Open book learning versus rote learning

       What is rote learning?

     Rote learning is the concept that you will memorize a procedure by endlessly repeating it until you “understand” it.  Some believe this is the only way to truly understand a topic in mathematics.  It is the “practice makes perfect” paradigm.  The rote learning idea is that understanding is derived from memorization and recall over time.  [edit:(9-24-2015) As we learn more about the human brain and the way it carves and hones pathways, we begin to see the the role of rote learning. We have come to learn that rote memorization of key concepts tends to in a way  free up "ram" ,working memory, in our brains. With key concepts being stored in long term memory, our brains are able to process higher level logic faster. ] Understanding means to comprehend or to grasp the meaning of. Students with good memories will just simply memorize the formulas and recall them on demand at test time, and the teacher will believe they understand the concept and move on.  Students who do not have great memories will struggle and get frustrated while trying to memorize the formulas. We can single them out in an attempt to give them extra help to understand, which in some cases actually embarrasses the students. [edit:(9-24-2015) A strategy to overcome singling out students with poor memory, is to implement a small section on memorization techniques. Proper application of memorization strategies can also teach concentration and focus techniques. (link 'www.psychologytoday.com')]

 Embarrassment even in the smallest amount begins a psychological impairment on a child’s ability to learn. No matter how we approach the situation singling out one student or even multiple students can impair learning.  Now I am sure there are some very exceptional teachers with the amazing ability to approach a student to find out why they are failing with minimal impact. Unfortunately, not all teachers can do this; it is a talent of charisma that we just simply cannot teach everyone. We are now left with the question: How do we give the children that need this extra attention help without singling them out? We first need to remove the extra pressure of rote learning exercises. We can do this by utilizing Open book learning approaches.

                           What is open book learning?

Open book learning takes away the pressure of having to cram for a test. Relieving a student’s stress will create a better atmosphere of learning. In introductory courses, having a system based on pure open book examinations can cause some problems of students not studying or reading the material before the test. To alleviate this problem you can implement both open book and closed book exams.  The exams need to be structure for whether it is open book or not. For the open book tests do not put in direct information that can be simply copied. Present the questions where the students will have to apply the knowledge rather than recall or look them up and simply copy it from the book. Keep it random as well don’t let the students know what kind of test they are going to be having, so you don’t discourage study.

                      Don’t be one sided.

               

Stay flexible and implement all of these strategies together. The mechanical rote learning approaches should stay limited to introductory courses. Rote learning should never be the pass/ fail in math education.  A final examination should be on concepts and understanding not recall of facts that anyone can look up.  

The purpose of education is career preparation.[edit:(9-24-2015) The purpose of education goes far beyond career preparation. It is the cornerstone of human development and understanding our world. While career preparation is a tangible by-product of education, it is not the 'sole' purpose.]   An engineer can still build a great bridge even if they have to look up a formula. However; if they don’t have a conceptual understanding of what to look up or how to look it up they won’t be an engineer for long. 

Some Mathematical FACTS about poverty in the U.S.

   According to the Dept of health and human services, the poverty threshold in the U.S is as follows.

2012 Poverty Guidelines for the 48 Contiguous States and the District of Columbia
Persons in family/household	Poverty guideline
1	$11,170
2	15,130
3	19,090
4	23,050
5	27,010
6	30,970
7	34,930
8	38,890
For families/households with more than 8 persons, add $3,960 for each additional person.

Above Chart from http://aspe.hhs.gov/poverty/12fedreg.shtml

 

LET'S DO THE MATH

Let’s break this down a little bit.   For the family of 3 the chart indicates that to be considered in poverty you have to make less than $19,090 annually.   The National housing Conference gives the fair market average price of rent on a 2 bedroom as $960 monthly which is $11,520 annually.  The U.S. dept. of Agriculture gives the cost of food for a family of 3 as $439 monthly which is $5,268 annually. The average cost of utilities (natural gas, water, electricity) varies widely but sits around $250 monthly for most families. This is $3,000 annually. 

Now to add all of this data up we get a base cost of $19,788 that puts us close to the poverty threshold.   This base cost does not include

Average fuel costs as reported by CNN are about $368 monthly which adds another $4,416 to the annual cost of living. Our total is now $24,204 annually

Let’s stop at this number for now and see how it compares to wages.   The current minimum wage is $7.25/hour At 40 hours a week that is $290.00 weekly( $15,080 annually  before taxes)   Now if both parents were to be working 40 hours a week we double this to get $30,160 before taxes.(this puts you above the poverty level and makes public assistance unavailable)   Now this is $5,956 more than the annual cost we have above, but with this situation we have a new problem(child care) Which makes a new expense.   

USA TODAY reports that child day care ranges from $3,803 to $13,480 annually, for those lucky enough to live in an area on the low average that will still leave you with $2,153 a year. However we are talking about a family of 3 here with a child. Nowhere in our expenses did we include the other basics such as clothing and toys(yes toys they are essential for a child’s cognitive development)

If your child is in diapers and you shop wisely you will spend around $30 a week $1,560 annually on diapers (this number can vary slightly depending on special needs… sensitive skin allergies etc. )   Subtract this from the $2,153 we had left above we are now down to $593 However, with diapers we also need diaper wipes. A person could bargain shop and get away with around $12 month on those. That is only $144 annually, and when subtracted from $593 leaves us with $449 clothes, shoes, toys etc….

Another expense I left out is motor vehicle insurance which is now a legal requirement in most states. The average costs varies greatly but is around $1,500 annually leaving our money left over -$1051   There are more expenses that are “necessary expenses” That I have not included, but the fact remains It is impossible to live on minimum wage with a family of 3 and both parents working full time. This is why many people get caught up in major credit card debt, have poor credit and stay in a cycle of survival by destroying their financial future. Bad credit means higher interest and high payments on any loan they try to get, which keeps them always broke. .

For those that do manage to survive by whatever means they can are on a slippery slope. One emergency (car problems, health issues preventing work, cut in hours etc…) can completely devastate a family living off minimum wage.