Wisdom Nuggets from Joyce’s Years of Interacting with Students and their Teachers and Families

How to Gently Introduce Math Concepts

Mon, 9 Aug 2010 21:37:53 -0400

Our newest author, Karen Stoll has written this article. She is also co-author of JoyceHerzog.com’s two newest releases: the Early Learning Kit’n a Bag and My Box of Ten, the first unit of the Math Boxes Curriculum. Karen is energetic, creative and homeschools five children ranging in age from 2 to 11. She brings new energy and creativity to our team.

By Karen Stoll

Many people have a mental block when it comes to mathematics. In fact, “math” is one reason why some people hesitate to homeschool at all. Instead of seeing math as THE ENEMY, we can approach mathematical concepts gently with our youngest students and practically with our growing students. Your approach to teaching mastery of fundamentals such as counting and addition can lead to confidence in advanced concepts from multiplication all the way to algebra and beyond.

Math begins before your child even reaches school age. In fact, we teach our children to count from their youngest years…and that is math! Here are a few ideas for gently incorporating math into your everyday life, not just during ‘math time’ at the school table.

๏ COUNT EVERYTHING! Count the steps in your house each time you walk up or down; count the spindles on the front porch; count the buttons on his shirt as you help your child get dressed.
๏ Give your child jobs that require one-to-one correspondence. Setting the table is a perfect example. If you have dishes that you don’t want your child to break, it may be time to invest in a few melamine items that you don’t have to worry about breaking.
๏ Sing songs – 10 Little Indians, 5 Little Monkeys, and songs that count up or down are perfect!
๏ Draw relationships between numbers. “We have 5 apples, but we only want to slice 2 for our snack. How many will we have left?” Mathematical equations are all about numeric relationships!
๏ Use your kitchen. The kitchen is an incredible tool in teaching math without anyone feeling like they are ‘doing school’. When your child asks to help in the kitchen, welcome them and let them actually assist – even if it would be easier to do it yourself! Recipes can teach fractions, measurements, and conversions. With your younger students, simply talking about the measurements will introduce terms that they need to know. As they get older, allowing them to double recipes is a great way to begin multiplying fractions. Plus, converting measurements is far easier in the kitchen than in the textbook.
๏ Take them grocery shopping. Little ones can count the produce as you fill your bags. The grocery has a wealth of opportunity for your older student to work on all kinds of math! Comparing prices, determining price per unit, staying under budget are all advanced math concepts that are also life skills which we all need to know!
๏ Learn to count to ten in other languages. Speaking other languages is fun and exciting to children and you can easily find the numbers 1-10 in an online search for whatever language interests your family.
๏ Match the date. In an idea I got from 1plus1plus1plus1equals1.blogspot.com is to allow your children to make the date using coins. If today is the 9th, your child can select a nickel and four pennies to represent the date.
๏ As your children get older, relate math to money. As adults, we often think in terms of money when we are working math problems in our heads. We tend to think about numbers in terms of quarters and can typically quickly add prices as we are shopping. Teach these skills to your children as money becomes more ‘real’ to them – usually around 10 years old.
๏ Estimate frequently. We say in our house that a trip to Sam’s costs you $10 per item as an estimate. And oddly enough, that usually gets us pretty close then we are estimating the total at the checkout. Teach estimation from early ages by emphasizing the difference in tens, hundreds, and thousands. As your student gets older, get more specific with your estimates.

Regardless of the methods you use, make mathematical concepts have meaning to your students. I would venture to say that you use algebra almost daily in your life. However, chances are that you saw little use for it in your high school textbook. Similarly rows of math facts are boring and seem useless unless you understand the practical application for math. Point out occasions when you use math during your day. Word problems are merely ways or relating math to real life, so create your own word problems when doing oral math with your child.

Above all, watch your attitude! I’m sure you have heard the saying that ‘Attitudes are caught, not taught.’ This applies to attitudes about academics as well. If you are constantly talking about how much you hate math or how hard math was for you, don’t be surprised to hear the same words come out of your child’s mouth eventually. Even if you struggled with math, your child may find math comes naturally to him. Don’t prejudice him against math before he has experience with it on his own terms.

Mathematics can be tolerable…not bad…even FUN! Step gently into math and watch your children develop the solid foundation on which they can build a lifetime of math skills!

From Happy Meal to Miserable Meal / 5 No No's

Wed, 14 Jul 2010 02:18:52 -0400

Want Whine With Your CheeseBurger?
Casey and I recently observed a common scene unfold at a restaurant. It may seem insignificant, but when these stressful episodes add up throughout the day, it creates 24/7 misery. The subtle messages begin to transform both us and our kids in negative ways, until our lives snowball out of control and we're at our wit's end.

A family walked in and the child was instantly drawn to the cookies. So began the whining. "I want a cookie. I want a cookie." The poor parents reacted like we often do and turned a potential Happy Meal into a Miserable Meal:

1. We whine back. The Mom responded to the son's pleas by harrumphing, "Why do you always have to whine, Jordan?" When we allow negative emotion to creep into our voice, it tells our kids that we are weak and vulnerable. It says there may be a chance to get what I want if I push. It's confusing to kids because they hear both "No" and "Maybe" at the same time. Use a calm, matter-of-fact "Not happening." No lecture, no explanation, no emotion. This is just the way it is. It's a very effective tone we need to master. But it takes practice.

2. We yell. The father snapped, "Stop it now, Jordan! Cut it out." How often do we tell our kids to stop, but fail to tell them what TO DO. Always, always give kids specific, concrete jobs to do, a way to get involved and be helpful. "Jordan, do me a favor and save us a table by a window." They like helping when we are involved. "Jordan and Sarah, could you help me get 7 packets of ketchup, 8 napkins and 4 straws?" Then praise for a job well done. It changes the entire tone.

3. We bribe. This is the last resort of tired, frustrated or emotionally weak parents, but it gives the child complete control. The child learns how to blackmail or negotiate to get what they want. Let your yes be your yes, and your no be no. Get accustomed to disappointing your kids. Life isn't fair. Fine. Deal with it.

4. We make vague promises/threats. The Mom then said, "We'll see. It depends on how you behave at dinner." Beware this trap. It's a way to put off making a definitive decision. We're basically saying, "I don't want to put up with your tantrum now so I'm going to string you along and bludgeon you with threats all throughout dinner." And that's exactly what happened.

It's too vague. What does "good behavior" mean? Does good behavior mean you only misbehave three times, seven times? Does the child really have a chance?

5. We allow our child's mood to determine ours. "This was supposed to be fun, Jordan, and now it's just not," we heard the parents say repeatedly. I know it's really hard, but we can't fall into this trap. They gave the child complete control over their emotions. It takes practice, but you can (and need to) learn how to be happy even when your kids are miserable. We used to have Chaos Camp days with ten kids, and we'd purposefully make them miserable as a learning experience. I would practice maintaining an even mood and tone, no matter how awful they behaved. It taught them they could count on me and my mood wasn't dependent on theirs.

Even more importantly, I was changing my environment rather than letting it change me. And this is key. Calm doesn't mean you don't feel real emotions--it just means that you learn to influence your environment and spread calm instead of allowing misery to overtake you. It transforms you from a passive victim of circumstances to a powerful shaper of your environment.  Can you see why this is radically different from other parenting programs? Instead of focusing on changing the child, I focus on changing myself. That is why this produces long-term transformation and works no matter how old your kids are.   I want you to picture in your mind all of these scenes in your daily life--whether it's the morning rush, driving to church Sunday morning, dinnertime, bedtime, leaving the house--but enjoying them instead of fighting, nagging, bribing or suffering countless meltdowns (ours and theirs!). Do you want to:
Enjoy stress-free mornings, dinner and bedtime. Regain power over your emotions, attitudes and moods. Help kids be calm in the car, classroom, restaurant and church. Eliminate stress over homework, finances, traffic and sibling fights. Helpful tools for single Moms, Dads, homeschooling and step-parents.

Please feel free to forward this newsletters to others and enjoy your kids!  Kirk Martin Founder, Celebrate Calm, LLC www.CelebrateCalm.com

“HomeSchool TroubleShooting”

Sun, 13 Jun 2010 23:16:02 -0400

Written by Carolyn Wallis,
Official JoyceHerzog.com Family
Author, Speaker and Leader

Note from Joyce: Carolyn is mom to five young adults, all who have been homeschooled from the beginning. She is now supporting the homeschooling of her oldest granddaughter. Carolyn has been working under and with me for thirteen years and has applied my philosophy and methods into high school learning. Carolyn is a wise and compassionate woman who speaks from her heart. She has just joined the JoyceHerzog.com Team and will be seen at conventions and in print in the coming months.

A homeschooling mother shared her concern, "I am currently teaching my daughter how to subtract with time and measurements. She is struggling to remember to apply each step needed. I feel frustrated because I feel I have explained the steps in every way I know how to. I am not sure why she isn't mastering it, so I feel limited in helping her at this point."

Usually, it is not the methodology (how you do these math problems) that is causing a struggle in learning. The math instructors and their formulas have stood through many generations as being effective. It is not that you need to come up with another formula but you may need some handy tools to implement a successful outcome. One of the points that stands out in this mom’s account is her daughter’s difficulty in applying each step. I wonder if the problem is remembering or understanding? It is a good question to evaluate to find the right solution.

1. Is it the right time? Sometimes, especially with more abstract concepts like you have mentioned, we need to give the child time to mature and understand. This does not mean that you ignore the lesson, but you might want to wait and set it aside for a week, a month or two. In the meantime, you can do some more informal teaching showing how you use these in everyday life. The rest of the points will assume that she is ready.

1. Where exactly is the problem? There are many things could contribute to a dishwasher not working properly. Sometimes, it is simple (turn up your hot water temperature) and sometimes complex (faulty wiring). Take your daughter through a problem and watch her eyes for that blank look that shows she just isn’t getting it. Stop and congratulate her on what she does know. Thank the Lord because now you know. Test her a few times to see if this is really where the trouble is. We have a tendency to look for the outcome—we want the final result—but we don’t always see that much of what we want our children to know they already do.

1. Are the steps simple? Look for the easiest way to do the problem and break it down into the smallest steps. You mentioned that you have tried many different ways of doing these types of problems. Let your daughter select the one that makes the most sense to her. Write it down step by step with an example. Or, if you daughter can write comfortably, have her write it down. Keep this concept sheet handy so your daughter can refer to it whenever she wants.

1. Is there a way to make it concrete? Find ways throughout your day that you are using these skills. Stop what you are doing and show your daughter how you figure out the time or measurement. Plan such activities. She is going to be watching you do the math but will be seeing how it works in life. Maybe it is time to do a craft that requires measuring or move some furniture and figure out (don’t just guess) what wall it would fit best on. Have her wear a watch or carry a measuring tape. Ask her throughout the day to figure out the length, time, etc . . . of an event or situation.

1. Is there a way that you can be silly? Something that makes measurement-math tricky is that you have to convert to the same units. In an empty egg carton place your daughters favorite animals (one per section) so you have twelve in the carton. Offer to exchange the one animal you are holding for the dozen she has in her carton. Of course, small treats in the carton work as well. She will have no difficulty in seeing that different units have different value. The fun thing about this very picturesque activity is that your child will gain an image that you can use to tip them off if they start to do it wrong, “Oh! You are exchanging your dozen for my one horse. Thank you very much.”

1. Is there a way you can bridge the gap? Does your daughter understand how to subtract money? If so, use the subtraction of money, which uses similar steps, to show her how to subtract other measurements. Since she is working on subtraction, we will assume that she knows how to add these sorts of problems. Addition bridges the gap to subtraction because they are opposites. So, go ahead and explore, working an addition problem backwards after you worked it forwards. The light may go on.

1. Can you link it to your child’s interest? We have already mentioned this before but it deserves its own section. Let’s say your daughter likes horses. If you involve measurement in making cardboard horse stables or timing a horse’s trip from one place to another, you child will be more engaged and also want to get it right.

1. Do you need to do more guided practice? This is a key teaching method that Joyce Herzog explains in Timeless Teaching Tips. Start with the very first step of a measurement subtraction problem and show her the step. You show and explain to her the step again and pause as you do it, allowing her time to think. You are still not expecting her to respond but rather to process. You can go through all the steps but when you come back to the first step—provide your daughter possibilities. It is not as difficult to select an answer as it is to have to produce an answer. Eventually, you will have her talk you through the steps as you are working the problem. You are building little bits and success in this process. Success does encourage more success. When she has accomplished talking through the problem three times, she is then ready for some practice on her own. But have her only do about three problems without you, not a whole page. If she doesn’t have it, you want to know that early on in the individualized practice.

1. Are you expecting that the child has already internalized these learning techniques? Just as a warning, each child may hit a roadblock with a particular subject at a different time. For one son, it was High School Algebra, and we had to use these very techniques. Each child develops differently in this aspect. One child may be able to accomplish this from their earliest academic years and others may take years of practice to get to this level. For others it has more to do with interest or growth spurts. As the teacher, I need to be willing to always go back to the needed steps so that my child can learn.

1. What is the cause of the teacher’s frustration? We have all been there. We feel like we have tried everything possible and our child still doesn’t understand. We have prayed, discussed it with others, used another approach, etc. Do not despair! But do figure out where the frustration lies. Do you think that your daughter just doesn’t understand? Are you tired of spending time on this? Are you feeling inadequate? Is your child rebellious and uncooperative? Is it absorbing too much of your school day? Evaluating the reason you are frustrated and doing something about that reason will help the create a more positive environment. Here is another idea-- Before you begin the lesson, both of you stop and thank God that He has measured the oceans but no one can measure the depth of His love. It will bring a smile to your lips and heart.

“Sounding Out” is Essential and Ineffective!

Sun, 9 May 2010 17:23:02 -0400

If your child seems “stuck” at the “sounding out stage,” Listen to this mom and try some of the suggestions below!

I've been camped out with my daughter on lesson two of Level Two for 4 months now, and she still cannot reliably recognize the words unless she sounds out almost every sound separately. She definitely seems to like having one on one "mommy time" doing the program, and does not seem overly discouraged. She has, however, made very little, if any, progress in all that time. (She could already sound out all the words when we started.) She can read all the words, she just has to sound them out. I know it is important for later progress that she be able to read the words easily, but I wonder if this is something that will just come with time, and I should move on. Speedwise, she hasn't gotten out of the high teens.

I was just wondering if you all would keep working on lesson two, or try to move on, or try something else? I'm open to any and all suggestions!

WOW... a tough one!

You don't want to discourage, but you don't want to overwhelm. Sounding out words is an essential skill – but it is NOT reading. Sounding out is a stage on the road to reading and it needs to be traveled, but eventually every child needs to recognize many words immediately and learn to SEE words and not individual sounds. If a child continues to sound out every word, he learns to hate reading and to get little out of a frustrating exercise! Help him move on to instant recognition of words.

Here are a few methods you can try. Likely at least one will work for you and your learner.

1. Choose five words you can picture (cap, tap, van, tag, bat). Make a set of cards - the same size... have her aw (or find) a picture of each word - one picture per card.

This may take a couple of days... just do one to 3 a day. When the set is done, lay out the pictures in front of her. Have her sound the first word and find the matching picture. Have her move from left (word) to right (picture) a few times, reading the word, naming the picture.

Then make a set of similar cards, but have her write the word on each card herself.

Start back with the printed words in a pack. Put the pictures in front of her to the left and her printed words in front of her to the right.

Have her sound a word. Have her find the picture. Have her find HER WORD.

Lay them on the table in this order: word card, picture, her word. Have her look and point from left to right as she reads the words.

Play concentration with any two sets of the cards.
Work with these five words for a large portion of your time while continuing to work with the whole set for a smaller portion of your time. When she can read those five words smoothly, add two more. Gradually work through the set this way, adding only two words at a time until those are mastered.

As she adds words, if she can't draw a picture of a certain word, just have her make a design (or you do it) that she will associate with that word.

1. A different technique is to "race" for the words. Lay a word in front of you both, facing him. YOU begin to SLOWLY, but smoothly sound the word. Then you say the word. At any time, he can jump in and SAY the word, but he may not sound it out. If he SAYS the word before you DO, he "wins" it. If you say the word first, you "win" it. See whose pile is biggest at the end. (Let him "win" sometimes, but not always; try to be fair.)

1. ANOTHER technique is to have her "sound silently" or “sound it in your head.” Do not allow her to sound it aloud. She may sound silently and say aloud ONLY THE COMPLETE word.  

1. Choose three words. Rotate through just those three cards, asking your learner to read them quickly... He WINS any card he says immediately without sounding out... see how many cards he can win in a minute! When he can QUICKLY read those three nearly every time, add 2 more... If he misses - or has to "sound it out," put it back in the pile (fairly near the front)... He ONLY WINS the ones he reads without sounding out! Keep adding a few more every few days... Any time he misses one, put it fairly near the front of the pile...

I don't think it will take long to get him MOVING forward and not being stagnant... also encourage him to sound them silently. Say things like:
"Sound them in your head... and then SAY the WHOLE word..." “Don’t let me hear you ‘sound out!’” (Do NOT say it in a mean way!) “Tell me the word after you figure it out!”

I gave just this last suggestion to one mom and within 3 days, her child had doubled his speed and in one week, he was up to 30 WPM! Find a way that works for YOU!

National Standards

Thu, 1 Apr 2010 22:48:53 -0400

I read a blog the other day about needing national standards for what is taught at every grade level. While I agree that the current system is missing a lot, there are hidden problems in that approach as well. Unfortunately, every five-year-old does not enter school identical and cannot progress at a prescribed rate. Therefore a national standard must be accompanied with a standard of entry and a standard of passage through the system. Age is not an adequate measure either of development or progress any more than shoe size is related to age!

First of all, to achieve this type of standardization, children would have to be at a similar developmental level when entering the system. In order to determine that, of course, an entry exam would be needed. Some might be ready at four or five; others might not achieve that level of progress until they are eight or nine – and of course, there could be no stigmas attached to early or late entry.

Secondly, passage from one level (grades?) to the next could not come merely because a year has passed, but must be based on mastery of the material presented at that grade level. And that presents another dilemma: what do you do with those who master math and cerebral content, but are not yet reading – or those who read, but cannot calculate? The movement by mastery assumes that children develop in all “subjects” or skills at a consistent rate; unfortunately, that is not often true.

All of the criticisms of the non-standard system are valid, but so are the problems with standardizing the system. Perhaps the solution is the way this country began – educating children in the home or in very small groups. This herd mentality is not working – or it is working, but not to the advantage of an educated generation. Stand up and be proud of the individualization that is possible in homeschooling!