scissors, glue, markers, lots of kinds of paper, fun craft stuff like feathers, jewels, etc. Tons of craft stuff with free access.

And tons of books.

Well, I’m prattling on. I told myself if I did the three R’s (and for our family: Spanish was mandatory), then that was what they needed. That and freedom to learn with curiosity. And a warm, happy home. (KEY! Don’t overlook this!!!) We did lots of other school subjects, but I as long as I could get them through the 3 R’s routinely, I relaxed, knowing they’d do okay. And so far, I’m satisfied.

Remember: You CAN make things too hard.

Cornering Fear in Your Decision to Homeschool

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Are you making the right decision to homeschool this year?

So many parents speak to me about homeschooling their children this fall due to the new COVID regulations. I love homeschooling and wouldn’t want to educate my kids any other way.

I homeschool my children because I WANT to homeschool them. I believe I am the most qualified, the most invested, the most capable person to guide and supervise their education. It is NOT because I have my MD. So many people say that to me, “Well, you’re qualified to teach your kids. Other people aren’t. They shouldn’t be homeschooling.”

I call that lying. A degree does not denote conscientiousness, concern, or passion. Ever. Any education succeeds when curiosity blossoms, resources (minimal ones needed) are provided, and concern by a leader (parent/guardian/teacher) is manifested and acted on diligently according to the needs of each learner.

I homeschool because I believe in myself and my kids. I believe there is a better way to educate them so they are all-around healthy people, inside and out. Physically and mentally. Spiritually and wordly. I watch them. Enjoy being with them. Enjoy meeting the challenges they dish out to me and themselves head on.

I homeschool from a place of confidence garnered from the belief I can observe my children and see if they’re learning or not and make changes as needed to help them learn.

Many of you will begin homeschooling this fall due to fear. How is FEAR? How does FEAR feel? It freaking sucks.

Many of you are afraid to send your kids to school and you are ALSO afraid to homeschool. This makes you feel STUCK.

You are not stuck. You feel stuck. But you are not. Fear is bringing this about.

You have to let go of one of your fears, either your fear of a COVID school environment or your fear that you won’t do a good job at educating your children. If you don’t ditch one of these fears, you will remain unsatisfied and grumpy, angry at this new world we live in.

If you choose to ditch your homeschooling fear and embrace the fun of helping your kids learn, then best wishes to you! I am happy to share any of our homeschooling stories and experiences. Just comment below.

But whichever choice you make, do it from confidence that this is the right thing and you can make this work. For homeschooling: Think of something you have confidence in. Something you know you can do well. You walked into that arena with the open mind that you could do it. You didn’t start off good at that thing–because none of us do. We all have to develop that “being good at something.” You can have confidence that you can make homeschooling work.

For sending them back to school: Think of someone you have confidence in. Someone you trust well. You walked into that relationship with an open mind that there are people in life to trust. You didn’t start off trusting. Been burned too many times for that. But you developed trust and confidence eventually in the person. You can have confidence that the administrators are trying hard to do what’s best for your kids. That they’ll make this work.

Which place do you want to place your confidence? That’s for you to decide. But, somehow, you have to come to the 2020-2021 education table with confidence and not fear.