Wednesday, March 16, 2016

Math in Year 2: A Snapshot

It has been a while since I've shared what we're doing in math.

At our house, we like math. This really does not have a lot to do with me. My eldest son had an early delight in math, and I decided then that I would do what I could to feed that joy and not take it away from him. My second son loves math as well.

We began in Kindergarten with Miquon Math. Miquon Math is a strong (and inexpensive) hands-on program using Cuisenaire rods. We enjoyed it a lot, and I will be using it this summer with JJ(5) when he begins Year 1. Even though SA stopped using the rods relatively early (he seems to have an ability to see things in his head), I think it was important for him to have that hands-on foundation.

In our third term of Year 1, we switched to Singapore Math Primary Math 2A. I had just had a baby, and I needed something a little less time-consuming for me than Miquon. SA wasn't really using the rods anymore anyway. I also planned a math game or activity from Family Math or Games for Math once a week.

This year (SA's Year 2), we fell into some less than delightful habits with math. Because I never really had to teach SA anything in Singapore (it builds concepts step by step, and he followed along easily by himself), I found that it became something to check off the checklist. Usually he was done his daily exercise within ten minutes and we went on to the next thing. There was very little delight in it anymore, and I found that we weren't even having the regular, everyday conversations about math that he had always initiated.  I also lost momentum with the weekly supplementary math activities, as it was hard to find time to plan them. We probably did them only six out of twelve weeks each term. I still thought of Singapore as a solid program, and felt that the way it built the concepts step by step suited SA very well. It also gave exactly the right amount of practice for him...not too much to bore him, but enough to develop fluency. I felt like we were plodding along steadily, which is fine except that there is not a lot of joy in plodding when you could be flying! I knew he could fly, and felt I was letting him down.

This term he began grade 3 math, and I made a new plan. I was inspired by a post at the Ambleside Online forum (thanks to Kati AKA PurposefulAbegnation) to consider a three-strand approach to math. Kati recommended specific resources to teach the Truth (arithmetic, number sense), Goodness (problem solving/puzzles/patterns), and Beauty (inspiration) of mathematics. I don't necessarily divide it like that (there's a lot of overlap between truth, goodness, and beauty) and for various reasons I didn't go with her specific suggestions, but I was excited about the idea of three strands, and based my plan on it.

I should say here that this plan is quite involved, and I am NOT saying that your plan needs to be this detailed. This is one plan for one child who happens to love math, and I want to lay out a feast for his delight.

Strand 1: Arithmetic - Three 20-minute Lessons per week
Singapore Math and

This is our basic, core strand to master arithmetic and develop fluency. I am continuing to use the Singapore Math workbooks. Primary Math is a mastery program. It teaches the concepts step by step, building on what has gone before. I find that a mastery program suits SA very well, as he likes to dive into concepts until he understands them. He also does not forget what he has learned before, so the periodic reviews are enough for him.

Rather than letting him plod through each exercise, I have lengthened our math lesson to twenty minutes. When he is finished with his daily Singapore exercise, whether it takes him five or fifteen minutes, he uses his remaining minutes on Dreambox Learning to develop fluency.

Dreambox learning is simply the best online math program I have seen. It is also quite pricey. I may have to go back to Khan Academy (which is free) before too long, but for the moment I am loving Dreambox. What's the difference between the two, you ask? Both teach to mastery, allowing students to move on when concepts are mastered. Khan Academy teaches using video with a teacher speaking and showing examples on the screen. Dreambox is more appealing to younger children, teaching interactively using virtual manipulatives. There is a two-week free trial at the website, but beware... you may get hooked and decide to keep paying!

Why do I use both Singapore and Dreambox and not just one or the other? I like having Singapore as the foundation of my program. I know it and trust it as a solid mastery program. At the same time, it can be a little boring day after day. I like supplementing with Dreambox because it is fun and motivating. I suppose I could use just Dreambox, but I don't feel I know it well enough yet to place that much trust in it. It is also quite expensive and I can't commit to that long-term right now. However, using Dreambox time as a supplement has become a natural motivator for SA to move quickly and cheerfully through his Singapore exercise every day.

I am planning to skip ten exercises in the Singapore workbooks as I go along in order to finish them in one year doing three exercises per week.

Strand 2: Problem Solving and Puzzles - Two 20-minute Lessons per week
MEP Math (Lesson Plans only), Family Math, Games for Math

This is real math, the kind that is fun and requires creative thinking, trial and error, and persistence. This is what I miss in programs like Singapore, and it is something SA needs. He is rarely challenged by his regular math, and it is good for him to have things to puzzle out.

I was very tempted by Beast Academy (though I must say the cartoon-ish look doesn't attract me at all). However, shipping is fairly expensive from the US to Canada, and since I'm already spending a lot on Dreambox, I decided to go with free resources and things I already have.

I looked into MEP Math when I was starting, as it is fairly popular among Ambleside Online users. At the time, I rejected it because I felt the spiral approach was not a good fit for SA, as it would not allow him to immerse himself in a topic until it is mastered. (I still think that...that's why this is not my main program.). However, the strength of this program is in its problem solving and puzzles. I also appreciate that it is easy to use and free!

I am mainly using the Lesson Plans, not necessarily the Practice Books for grade 3 (unless the lesson plan involves a problem from a practice book). The program has four 45-minute lesson plans per week. Since I am spending less than one quarter of that time on this, I am selective in the activities and problems that I think will be interesting and challenging for SA. Then we have fun figuring them out.

I also plan to pull out Family Math and Games for Math for an activity or game now and then.

Strand 3: Inspiration - One Lesson per week
Living books, Biographies, YouTube Videos

I really believe that math is the expression of the glory of God in the order He built into the universe. I want my children to see that. I want to foster a sense of wonder. I also want them to be inspired by the history of math, getting to know great ideas and inspiring people.

For this, we read books and watch videos and have conversations along the way. I added "one lesson per week" to my plan to remind myself not to forget this aspect.

Today we read The Man Who Made Time Travel by Kathryn Lasky, a wonderful biography of John Harrison. Harrison was a British clockmaker who worked almost all his life inventing clocks that would keep accurate time even at sea. This allowed sailors to calculate their longitude as they compared the time in their location with the time at home.

Last week we watched a YouTube video detailing a little bit of the history of math. Then we had some fun figuring out Roman numerals.

I just picked up a book at the library called Think of a Number by Johnny Ball. I am not terribly keen on its is one of those busy, visually overwhelming books with too many ideas on every page. However, the ideas in it are wonderful, and I think I could use it as a guide to begin to introduce quite a few "captain ideas." It is divided into four sections:
"Where do NUMBERS come from?" has history about Egyptian, Mayan and Roman, and Indian numbers.
"MAGIC Numbers" has pages on Magic squares, the Fibonacci sequence, the golden ratio, Pi, Pascal's triangle, and more.
"SHAPING up" is about geometry: hexaflexagons, shapes in nature, Platonic solids, and more.
"The world of MATHS" has a timeline of great mathematicians and a number of interesting ideas such as chaos and "freaky fractals."

I started implementing this plan a little over two weeks ago, and I'm very pleased with how it's going. We are doing more math than we used to (twenty minutes per day instead of five to ten minutes per day), but I feel that is appropriate for SA, given his interest in math. I feel it is more balanced with the rest of the work we do, now. We are also doing arithmetic less often (three instead of four or five days per week) in favour of more interesting and challenging problem-solving. Most importantly of all, I think, we are spending some time every week exploring ideas and meeting inspiring people from history.

Monday, March 7, 2016

Dear Canadian CM Homeschoolers,

Let's Help Each Other Find Living Books!

There is such a wealth of resources and book lists for homeschoolers using Charlotte Mason's methods. I appreciate these even more when I realize how difficult it is to start from scratch to find living books for a particular subject. I need all the help I can get to find living books on Canadian history, geography, literature, and art!

Yes, I have found little helps here and there. These are some helpful websites I've seen:

-Ambleside Online's Canada page has a number of suggestions.

- The Ambleside Online forum has a post entitled "Comparison of Canadian History Books" with excerpts from several books that could be used as "spines" for Canadian history. 

-The Simply Charlotte Mason bookfinder has quite a few pages of Canadian resources. Not all of them are living books, though. This resource will become more helpful as more people leave reviews for the books listed. 

-O Canada History is the blog of a Canadian homeschooling mom listing many Canadian history resources by time period.

-Maple Hill Academy. This is the personal blog of a Canadian Charlotte Mason homeschooler. It has not been updated very often lately, but it has several posts with her past plans for Canadian history.

-The Canadian Homeschooler has a "Canadian History Through Living Books" page. I haven't explored it yet, but it looks like it might be a great starting point for living books from different time periods in Canadian history. (post edited to add 08/03/16)

-Tea Time with Annie Kate has reviews of several Canadian books that Annie Kate has used with her family over the years. (post edited to add 08/03/16)

Still, there is a lot of trial and error in finding living books, especially when you buy online and can't actually see what you're buying beforehand. One of my early mistakes was The Story of Canada by Isabel Barclay (not to be confused with any other books with the same title). It was mentioned briefly as an overview of Canadian history for early elementary on the Ambleside Online Canada page, and I ordered it. It was written in simple, short sentences, perhaps suitable for early readers, but lacking any detail that might capture the imagination. So even with the help of recommendations from websites like the ones I mentioned above, you can end up with a book that is not suitable for reading and narration. 

I think the best way we Canadian CM homeschoolers can help each other is to share whatever wonderful living books we're finding on Canadian history, biography, geography, literature, or art. I think it's also important to share in places others will find our help. Sharing on a Facebook wall in response to a question is great for the moment, but a few days later it's hard to find again. Some places you can share that might help others for the future:

-Charlotte Mason Canada FaceBook group. Click on "Files." There are several documents, including a "Canadian History" document with an editable list of books.

-Simply Charlotte Mason bookfinder. With a basic (free) subscription, you can review books already in the bookfinder, which will really help others who are trying to sift through the many, many options listed (16 pages of books come up when you search for "Canada."). Not all of the titles included in the bookfinder are in fact living books, and it will be so helpful to the rest of us if you share even a brief review of the books you know.
With an upgraded (paid) subscription, you can also share resources publicly.

-Ambleside Online forum. If you are a member of the forum, you can add a short excerpt to the "Comparison of Canadian History Books" thread that will enable other forum members to compare different texts and decide what to buy.

-On your own blog or website. If you have a blog, please review Canadian living books and resources you have used. If you leave a link in a comment below, I'll add your links to my "CM in Canada" page so others can reference them long-term from my page.

And now over to you. What is your favourite place to go for recommendations for Canadian living books? Where would it be most helpful for you if others were to share their recommendations and reviews? Let's talk!

Tuesday, March 1, 2016

Highlights from Year 2, Term 2 Exams

Last week Thursday, SA(7) finished Term 2 of Ambleside Online Year 2. Since we had one day left in the week, I decided to do just a few exam questions over the rest of Thursday and Friday rather than carrying the exams over into this week.

He answered two exam questions on Bible, one from the Old Testament and one from the New Testament. For the New Testament, I asked him to choose a parable and tell it to me. He chose the parable of the sower.
"There was a sower that sowed seeds on the path, and they got picked up by birds and the birds ate them. The ones that fell on the rocks sprang up, but then because they had no water and no roots, they withered away. The ones that fell where the weeds were got choked up. When they started growing, they got choked up by the weeds. The ones that fell on good soil were just... they didn't have any problems. They didn't get eaten by birds, they had roots and water. They just grew."
"Do you remember anything about what the parable means?" I asked.
"The seeds that fell on the rocks was one that Satan snatches the Bible. They read the Bible but it means nothing to them. The seeds that fell on the good soil are the ones that read the Bible and it meant something to them. I don't remember the ones that fell among the weeds or the ones that fell on the path."
I was very pleased with how well he remembered the parable, which we read about six weeks ago. He didn't remember Jesus' explanation very well, just some tidbits and interpretations of our discussion afterwards.

SA also recited our Bible passage for the term, Colossians 3:12-17. Normally we try to learn two or three passages per twelve-week term, but this time we had some Sunday school memory work leading up to Christmas and we only started with this in week five of the term. He began well in his recitation, but things fell apart a bit when he missed verse 16 and mixed a little of verse 15 into verse 17. He recited verse 16 when I pointed out his omission.

Picture Study

I did a picture study exam question on the spur of the moment as I was nursing the baby. "Close your eyes," I told SA, "and think about the Tom Thomson pictures we studied this term. Choose one and picture it in your mind's eye. Describe it to me, but don't tell me what it is. Then I'll see if I can figure out which one you're describing."

He willingly did this (It's the willingness that amazed me... picture study might be his least favourite thing.) and described "The West Wind" well enough for me to figure out which one he was telling me about. He started with the hills in the background (hills are very common in Tom Thomson's paintings), then described the rocks in the foreground with their reddish tint, and the wind in the sky. He didn't get around to the pine tree in the foreground until the end of his description, but I already could see the whole painting in my own mind.

"Was that your favourite painting?" I asked him.
"I don't know. I didn't know I was supposed to choose my favourite," he said.
I quickly reassured him that he didn't have to have a favourite, and the one he chose was fine. :)

I asked SA two questions about literature. One was from Pilgrim's Progress, Part Two, and one was from The Wind in the Willows.

"Tell me three things Christiana saw at the Interpreter's House."
-"The fire which was burning. On the side you could see, you could see water, but on the opposite side was oil. The water was the evil one, and the oil was the 'good one.'
-A robin with a spider in its mouth. Christiana didn't like them anymore when she knew robins ate spiders. When they are roaming, they are nice. When they are by themselves, they eat spiders.
-A tree that was rotted out in the middle, but it still grew and bore leaves. The leaves were for the devil's tinderbox." 
"Tell me your favourite part from The Wind in the Willows."
"The Barge. As he was walking, there was a barge woman, and he said he wanted to go to Toad Hall. And he asked the barge woman, 'Is Toad Hall near where you are going?' And she said, 'Yes, it is near.' He said, 'because my girls might be smashing the glass.' She said she thought they were horrible hussies. He said that he wanted to do the steering, but the barge woman told him to do that laundry that he was fond of. She saw that every moment he was getting crosser, and that he lost the soap for the fiftieth time. And then he untied the rope to the barge and mounted the horse and rode away."

I had time for only one exam question in history. "Tell me about the Seige of Calais." As he thought about how to answer he was frustrated to tears because all the details of all the stories we've read were blurring in his mind - he wasn't sure which details belonged with which battles. There were several King Edwards in a row and that didn't help, either. It wasn't my intention to frustrate him, so I tried to help by listing the people involved in the story:

Edward III
Governor of Calais
King Philip of France
Eustace de St Pierre and five other prominent men of Calais
Queen Philippa

Happily, he remembered which story this was when he heard Queen Philippa's name. Even so, he started somewhere in the middle of the story.
"They asked if they could be free people. And then the king said they could be free if they bring him the keys of the city and six men. And they told the king that they wanted to be free six times. They brought him the keys of the city and asked the king to let them live. Then Queen Philippa begged him not to kill them and he finally let them go without killing them and then he had a feast."

I had SA copy "The Badger strode up the steps." His copying wasn't as neat as I know he can do it, and I made a mental note to emphasize that he must do his best work as we go forward. However, overall he has made great progress in his writing skills this term. At the beginning of the term I was having him copy my model line by line, and he was copying word by word directly beneath the model. We continued to limit our time to five minutes, but the amount of work he could do in five minutes increased from less than one to more than three lines. Towards the end of the term, I began to have him copy paragraph by paragraph. I modeled three to five lines at the top of a page, and he copied them at the bottom of the page. His neatness suffered, which I assumed was due to him copying more line by line rather than word by word. (I do want him to do is what will help him exercise his visual memory and begin to learn to spell.) However, the fact that this one-line exam question was also not very neat made me think that perhaps he is getting into bad habits and I need to keep a closer eye on it.


SA did his final Review for Singapore Primary Math 2B. We will begin grade 3 next term. He continues to do well with math. I rarely have to teach him anything...he simply absorbs whatever comes his way in the daily exercises. I have been considering how to spread more of a feast for him in math. I begin every term with the intention of doing math activities and games one day a week. I have wonderful resources for this, but somehow the planning involved and the little ones underfoot have meant that I did this maybe six times in the twelve-week term. Somehow I need to streamline a process, or perhaps have more of an open-and-go program that emphasizes the problem-solving/puzzling/pattern side of math. I have been thinking about supplementing his Singapore Math with Beast Academy (a big decision because it's so expensive to get here in Canada), or perhaps doing some beginning algebra with Hands-on Equations. I also continue to be periodically tempted by Right Start Math (also very expensive.). I know I have a good thing for him in Singapore Math. It progresses in a methodical way that makes sense to him. It's just that when his daily exercises usually take him about five minutes and seemingly no challenge or effort, I know I need to be doing more for him. He needs more "captain ideas" coming his way to really feed his mind and inspire him.

This week I am thinking deeply about math and history before we jump into our third term next week. I expect I'll have a post or two about those subjects before long, too.