1+1 = ? Remember to Explain Your Answer

I am meeting more and more children who are having difficulty with basic arithmetic. Many of them are finding 1st and 2nd grade math difficult, if not impossible. Their parents are dealing with crying, frustrated, bewildered children. Parents, not sure of what the problem is, are turning to tutors for help. Often I find the child is struggling not with math but with language requirements. Many of these children can do simple arithmetic, but they can't explain how they do it. They also cannot explain how gravity takes them down a slide or explain the difference between the words a and the in a sentence. Children manage, however, to play on a slide and to use correct articles when speaking.

The new standards for math demand explanations. The mantra is, "We want students to understand math." One would hope that those who create tests reported to measure a child's "understanding" of a subject would themselves have an understanding of child development. 

There are many things in life a child does before being able to explain them. There are many things an adult does that he may have difficulty explaining. How many drivers can explain in detail what happen mechanically in a car when they hit the brakes? How many can explain the physics involved as the car stops?

A recent Atlantic article about the push for students to explain math was one of the few articles I have seen that discusses the problems some students have with this process. Although this article referred to middle school I have found that the push to explain one's answer starts in elementary school. Students on the autism spectrum, students with language problems, and students with delayed speech are put at a disadvantage when asked to explain, even with they can quickly and accurately find the answer to several of the same types of math problems.

Many younger children may not have yet developed the thought process which gives them the ability to explain the abstract. Some young students have problems with the eye hand coordination needed to circle or created the tiny lines and blocks needed to show regrouping in addition and subtraction. It is important to allow children to use concrete items when learning arithmetic. The fact that many children need these items makes one question their ability to then verbalize let alone write about an abstract algorithm. The other reality is that sometimes it is very difficult to explain in words something very simple. Some ideas are so simple that it takes a philosopher to make it convoluted through an explanation. 

Too often teachers are asked to encourage math discussions with children who get confused by the various suggested methods. While middle schoolers may have an aha moment when a peer discusses a math shortcut, a 7 year old may tune out because they haven't mastered the method, and don't have a true foundation to understand shortcuts.

Some students hit a math wall when introduced to fractions. Others hit a wall when introduced to algebra. I would be interested to see how many are hitting the wall when learning addition and subtraction today compared to a few decades ago.

There are many adults who claim to be "bad at math." Because of demands placed on them to "understand the math," some children who may get the process, and later with practice and maturity might understand the underlying concepts, decide early on that math is too hard. What good does it do to work one's way through a math problem, get the correct answer, and then be deemed ignorant because you can't give an adult explanation of how you got that answer?

We are not even going to touch the problem of children who can explain what they did in math (perhaps through memorization) and get credit for that explanation; but who seldom get the correct answer to a basic arithmetic problem. While it is true they will be using calculators someday, one wonders at the ability to explain without the ability to produce.

Reflections on Dyslexia

An Introduction

The diagnosis of dyslexia is often the beginning a long journey, starting with the question of what exactly is dyslexia?

The International Dyslexia Association' s definition is "Dyslexia is characterized by difficulties with accurate and/or fluent word recognition and by poor spelling and decoding abilities. These difficulties typically result from a deficit in the phonological component of language that is often unexpected in relation to other cognitive abilities and the provision of effective classroom instruction. Secondary consequences may include problems in reading comprehension and reduced reading experience that can impede growth of vocabulary and background knowledge."

I almost felt dyslexic reading the above definition. I think of dyslexia as difficulty reading because of the way an individual's brain processes print. The reading difficulty is not due to lack of intellectual ability, vision, hearing, English as a second language, or poor teaching.

People with dyslexia usually have difficulty interpreting the sounds (phonological components) of the language. Most people hear and process the sounds in a word so rapidly that they don't even realize they have done it. We hear the sound each letter makes in the word p-i-g and read it without dividing the sounds. People with dyslexia need structured, sequential, reading instruction that retrains the brain to decode letters into a word. People who have dyslexia also may have trouble with spelling, writing, or learning a foreign language. 

As a former teacher I have seen several issues with the diagnosis of dyslexia.  They include;

• Difficulty for parents and some teachers to understand how much effort a dyslexic person needs to make to learn to read 
• Acknowledging that the  diagnosis of dyslexia does not take away the individual characteristics of a child. A mildly, dyslexic child with an IQ around 85, ADHD, and little concern about learning may need a different approach to remediation than a severely dyslexic, focused child, with a 140 IQ,  and high anxiety about learning.  
• Unrealistic expectations of the amount of time needed to remediate a poor reader. Even the best instruction will require a long-term commitment. 
• Lack of awareness of all the other things a child is learning while trying to improve reading skills. Children are expected to learn sports, social skills, math, history, science, music, and art while they are working at learning (for them) the very difficult skills of reading and spelling. Most adults would not like to tackle that many subjects at one time.
• Severity of the dyslexia. Some children are mildly dyslexic and with good instruction fairly quickly become better than adequate readers. Some children are severely dyslexic and need many years of instruction along with modifications in their other work so they do not fall behind.
• Problems with terminology.  Parents often feel that they are listening to a foreign language when professionals discuss dyslexia: Phonemic awareness, orthographic processing, auditory processing, aphasia, executive function . . .  and then there are the acronyms: ARD, IEP,LD, ADHD, FBA ...! Never be afraid to stop a person and ask  the meaning of a word.
• The specificity of definitions of dyslexia.  For some testers the term dyslexia covers just about any reading problems. In fact,  parents may be told dyslexia can include problems in math, organization, or handwriting. Other testers give problems with math or handwriting  their own term (dyscalculia or dysgraphia). Some believe dyslexia only refers to the problem of phonological (sounds) awareness. They insist that other reading problems should not be labeled dyslexia. And some testers use more specific terms such as auditory discrimination problem, orthographic deficit, phonemic awareness deficit, short or long term memory deficit or visual motor integration disorder.  
• The reasons why a child can't read. Although most people with dyslexia are helped with a structured, phonemic based, multi-sensory approach to reading, the reality is there may be many factors making learning to read difficult for them. A person may have short or long term memory problems, attention deficit, spatial problems, motor problems, or a number of other issues that make learning to read difficult. Some children need more than the standard program given for remediation.

So if your child is having difficulty learning to read, get him tested. The schools are required to test on request. Find an organization that can help guild you through the process. Don't be afraid to ask questions. You are your child's best advocate, not just because you know your child, but because you are the only adult your child has who is in it for the long haul.  

Look for future posts of what can be done, and where to find help for the poor reader.

Random Reflections - Testing

According to The National Assessment of Educational Progress (NAEP)  only 32% of males and 38% of females in 4th grade scored proficient in reading on their 2013 test.  http://www.nationsreportcard.gov/reading_math_2013/#/ My first thought was who decides what is proficient at the 4th grade? Are our students really non-proficient or are the standards unrealistic? Someone, or a group of someones, had to decide what a 4th grader should be able to do.

Think about it: 4th graders probably range in age between 8 years 11 months to 10 years 9 months, depending on the state’s age requirements and a child’s birthday. This age grouping doesn’t take into account the child who was held back or who skipped a grade. The slow maturing 8-year-old is a far cry from the fast maturing 10-year-old. Published test results includes scores by race and poverty and (surprise!) that makes a difference in scores.

So I checked on the validity of this test. In other words, is it measuring what it says it measures?  A  2011 Washington post article quoted two experts associated with NAEP’s National Assessment Governing Board as saying, “The proficient achievement level does not refer to “at grade” performance. Nor is performance at the Proficient level synonymous with ‘proficiency’ in the subject. That is, students who may be considered proficient in a subject, given the common usage of the term, might not satisfy the requirements for performance at the NAEP achievement level.”

http://www.washingtonpost.com/blogs/answer-sheet/post/naep-a-flawed-benchmark-producing-the-same-old-story/2011/11/03/gIQAbnonmM_blog.html

According to Fair Test http://fairtest.org/naep-fair-and-valid-benchmark  “The National Assessment Governing Board (NAGB) oversaw setting of NAEP levels. A set of experts hired to evaluate the results were fired after sharply criticized the levels-setting process. Subsequently, the National Academy of Sciences, National Academy of Education, General Accounting Office and many independent researchers all reached the same conclusion: the levels-setting process was flawed.”

My personal opinion is our school children are exchanging valuable learning time for testing prep and test taking. This in only one test (for which our government has spent billions on in the last 20 years), but how many other state and national tests have proficiency levels determined by some faceless group, many of whom have never worked in a classroom or even meet a 4th grader?

The sad thing is I believe many children are not getting the education they need. However, to   build on the quote “Quality cannot not be tested into a product,” I would say it also can’t be tested into a child.