Saturday, March 19, 2011

Clear Thinking about Math Part 1

Sometimes, the best plans fall apart. Pamela seemed to track the review of fraction addition I did early last month. When we went back to area and perimeter problems, something got lost in translation. Fortunately, a friend posted about how she made tiles with numbers and symbols to use on a magnetic board with her grandson. Having to write added enough challenge to chip away at his working memory and make it difficult to a new concept to gel. Pamela writes and draws very well, but I thought it worthwhile to remove any potential memory drain while she was trying to visualize adding fractions. I suspect Pamela lost her thread of thought every time she had to stop and draw her thinking.

I also heeded Mary Boole's advice in an old Parents' Review article,
"Beware of writing, in play-lessons, anything which does not represent some process actually going on in the child's mind."
I created a set of pie charts in a spreadsheet, some representing wholes, some representing wholes split into fractions, and fractions. I stayed simple by limiting it to halves, thirds, fourths, and sixths. I cut out all the shapes, covered them with clear contact paper, and cut them again to make them more durable. Before we worked on a problem, we sorted between wholes and fractions to help Pamela familiarize herself with these homemade manipulatives. You can see the first step in our first lesson in the video below. Since Pamela understands fractions, I am using very declarative language as we collaborate.

Then, we started working on her problem, adding 4 3/4 and 4 1/2. Before writing, she set up a model for each addend so that she could represent her mental process visually and spotlight what adding fractions and simplifying meant. You can watch how we worked through the problem together: first, she made both denominators alike. Because I didn't build any models for eighths, she had to think through another option: fourths.

Then, she added them and ended up with an improper fraction 5/4.

Using the models helped her see what she was doing when converting to a mixed fraction and adding the wholes again.

The video below shows how we collaborated step by step. We wanted to show what we were doing physically and write it on paper.
Working together like this cleared up other glitches. Pamela had a habit of forgetting to write the wholes until she needed them again. While she usually remembered to pick the wholes back up when she needed it, that mathematically incorrect habit could lead to disaster in algebra. When finding a common denominator, she tended to multiply the denominators (2 x 4 = 8) rather than going for the least common multiple (4). The lack of eighths forced her to think of a smaller denominator, which turned out to be the LCM. We worked on similar problems together for about a week. I made a set of twelfths for more challenging ones. Then, I faded myself out of the picture and she did well flying solo without anymore issues.
"Let his arithmetic lesson be to the child a daily exercise in clear thinking and rapid, careful execution, and his mental growth will be as obvious as the sprouting of seedlings in the spring." ~ Charlotte Mason (page 261)

Wednesday, March 16, 2011

Semi-Wordless Wednesday: Nature Notebook Pages

An update to what we have been doing with our nature notebooks and I have enjoyed keeping my own as well!

Tuesday, March 15, 2011

JC RIP Deathday Party

Here at Aut-2B-Home in Carolina, we go where angels fear to tread.

We try to learn Spanish while English is being still learned as a first language.

We read poetry and teach vocabulary with nary a worksheet in sight.

We are NOT afraid of Plutarch or the bard.

We are in the middle of Act I, Scene II of Julius Caesar.

Why Caesar? Because Pamela likes him!

We have been reading some Plutarch for more background information and have been previewing the BBC version of this play. Then, we tackle reading a scene or half together. Pamela loves it as you will see in the still-shot and video coverage of our first annual JC RIP Deathday Party. I baked a semi-red velvet cake that is red-dye free, gluten-free, and casein-free in honor of the occasion. Yum! (Seriously, it was delicious.)

Saturday, March 12, 2011

David's Home Next Year

For the past two days, we have driven back and forth to Charleston, SC, where David stayed overnight at his number one pick for college: The Citadel, a military college with a long tradition, longer than my alma mater (United States Naval Academy). Steve and I figured that one of two things would happen: David would come home (1) fired up to put on the uniform of a cadet or (2) wondering what on earth he had been thinking. He ended up being the former and even shaved his head last night! We snagged these photos from The Citadel Admissions Facebook page.

The pre-knob visit not only held David captive with programs, classes, and experiences for 23 hours but it also provided the parents with presentations on what parents need to know to get students prepared to become cadets. David has his head and heart set on Marine ROTC and, in the next few months, he will continue to drive up the number of pullups and crunches he can do and drive down his three-mile run time. Actually, he can already pass the PFT's minimum standards but he wants to be competitive for the three-and-a-half year Marine ROTC scholarship and must work hard to be one of the few and the proud. He is excited, and we are excited for him. Ultimately, it is his choice. Nobody wants to be stuck in a place like that unless they really want to be there. I know from personal experience of having seen the most miserable human beings on earth: kids attending USNA to please their father and grandfather who were both graduates.

My biggest challenge is not to call cadets David will bring home on weekends "bus drivers" . . . gotta love the military college rivalries!

P. S. The folks at The Citadel told us this was their largest pre-knob visit ever, which makes sense since last summer saw its highest number of applicants ever.