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Mathematics: An Instrument for Living Teaching ??….thoughts/discussion
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Do your children have the concept of 1, 4, 6, 9, 0? If not, facts practice is still a way’s off. If they do understand amounts tied to these numbers, then practicing facts is fine (IMO) for them to pursue. You may do this with/without flash cards. Another very helpful resource is http://www.xtramath.com. We fit this into our day easily. It takes only a few minutes of daily practice to see improvement whether you use flashcards, oral practice, or software/online games.
We’ve done facts songs…I will tell you that one of our children was thrown way off track after memorizing his math facts when he was required to memorize skip counting songs. Another child in the same cooperative setting that year had the same thing happen. Did this mean they hadn’t truly memorized their facts? Maybe, maybe it was just an out of practice kind of thing. Either way, they were side tracked. So, just be aware of the differences between the two while determining needs/goals.
Now, there are pros/cons with regards to math fact memorization. I’m not going to argue about whether you should/shouldn’t memorize facts. It’s what we do at our house after they are able to attach an abstract number to an amount. Addition, subtraction, multiplication, and division are the facts our children memorize. I will tell you that middle school and highschool math are tackled much easier with fewer mistakes if the facts are memorized. Every once in a while, it helps to review. Our kids love the challenge and it seems to keep them sharp.
If you want to include facts memorization in your daily to-do list, just put it down on the schedule and spend a minimal amount of time on it. It soon becomes a habit. If you use xtramath, you’ll find it in the CMO if that’s how you track daily studies. There may be resources like “flash cards,” or “facts practice,” too. If not, you can create your own easily if you want to keep track of it in the CMO. If you want to do this without the CMO, just add it onto a handwritten, or printed schedule. We rotate our subject times depending on the day, but math is a daily topic of study at our house.
HTH,
Becca<><
Oops! It should be http://www.xtramath.org.
Ack! I am borderline tears. Just wrote a long reply with examples of why I don’t necessarily agee with part of Miss Mason’s quote…it disappeared as I was finishing up. 🙁
In some way, I see her as suggesting that “partial credit” should not be given.
I agree with “That which is wrong must remain wrong.” However, the way my 13yos has been able to “start with new hope,” is directly related to the fact that I helped him to recognize that his math grades weren’t a reflection of his ability at this point, but an evaluation of is honesty. That may sound shocking to many of you. Let me explain.
We’ve added an extra resource to our Bible Study time. While directed at younger students for the most part, I chose to add God’s Armor to our GOAL Bible Study.
Our study of The Belt of Truth revealed several areas that we each needed to work on that were never acknowledged as an issue of honesty. Math studies were one of these areas. This is not spelled out in the resource, it was just a revelation during our study. I began reminding our children to be honest students. This especially helped our youngest son in math and our youngest daughter with her handwriting. ;0) Little things like this are a blessing from God! Honesty (at our house) is now carefully tied to CM’s idea of the Habit of Attention. If we’re HONEST, attention is directly related to honesty. Am I able to learn this? Yes! If so, am I able to get the correct answer? Yes!
In less than two weeks, with a diligent review of math facts and careful review of mistakes (checking for honest answers, not correct math,) his grades have gone from the middle C range to high As! This would not have happened without going back over answers marked wrong. Let me explain why I think this is true.
In the beginning, we discussed which types of problems he was missing on a daily basis. His errors mainly fell into two categories. The most were errors of attention (honesty, am I capable of doing this and in a timely manner?). The remainder were errors based on inaccurate calculations due to sloppy work, or forgotten facts. So, he has been rapidly reviewing his multiplication facts and working on attention/dawdling/execution issues. Being honest about his ability to learn and memorize facts bolstered his confidence and gave him this hope CM suggests is so important. Working on accuracy and neatness proved that he knows what he’s doing, he can do it well, and caused him to set huge goals for himself in the area of math. I did very little to cause this change in attitude. Let me share what I did do.
I sat by him after marking his assignment. I had him talk me through the problems that weren’t correct. I did not change his grade! He was able to find most errors from the beginning of this process. That proved to him that his focus was of most importance. He then recognized that his sloppiness was a serious issue. Because he was doing a dishonest job of writing problems down neatly, errors were made that would have been avoided otherwise. Again, an issue of honesty. When he spotted that some multiplication and division problems (long, long) were based on forgotten, or never learned facts, he was more than willing to again review facts….though he had been very opposed to it for several weeks….defiant dishonesty. We had an honest discussion about his capabilities, how he could improve just by being honest, and prayed for a change of heart.
The change has been miraculous! His hopes for math success are quite solid now. He realizes that his capabilities are directly related to being honest with himself and not based on some sort of mental skill he may, or may not already have been given. Pursuit of math success is now an honest possibility for him. He’s set goals for completion of pre-algebra by his own deadline. He has looked out farther down the math road and is no longer afraid. Once he recognized the source of his errors, he was able to “turn the car around” and head in the right direction.
Here’s where Miss Mason’s Motto comes into play more than this quote IMO.
“I am. I can. I ought. I will!” BTW, his ability to complete word problems successfully has dramatically increased in the same short amount of time. This is directly related to honesty and Richelle’s suggestion to keep CM’s reading and narration suggestions in mind. Being focused on what is being read and narrating back the problem has meant extremely rare mistakes for him now. In fact, I don’t think he’s missed a word problem in close to two weeks!
“The wise teacher will see that he does (get the next sum right).” I feel like this can be done much earlier than I have with this particular child. This is how he’s overcome his struggle recently. But, our youngest daughter (7yo) is making just as many strides now as her older brother because we are “keeping our belts on,” so to speak, during our studies… She’s needed to be honest about her handwriting…In math, that looks like….”Are you being honest about your math studies this morning?” (Looks at paper.) “Yes, look at my 8’s!” BIG SMILE! Or, “Just a minute…” (erases 8 and rewrites it neatly.) “Yes, now I am!”
Just how we’re learning at our house now. Of special note…being honest has greatly reduced dawdling and the length of time it takes for lessons to be completed. Short lessons! Happy relationships! Atomsphere, Discipline, Life! Breathe in, breathe out. ;0)
Please know I haven’t forgotten about you all either. When I told you my schedule, I forgot to mention we were also hosting 16 children and their parents for a live-action role playing game through our woods yesterday so we were humming with the preparations. 🙂
Aah, how I wish I could have you all over for coffee! I’ve set this day aside though to give a thoughtful response to the questions and am also looking forward to TailorMade’s repost.
Soon,
Richele
TailorMade that was an encouraging post. Charlotte had a few interesting answers to the question of the importance of Mathematics and Becca has just hit on one of them in her above post which discusses the trait or habit of honesty. Using Charlotte’s methods, arithmetic becomes a means of habit training.
“Intellectual truthfulness” was a mental habit Charlotte spoke of in regards to mathematics, as were the moral habits of “truthfulness” and “honesty.” Intellectual truthfulness would mean a full and sincere engagement of one’s brain, no double standards, an appropriate standard of accuracy, consistency…intellectual integrity if you will. This intellectual truthfulness is the opposite of the slipshod habits of mind
that Charlotte refers to in the section Arithmetic a Means of Training that Melissa brought up in her original post (pp. 260-261 of Vol. I of Home Education).
Tristan, and others, there are variables that I can’t see in your own home. When faced with the question of reworking, I personally would read this section and ask the Lord to show me if I am fostering a habit of carelessness in my child. So many times and in many different subjects, I find myself trying to help a child over a difficulty and not let them make the headway themselves. I would also wonder if the lesson were engaging or just an endless procession of facts and rules.
Charlotte’s methods were very deliberate but habit training was not the main pupose. It was the beauty and truth of mathematics that gave the study its rightful place – that awakening of a sense of awe in God’s fixed laws of the universe. The truth is, God has given His creation a beautiful and orderly character that lends itself to mathematical description. Psalm 19 tells us that creation even responds by “declaring the glory of God.” We read in Jeremiah 33:25 “This is what the Lord says: ‘If I have not made my covenant with day and night and established the fixed laws of heaven and earth, then I will reject the descendants of Jacob and David my servant.”
God has created the universe to have such order – we also see a declaration of love in His promise to not deny us as He upholds the laws of the universe. Math is also a wonderful tool He has given us. We learn our multiplication tables because no matter what we are multiplying, whether buttons, beads, cups of flour or money, we can rely on them to work.
Mrsmccardell, this is why I use her methods. This is also why I recommend following the scope & sequence found at the end of pp. 46-47 of the handbook along with Ray’s Primary Arithmetic and Ray’s Intellectual Arithmetic utilizing Mason’s methods. Ray’s gives you that direction…something to hold and turn to daily and it is an oral program, just as Charlotte’s was.
greenbalts (Melissa) I also want to address what I call the “fear factor” we have in teaching our children math but I pm’d you why I’m going to hold off a moment…to be continued. Melissa, you’d just begun reading the handbook, as you’ve continued, I hope you have been able to “get your head” around it a bit more. Charlotte’s methods are simple but not simplistic.
Peace and joy!
Richele
The truth that can be found in mathematics is what I have been trying to help my ds with who struggles with math and the memorization of the facts. I do try to encourage him to have faith in the fact that God made these truths to be so, as a benefit to us, something we can rely on. I try to gently remind him that they will not change, no matter what is being computed (meaning, apples or oranges/toys or shoe), he can trust it will always be the same.
Great discussion!
Me, too. I have it on my desk to read, and this has made me decide that I want to stop the LA book and read the Math one instead. I am just starting math with my youngest and would prefer not to screw up this set of kiddos with math. =}
Quite honestly, if I’d been taught mathematics based on CM’s suggestions for foreign language studies, I’d have most likely loved it. Richelle, your reminder to study math orally in the beginning is what brought the foreign language methods to mind….for many of us, math seems foreign quite frequently. ;0)
Richele – Do you recommend Ray’s through 8th grade with primary, then intellectual, then practical, then higher? If so, what do you prefer for high school mathematics?
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