April 22, 2013

We go on in circles or, hopefully, in  spirals.  Just a month ago we celebrated completion of level 4 Saxon Math by Nancy Larson.  In anticipation of upward movement I ordered and received Saxon Math level 5 by Stephen Hake.  I looked at it.  I compared the two programs.  For now, I decided to return to Nancy Larson’s  edition of Saxon Math 4.

There is nothing wrong with Stephen Hake’s textbook.  It is well-organized.  The presentation is clear and simple.  The problems are chosen appropriately to provide a good practice of the topics covered in preceding chapters. The level of difficulties would not intimidate Robert as, I believe,  he already knows approximately 80% of the material covered there.  It would also benefit Robert to become familiar with a type of textbook that he could, theoretically,  read on his own.  Until now, he got all the information from his teachers and me.  We introduced all the facts. We  presented tools for solving all the problems. Nancy Larson books, did not explain anything directly to Robert, they left explanations to instructors.  Stephen Hike’s textbook, on the other hand, would give Robert a chance to learn by reading, by studying examples of solutions, and by solving new problems himself.

Of course, Robert would have to learn first how to learn from a textbook.  I would have to teach him how to study by himself.  The fact that Robert is familiar with most of the topic presented in  the book might be either beneficial or disadvantageous.

Beneficial, as Robert might recognize the information as familiar.  Disadvantageous, as recognizing something familiar might lead to ignoring presentation and/or skipping over it as not relevant and thus not accepting it as a tool of independent learning.

While Hake’s edition offers a chance to learn by following a written lecture, Larson’s edition presents such opportunities by allowing the student to follow the pattern of solving problems  from part A to part B of each lesson.  Parts A and B present similar problems requiring application of similar methods.  Ideally, Robert should learn techniques from part A with the help of the instructor, and then use them to independently solve problems in part B turning, when necessary, to part A for additional cues.

That is  what Robert is  doing at school with level 3 of Saxon Math.  He carries on the knowledge of facts and/or skills from part (A) to part  (B).  Except that  in the school edition, part B is called “Homework”.  That is what he has been doing at home with level 4.  It has to be said that level 3 is not necessarily easier for Robert than level 4.  It is because the main problem Robert has with math is really language.  Following written directions is still a problem because Robert bases his “solutions” on one or two words in the text. For instance, while the expression,  “How many are left? ” immediately leads Robert toward subtraction and ” How many altogether”  results in Robert’s adding numbers, the word “more” confuses him a lot.  On one hand, “10 more than 30”  should lead to adding, on the other hand “how many more is 30 than 10?” should lead to subtraction.  When Robert sees “more” he ignores all other words and mostly do addition.

(I remedy that in many ways, mainly by slowing Robert and asking him to read again, or by giving the clues, which might be as confusing as the problem itself.  That topic is so wide and complex that it would require another entry on this blog.)

Because of Robert’s difficulties with understanding  language, both level,s 3 and 4, present similar challenges.  That is why Robert simultaneously work on both grades, one at school, and one at home.

There are four reasons why I decided at this point to repeat level 4 of Saxon Math and only carefully explore level 5.

1. Importance of language.  This is the program that allows Robert to still practice such important words like,  for instance, ” ago” , ” before”, “from now” as they relate to time.

2. Flexibility. By presenting problems requiring application of different information as the student moves down the page, the arrangement forces the student to switch from one mode of thinking to another. Yet the student still has the ability to support himself by lurking at the  problems on the previous page,

3. Generalization. Application of the same concepts in different problems, allows for generalization.  For instance, after introducing terms: “vertical, horizontal, oblique lines” , the student has to find such lines in polygons.  In another lesson, the student is expected to draw horizontal or vertical diameters.  A few lessons later, the student is asked to circle letters that have horizontal (or vertical) lines.

Of course, one might rightfully argue, that to learn quicker and easier it would be better for a student to concentrate on just one topic during one math session and solve variations of similar problems at that time. In one lesson Robert would have to find all those lines in different polygons or different letters and draw them as diameters in circles.  That still would allow to generalize the skills.

But, the time of presentation of tasks is different and that might lead to different ways of retaining materials.

4. Real life applications.  Level 4 Saxon Math presents many tasks that do apply to real life in a very straightforward ways – calendar skills, time skills, time zones, writing checks, counting change from the store.  Those tasks are spread over entire program and mixed with other tasks.  Just like in life.  At store, the student has to estimate the price of two items not ten times in a row, but just once while being preoccupied with something else.

I have to say, I don’t dismiss Stephen Hake textbook   As I stated before, it might be a good place to start teaching independent learning.  I am not sure Robert and I are ready for that step.  We will try and see.

Maybe, to simultaneous studying level 3 and level 4 we add level 5.

I don’t know.  I wish, there were more research done on the way children learn, and specially children like Robert.

I suspect that because Robert does learn slowly, the steps in his learning are easier to observe. The obstacles to learning are easier to define and remedy.  From the way Robert’s learns many researchers of methods of education could learn so much and so well.

So where are they?  WHY ARE THEY NOT LEARNING ?!