I like Saxon Math texts because they daily launch our family into so many discussions which inspire our love for learning classically at home. The authors of the Saxon series have gone out of their way to incorporate both silly and culturally varied word problems along with very serious and even patriotic word problems.
Today, William (10 years old) had a word problem about burros. He asked, “What’s that?” and I responded with “Another name for donkeys.” Then he said, “There are so many names for donkeys – asses, burros…” which gave him a brief word substitution lesson and a chance to say a bad word without getting in trouble. I was concerned that he would confuse the spelling with the English word burrows, so we had a brief spelling lesson. I pointed out that ‘burros’ is Spanish, but ‘burrows’ is English and requires a ‘w’. They both end with the long o sound but use two common rules for spelling ‘o’ and ‘ow’. (Here is where w acts as a vowel, as in “when two vowels do the walking the first one does the talking and says its name.”) The above conversation only caused a minute interruption from our assignments (I sit at the table and write books while the boys work on assignments) and took place while David (just turned 8 years old) was listening.
As William proceeded with his lesson, David needed my help drawing multiple triangles to measure and count inside of larger shapes in his Saxon math lesson. Second grade math is too easy for David so he delights in any new material. This is why I make my boys work ad nauseum at grade level math and even below. I want old concepts mastered which means they come quickly and easily to them and new concepts to be a delightful challenge. Saxon’s incremental process allows this to regularly occur. David has been through Spectrum and Rod and Staff second grade math already this year, which has prepared him to complete about five Saxon Math lessons an hour, including breaks for kisses and hugs.
David just asked me “What does vertical mean again?” I said, “You tell me.” He said, “Up and down?” and I said, “Good” and kept typing this article. Then he interrupted me to help him do his first Venn diagram. William looked over from his side of the table and said, “Oh! Those are fun. They’re easy!” So I stepped David through his first Venn diagram. There is another Venn diagram on the next page for him to try on his own. If he can’t do it well, I’ll help again. If he can, I get to shower him with praise. The verdict is in… He got it all correct and gave me lots of kisses when I said, “Good job!” Now he wants to skip the rest of the problems and do a bunch of Venn diagrams. I said,”No, do all the problems on the page.” Am I squashing his delight in Venn diagrams? Maybe. But my job is to train him to complete an assignment in a set amount of time so he is effective at studying. And if he can do the Venn diagrams again tomorrow without my help, I will know that he understands the concept. If I have to teach him Venn diagrams tomorrow, it means the concept was in his short term memory, but he needs to keep at them over a period of time to ensure understanding.
Meanwhile, William is working almost exclusively on fractions today even though they are presented in a variety of forms in a Saxon lesson. In other words, if you looked at the lesson page, it’s not obvious that most the lesson is on fractions because there are a wide variety of symbols, words, and graphics on the page. It doesn’t look like a fraction worksheet. He isn’t required to work on a single pattern that looks exactly the same; instead he has to constantly stretch his brain and apply the same idea of multiplying fractions in different contexts. To learn, he is processing out loud any thing that seems new to him. He tells me his steps and the numbers and answers. I just keep typing away and don’t pay attention. If there is a pause in his voice like he’s thinking or unsure, I look up and offer help. He doesn’t need my input as much as he needs a face to talk to so he can think things through. I go to the white board and make up examples of the problems he is not sure of.
If my boys feel confident about a concept, there are plenty of practice problems in Saxon. If they are not confident, I make up some problems at the board with them.
Now, William is finished with his Saxon lesson and is checking it himself. He marks the problems that are wrong and recalculates the answer. He actually found a wrong answer in Saxon yesterday. The text had switched a divisor and dividend so the answer key had an inconsistent answer. William could not correct his problem and come up with their answer so he called me for help. I was confused for a moment because the answer key is so rarely wrong. So we called in the big guns – Dad. He figured out what had happened. It was a two part answer and both answers were correct if two numbers in the original problem were switched. This situation reveals the various levels of understanding math. William is trying to memorize and understand the rules. I could find the right answer consistent with the text’s data. But my husband could think through to the author’s intent and the lesson being taught to evaluate why the error occurred in the first place.
William is ‘behind’ in math as he is working in the Saxon 5/4 for the second time. He just had too many problems wrong the first time through the text and he could never correct them on his own. This time, if he gets something wrong, he can figure out why it is wrong. He is getting past finding the answer to understanding the concept. He still gets too many wrong so we will complete the Rod and Staff fifth grade text over the summer so he can move into the Saxon 6/5 more confidently this fall. Words are easy for William. Math is a foreign language. We are tackling math as verbally as possible for him so he can use the tools he know well – word and definition analysis – to apply to what he doesn’t know well - mathematical patterns.
I am not naturally good at math patterns either, but I am good at word analysis and learn math through ideas. Speed and accuracy are difficult for me, but if I slow down I can get the right answers. I work on math so much that other folks think math is easy for me. It’s not. It is easy for my husband so he both understands concepts and makes few calculation errors. I can get excited over the theological implications of calculus, but can’t add very well. The great thing about pursuing math with an attitude that pleases God is that He helps us get through our weaknesses and strengthens our gifts at the same time. As I pursue accuracy in calculations, I get to learn even more mathematical ideas that provide even more pleasure to me.
David is naturally good at math. Educators mistakenly let good math students move ahead too quickly. There are many basic skills to practice besides understanding concepts. David will be permitted to accelerate his progress through texts after he is mature enough to write down every step of every problem, sit still for a whole hour, and check his own work. These are crucial skills that would get missed if I let him move forward with just his strengths. His natural strengths will stay strong. As his parent I need to help him develop the discipline needed in weaker areas which will then allow his strengths to soar!
I love Saxon for young children because I can also use it as David’s reading lesson. The words are above average grade level; for instance, oblique and vertical aren’t typical 2nd grade spelling words or vocabulary. Yet thanks to Saxon, we read a few words like that every day and they are part of my second graders reading vocabulary.
David also loves the problems. He ended his lesson today by saying, “Mom, listen to this funny problem.” It was a logic problem about some crazily decorated socks. It really wasn’t funny, but some how all those silly socks delighted my eight year old son. Being able to hold him on my lap while he laughed over a math problem delighted me. Catechesis which is Greek for “resounding in celebration” is the goal of Christian education. I praise God that we can resound Saxon problems in celebration of math loved and learned as a family.