Gavin took a math test. It was monumental. That’s right – in the homeschool mecca of New Jersey, we are not forced to engage in testing or other educational practices that we are not fond of – like actually attending school 😉

He is using a new approach to learning mathematics than we have previously employed, which was extremely informal. He has transitioned to an incremental, textbook based program. Gavin is at a developmental level that he is able to sort through math curriculum to find what works for him. He also acknowledges that formal math will help him meet some criterion that will be necessary to participate in activities he thinks he would like to spend his High School years engaged in. That makes all the difference in conversations when the going gets tough.

He sat down to his first test ever. I don’t know what either of us thought would happen. He handed it back and we marked it together. We put big Xs where the answers were not exactly what the book expected the answers to be. Gavin quickly figured out that he ‘did well’ according to conventional ‘school standards’. “That would be a good grade, right?” he asked.

Grades?! Who the h$%@ cares about grades?!

I pulled out Sal Khan’s The One World School House.  Here are some of the quotes from the chapter entitled ‘Swiss Cheese Learning’:

“Chances are that the topics themselves have not been covered thoroughly enough, because our schools measure out the their efforts in increments of time rather than target levels of mastery.”

“In most classrooms, in most schools, students pass with 75 or 80 percent. This is customary. But if you think about it even for a moment, it’s unacceptable if not disastrous. Concepts build on one another…A shaky understanding early on will lead to complete bewilderment later.”

“We are telling students they’ve learned something that they really haven’t learned. We wish them well and nudge them ahead to the next, more difficult unit, for which they have not been properly prepared. We are setting them up to fail.”

“Even worse, many deficiencies have been masked by tests that have been dumbed down to the point that students can get 100 percent without any real understanding of the underlying concept (they require only formula memorization and pattern matching.)”

…and the biggest one for me:

“But she should also have been given a review of the 5 percent of problems that she missed. The review should have been followed by a rigorous retest; if the retest resulted in anything less than 100 percent, the process should have been repeated. Once a certain level of proficiency is obtained, the learner should attempt to teach the subject…As they progress, they should keep revisiting the core ideas through the lenses of different, active experiences. That’s the way to get the holes out of Swiss cheese learning.”

Sal acknowledges that this would be a practical impossibility in most school settings. As homeschoolers, we have plenty of time for this approach.

I am not interested in giving Gavin grades. I am interested in assisting Gavin as he pursues a deep understanding of mathematical concepts, using tools that fit his learning style, in a setting that provides hot waffles on demand 😉

Pure mathematics is, in its way, the poetry of logical ideas. 
~Albert Einstein

I am not ashamed to say that I cannot ‘teach’ math to Gavin. Come to think of it – I cannot ‘teach’ much at all. I do not have a clear and solid understanding of the level of math he is at. I took Algebra I, Geometry and Business Math in High School – did not understand most of it – and apparently got decent grades. I am passionate about not giving this type of education to my boys. I am teaching the boys to teach themselves and how to find the resources they need to get the answers they need and want. If I can help them figure out how they learn best and provide them with access to the best resources our technology fueled society has to offer – what couldn’t they learn? I refuse to make them dependent on a teacher. They should not be stifled by what I can teach.