Thursday, August 27, 2015

Two weeks

I will not be posting for a couple of weeks. Check out the topics on the right under labels for specific previous posts. Future articles will cover sleep, how ADHD affects learning, and communications with your child's teacher.

Wednesday, August 12, 2015

Speaking of Curriculum

I liked this article because it showed that research indicates content and practice may be the most important part of lasting education. 

Monday, August 10, 2015

Math Education Rant - Part 2

What Can be Done 

The previous post Math Education Rant - Part 1 divided young math students into three groups: the top students for whom math makes sense and is generally pretty easy, the middle students, usually the majority of a class, and the poor students who find math extremely difficult. My opinions about math education in elementary school take into account all three groups.
  1. Maria Montessori based her educational methods on child development. She understood the prerequisites for a child to be ready for math (and other subjects) in a classroom. Her prerequisites were "First a child has established internal order, Send the child has developed precise movement. Third, the child has established the work habit. Fourth, the child is able to follow and complete a work cycle. Fifth, the child has the ability to concentrate. Sixth, the child has learned to follow a process. Seventh, the child has used symbols." Once a child reached this maturity of mind and a readiness to work, it was time for them to work with concrete math materials. There are far too many students who start kindergarten without these prerequisites. These children need to be given time and a curriculum to make sure they have "a readiness to work." 
  2. Speaking of time, there is a continuous pushing down of the curriculum. When five-year-olds are expected to do first grade work we are pushing them to learn concepts they may not be developmentally ready to learn. There are complaints about the number of students who require remedial math classes when they start college. Perhaps if children were given time to learn at the beginning of their academic careers, they wouldn't need as much at the end. I have seen first graders who were having difficulty with double-digit addition. When tutoring these children it was apparent that they were still having trouble identifying written numbers such as 11 or 12!
  3. Most children in elementary grades need concrete materials to help them understand abstract ideas. Using Unifix blocks, Cuisenaire rods or other math materials needs to be a continuous activity. One day of demonstrating a concept doesn't give children enough time to work through the process on their own. Many teachers stop the use of concrete items in the upper elementary grades, but most children still need concrete items to understand fractions and decimals.
  4. Teachers need to understand that manipulating concrete items like beads, while necessary for young children, doesn't mean the children transfer that knowledge to the abstract symbols of numbers. The symbols need to be taught with the items, but that still does not mean a child will totally understand an abstract concept. 
  5. In a effort to insure that children "understand" the underpinnings of math we overwhelm them with explanation. Some children who might be good at math are hindered by this overuse of words. An explanation of how to do a complicated process, even with a demonstration, is very difficult for some young children to understand. Requiring students, themselves, to explain the process is even more difficult if they have poor language and/or writing skills.
  6. While in theory teaching a child more than one method to do basic arithmetic sounds good, that approach adds a layer of confusion to some children. They may decide to combine the methods, and do so incorrectly, or never thoroughly learn any one method. Adults may readily see how the methods are related, but an eight-year-old may not have the language, or cognitive ability to see this.
  7. The visually busier the page (lines, boxes, circles) the more difficult it is for some children to comprehend what they are suppose to do. Lattice multiplication is an example of this. I have tutored children frustrated by required lattice multiplication because the spaces were too small for their large handwriting. A child with visual perception problems can even be confused by graph paper!
  8. Some children need more time to learn than others. We have no problem understanding a young child wanting to hear the same book read again and again. We need to give the children who need it time for repetition, or a break to do something else, and then come back to the concept. I worked with classes of children who had difficulty with math (as you can see in the example I gave in Part 1) Parents raved at the progress their children made in my class. I often felt it was just lucky that I taught a child the year he or she was finally able to understand the lessons. When I tutor I meet young children who obviously can't understand something (glazed eyes, a look of panic and complete confusion, etc.) who three months or even three weeks later find it suddenly makes sense. Educators have to be aware if something is beyond a student's ability at a given time. If we can't give an elementary school age child the necessary time, there is something extremely wrong with our education system.
The above eight points concern the need to look at children's ability to learn rather than what is being taught. Too often curriculum ignores the learning differences in children, the various developmental stages of the young student, and the variation of abilities in the new student. The next paragraphs concerns how to implement teaching a curriculum to groups of young children. 

I had the privilege to do student teaching in a school with an excellent math program. The entire school (k-5) had math the first period. The math curriculum had been divided into weekly modules. Each module had a pre- and post test. This allowed a child to test out of a module. The school had specific teachers who worked with children who had to repeat a module. Repeat modules tended to include more hands-on materials and more individual attention. Because everyone had math at the same time, the student who tested out of a module could move up right away. Math classes might consist of children in 3rd, 4th and 5th grade. A child who found math easy was not held back, but still could repeat a module when she came to material that gave her difficulty. A student who might have difficulty in subtraction could still move up if he found it easy to measure perimeter. Some modules were reviews of pre-requisite skills for new concepts. 

The children seemed to love math. The math-adept second graders got to go to class with fourth graders. All children knew that if they didn't "get something" they would have a chance to try it again. No one seemed to feel bad about having to repeat a skill because everyone had to repeat now and then, and you got a different teacher when you repeated a module. Worksheets tended to have large print, simple instructions, and plenty of white space since there was a limited amount of material and it was understood that there might be very young children in a class with subject matter often taught only to older children.

The U.S. tends to have a math curriculum that is very broad (many topics) and fairly shallow (not much depth to each topic.) Modules allowed students to get the depth they needed.  I am not suggesting that all schools use this method but I believe elementary schools should have math programs based on the idea that children need to be able to work at different speeds and move up or down at their own pace. The emphasis should be on children and how they learn, rather than on speeding through a curriculum, holding children back who could readily move ahead under the guise of saying, "Why those children learn while they are helping others," and refusing to recognize that individuals might find some areas of math easier than others.  Such a program would give all children a change to get a firm foundation to build on, rather than a shaky platform to start middle school. 


Saturday, August 8, 2015

Math Education Rant - Part 1

I just finished reading an article about classes created to help parents help their children with Common Core math homework. I also read the comments following the article. My reaction to the comments are the reason for this post.

Every few years the U.S. decides we need to change the way math is taught. This is said to be a response to students doing poorly of some national or international test. (It is seldom mentioned that changing a curriculum is a huge financial gain to those who sell curriculum, but that is fodder for another post.) 

Anyway, with the change new books and materials are purchased, websites are formed and subscribed to, schools pay consultants to train the teachers, and finally the new program is presented to the students. Ten years later it is discovered that some students are doing poorly in math and the process starts again. As the quality of children's understanding of math is bemoaned in the media, comments come in from math authorities (often engineers or other professionals who use math in their jobs) who insist that: 1. Math is easy, 2. Elementary teachers don't know how to teach it, and 3. It is a shame that young people can't make change anymore. As a teacher I have observed the following:
  • There are some children who find working with math to be a wonderfully ordered process. They see the patterns, think math is an easy subject, and will learn and understand math regardless of how it is taught and who teaches it. These students easily learn whatever method is taught to do basic addition, subtraction, multiplication and division, grasp the concepts, and utilize their own shortcuts.
  • The next group of students are the majority, who get through math class in the elementary grades with a bit of work. Some things come easily, some take a bit more work. Some of these children love math class and some hate it. But they get through it and have the ability to work with basic arithmetic before tackling algebra. 
  • Finally we have a group of children who find math extremely difficult, if not impossible. Some of these students have dyscalculia, some have other learning differences (LDs), some have cognitive disabilities, but math to them has no logic. Every math class is a new day with no connection to material presented the previous day.
Let's look at how arithmetic may be presented to this student.
Example: 221-35 = 

  1. Old math: We borrow one from the two next to it then subtract the 5 from 11, change the 2 to one, borrow from
    the next 2, subtract 3 from 11,  etc.
    See example 1. below
  2. Newer old math. Regrouping - Same as borrowing only we show the place value concept so we don't borrow one, we borrow ten, (and 100) but the problem looks the similar to the first example with more changing
    numbers on the top 
    See  2.
  3. New math: See example 3. Understanding numbers - It is easier to subtract a zero so we round up the 35 to 40 and because it is easier to subtract 20 we first subtract 20  and then second twenty from 201 and add five to  181 giving us the 186 answer or one can subtract 30 from 20 for 191 and subtract five to get 186
So what does the really poor math student do? (The first time I saw a 4th grade student do this I was amazed. The second time I almost cried.)  221 - 35  =    Hmmm . . .  Can't take five from one but I can take 1 from 5,  and can't take three from two, so 3 minus 2 is 1 and two minus nothing is two, ergo the answer is 214! (This student is so happy to get through an easy problem without having to round, think about place values, write funny numbers on top, or subtract more than once that the thought of just looking at the answer and logically thinking it has to be less than 200 doesn't even make a blip on his radar.)

Of course the adult who found math easy rolls his eyes and blames the teacher. (This adult usually has a child who also finds math easy and has never enjoyed the experience of working with a child who sees math as the seventh circle of Hades.) The teacher sighs and works with the child using demonstration, questions, and maybe even concrete materials. The child nods and suddenly seems to remember that yes, we did do something like that last year. He dutifully corrects his work (with no real understanding of it) but if he doesn't have to subtract for the next few days he reverts back to old habits. So what can be done?

Next Post: What Can be Done 



Tuesday, August 4, 2015

Grade Level?

When I was a classroom teacher one of the most common questions I heard was, "Is my child doing grade level work?" Often a parent would be more specific asking questions such as, "Is my child reading on grade level?"

I understand the reason for these questions because when my child was young I remember comparing his work to the other work posted in halls and bulletin boards. Most standardized tests also include a grade level score which compares children to others in the state or nation. So what influences a grade level expectation? When you think about grade levels remember:
  • Although we think of grades being synonymous with age, in the U.S. a first grade class may have children ranging in age from 5 - 8.  How does that happen? Birthday cut off dates are determined by the states, and people move. Some parents talk a school into letting a child in early. Other children must repeat first grade or kindergarten so they are at the high end of the age range. 
  • A child's classmates often influence the instruction level in the class. While it is true that teachers follow curriculum, the behavior and academic ability of the children always influences what is being taught and how it is presented. A child who goes from kindergarten to 5th with a disorderly group of children who entered school already behind in basic skills, receives a different education than one who takes classes with mannerly, well-prepared classmates. 
  • The U.S. does not have a national curriculum. Moving to another state, or even another district may mean your child is ahead or behind her classmates.
  • Teachers hate to define the grade level of most children. They may have experienced two extreme reactions from parents. One reaction is absolute denial and excuses. The other reaction is extreme activity to correct the situation: various therapies, tutors, requests for more homework, etc. These reactions tend to make many teachers tread lightly.
  • Teachers tend to be optimistic about the gains a child may make during the year. Often a verbal child is rated higher than his or her test scores indicate. Teachers may feel sympathy for the sweet child who tries to do well in class.  Sometimes a teacher is aware that a child is anxious (due to a home situation) which influences scores. A new teacher may not have the experience to really say what an  "average" child should be able to do. A long term teacher may have had too many good surprises from supposedly poor students to want to label a child too early.
  • The term "grade level" ultimately means a child is able to function in a specific grade. This is different than subject matter competence. A child may be able to read fairly well, or do math very well, but is unable to function very well in the group environment that is public school.
So should parents ignore the idea of grade level competency? Of course not! A child functions best if he is correctly placed. Parents also need to be aware that their child is making progress and, if not, need to question what can be done.

Many children are pretty competitive in our society and most children at a certain point pick up the fact that they can't do something that their friends can do. I have seen six  year old children who have become anxious because they can't read. While it would be wonderful if this didn't happen, and we can work for a change in education, the reality is that the change probably won't come in time for your child. Parents should look at their child's progress with the following mindset:
  • Young children do not develop lockstep with other children and there may very well be a large variations in the ages of children in the elementary grades. 
  • The younger the child the more a parent needs to consider physical needs - children don't know if they need glasses, or tubes in their ears, or even if they are grumpy because they didn't get enough sleep. 
  • School continues to be a group activity. Some children need modifications in the learning environment due to learning differences. Some children need a slower pace. But. . . parents need to be realistic about what a school can provide.
  • Parents should be aware of the quality of the school their child attends. 
  • Questions about specific skills give more answers than grade level questions. How is my child's reading fluency? Is she having problems with sight words? Is he usually the first or the last to complete his work in class? 
  • Teachers seldom compare students when talking to parents but classwork is often on display somewhere in the classroom. This is where, if you want to, you can discretely check out your child's work compared to her classmates. Is your child's work messier, shorter, longer, or is he following the prescribed presentation method- title centered, etc.? 
  • Finally, if you are concerned about grade level expectations, here is a link to hear children in the U.S. reading at first grade level  The Internet has various sites to check out grade level expectations.



Saturday, August 1, 2015

Great Resource

I just discovered and now recommend this link if your child has learning or attention issues.