For many students Standardized Tests don’t measure facts or process.
Standardized tests measure the parents income and education as much as they measure the student’s skills in a particular subject. There is so much debate and literature on this that I’m not even going into it. My purpose here is to show parents, other teachers, and policy makers what MY experience has been, what I did about it, and perhaps influence a few decisions about assessment.
The vast majority of my students had math skills and knowledge far below grade level. Read Part 1 for the statistics. Rather than rehash my earlier arguments let’s look at examples of what I encountered with my 14 to 17 year old, high school, algebra students.
Multiplication of decimals – a 5th grade standard
Suppose you were giving a multiple guess test and you gave the problem:
With the following answer choices:
What would the student answers tell you about their math skills?
Obviously you would want to look at more problems of this type. But on my 60 problem entry assessment, there are only 3 problems like this. With a multiple guess test you can’t be sure if it’s a result like I wrote about in Part 1. I wrote about Javier who had passed trigonometry by guessing correctly on 2 out of three problems. Since letter C) is the correct answer in this example, what if the student didn’t know his multiplication facts and knew nothing of decimals but had remembered that old saw of when in doubt about an answer, mark letter C)?
I had a student get all three of them correct on my constructed response test. He showed no work (which was a requirement). I gave an alternative to showing his work: stand there and demonstrate to me you can do it in your head. He could not. Looking at other problems it was plain to see he had little idea of what he was doing.
This is also a great illustration of why those who say, “Just give them a calculator or a multiplication grid and they’ll do fine,” are only correct in rare instances. What good is a calculator if you don’t realize (i.e. know on some level whether from rote learning or intuition/discovery) that subtraction and division are not commutative [8-0≠0-8 and 35÷5≠5÷35]?
Or as Natalie Wexler wrote in Forbes (July 1, 2018):
“…when students don’t know much about a topic, it’s extremely inefficient—at best—for them to try to construct their own knowledge. At worst, they’ll ‘discover’ facts that are just plain wrong.”
What Facts? What Process?
I wrote in Part 1 that standardized tests don’t show any distinction between knowledge of facts and knowledge of process. Imagine a student doing my multiple choice example problem (34.6 x .03) in a constructed response test and coming up with the answer in letter B) 10.38. If that student showed their work you’d know that they knew their basic multiplication facts and just needed a refresher on the process of decimal point placement. I had just such a student who was quite bright but had gaps in his understanding of math processes. When I pointed out how to correctly place the decimal point he remarked, “Wow! No wonder math has been hard and I’ve failed so many tests. No one ever told me about that.”
I accused the student who gave me those tragic answers to #10 and #17 of using a calculator on what he perceived as some of the more difficult computations (like #17). He loudly and angrily argued, “You didn’t see me use a calculator!” I reminded him that certain watches, like his, have calculators in them. Anyone could tell that he didn’t use it on every computation because on many of the easier ones (like #10) he showed that he either didn’t know his basic single digit facts or process (both 3rd grade standards). I put him in a 4th grade book which I did with all my students who tested out low (i.e. most of them). He was not happy.
Dealing with the District
I got reprimanded for having 4th and 5th grade books in my high school algebra classroom. So I hid them if I had word the suits were coming [see Dog and Pony Show]. I did get caught and I did get reprimanded but only from those who never taught at a CDS school. I would justify my instructions as ‘Standards Based’ by quoting the California Algebra I, Standard 1.0:
“Students identify and use the arithmetic properties of subsets of integers, rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable.” [emphasis mine]
My constructed response tests and the Algebra 1.0 standard gave me a baseline. Once I had a baseline to start from I put two very similar yet effective learning strategies to work. They were from two different disciplines but they helped me. I’d use what I learned from Maximum Performance [Laurence E. Morehouse, Ph.D., Leonard Gross. Maximum Performance. New York: Simon & Schuster 1977. p.62] (a book about performance in general and athletic performance in particular) and from ‘Krashen’s Input +1 Hypothesis’ [Stephen D. Krashen] (a language acquisition theory that is beautiful and actually worked in my math classroom). Details:
Morehouse & Gross
At the time of writing Maximum Performance, Dr. Morehouse was a professor of exercise physiology at UCLA, and Mr. Gross was a prolific author and co-author. Morehouse and Gross defined a ‘maximal performer’ this way:
1) The maximal performer never tries the next step until he’s mastered the previous one.
2) He interprets failure as his having done something the wrong way.
[i.e. Only perfect practice makes perfect]
3) He quickly discards what doesn’t work and concentrates on what does.
4) The maximal performer specifies his target and focuses on it.
You may object to their wording of those ideas or you may say the concepts are stifling. I adjusted them as I needed. I never insist on using any one technique absolutely one way. Those of you who have read my musings before know that the only absolute I ascribe to is, “Don’t shoot the piano player!”
For an example of learning to maximize performance and success at all levels, Morehouse & Gross used golf. They said if you wanted to learn the sport of golf, it’s best to start from putting (half of par) rather than the traditional way of starting to learn golf by trying to master driving the ball [p.62]. This accomplishes two goals. It teaches you a fundamental skill and it succeeds right away. That approach worked in my physical training, in my music, and in my math class.
Krashen ‘Input + 1 hypothesis’
I heard of the ‘Input + 1 hypothesis’ both in my regular language arts methods classes and when studying the teaching of English as a second language. It’s about language acquisition, but I submit that math is a second or third language. Evidence of this is that this approach worked in my class. Here is part of an excellent Summary of Stephen Krashen’s Theory of Second Language Acquisition which focuses on Input + 1, by Ricardo Schütz (Available since: April 1998, Last revision: March 12, 2017)
“The Input hypothesis is Krashen’s attempt to explain how the learner acquires a second language – how second language acquisition takes place. The Input hypothesis is only concerned with ‘acquisition’, not ‘learning’. According to this hypothesis, the learner improves and progresses when he/she receives second language ‘input’ that is one step beyond his/her current stage of linguistic competence. For example, if a learner is at a stage ‘i’, then acquisition takes place when he/she is exposed to ‘Comprehensible Input’ that belongs to level ‘i + 1’. We can then define ‘Comprehensible Input’ as the target language that the learner would not be able to produce but can still understand. It goes beyond the choice of words and involves presentation of context, explanation, rewording of unclear parts, the use of visual cues and meaning negotiation [emphasis mine]. The meaning successfully conveyed constitutes the learning experience.”
I’d put the student in a math book or lesson or whatever seemed appropriate at his or her ‘current stage of…[mathematical] competence’ and ratchet it up one level (i.e. “he/she is exposed to ‘Comprehensible Input’ that belongs to level ‘i + 1’ ”).
In my classes:
In my classes there actually were those who genuinely wanted to learn (more than you’d think from reading some of the bizarre behaviors about which I’ve written). They appreciated starting at a comfortable level and usually progressed quite rapidly. Of course, this was after earning their confidence by actually paying attention to what they were doing.
In practical terms that meant
grading every assignment and helping each kid when they needed it.
All of which takes WAY more time than most teachers are given. I had smaller ratios but 20 to 1 still means 100 kids a day and school dominated my life and my time with grading as well as all the other duties of a classroom teacher.
What if the kids don’t take your test seriously?
That is a tough question. By the time in their lives when I got most of my students they had been beaten down by a system that paid lip service to caring about them, but they frequently told me they experienced a different reality. They felt cast off by parents, teachers, administrators and a school district too busy justifying its policies by testing. They had been taught that doing poorly on a standardized test had no consequences due to de facto social promotion [see: Unspoken Obstacle]. Doing standardized tests in math class had no effect on their lives so, “Why try?” This also spilled over into student attitudes about school and teachers in general.
My success could be directly linked to how much time I had with the student.
I had Dashawn, early in my stay at West Hollywood CDS. Dashawn showed his defiance of me and my program by answering every problem on my constructed response arithmetic test with 187. 187 is the California penal code for homicide. I went to the Principal with the student’s test. I wasn’t afraid. But since ‘you never know’, I wanted to make sure the proper authorities knew. Dashawn did’t stay with us long [read: 1 Teacher 2 Outcomes]. I wasn’t successful with him but I didn’t have much opportunity.
In Andrés’ case, [Part 1] he was showing his defiance of standardized tests. He had no reason to have faith in standardized tests. I was able to get him to trust me. So when he took my test he actually tried and he scored well enough. He took my program and me seriously enough that he learned some math. He eventually graduated but never did do well on any standardized tests. I had Andrés a bit longer than Dashawn.
Then there was Angie, my pride and joy. She looked like defiance personified. She had more tats and piercings than any other student on campus (and we had a lot of tattoos and piercings on campus). I don’t care what a kid looks like. I had an afro and wore platform shoes when I played with a funk band back in the early 70’s! How you treat others, how you treat yourself, and how you work were important in my class, however… Angie didn’t do well on my entrance exams.
I put her in the 4th grade book. She worked consistently and was well behaved. She kept getting As. I said to her, “It looks to me like you already know a lot of this basic stuff. Were you having a bad day when you took my entrance exam?” She said, “Yeah , kind of. But I also didn’t know if it was worth it. Let me take it again and this time I’ll try to do well.” She did great. Turned out she was one of my best students and a real honor and treat to teach. I had Angie in class long enough to earn her trust, and that allowed me to be of some help to her.
We won an award but time is the issue.
Statistics can be helpful but they can also mislead. Our school won an award one year for dramatically increasing our overall test scores. We hung it on the wall and pointed to it proudly, but we smiled when we remembered how we got it. Ours is a school with a high ratio of violent offenders to good kids who did foolish things. Most consistently tested low. When an honor student transferred in (yeah even good kids do crazy things) his scores alone shot up our overall average. We won an award for that!
Standardized tests do have a place.
There are those parents who would insist that their child should be tested, along with those parents who refused to let their child be tested. Teachers need to be able to choose (or at least have more of a say so than they do now) as to which tests are helpful and which are an intrusion on learning, class by class and – if justifiable – student by student.
What really helped Angie (and me) was time. Time for Angie to get to trust that I wouldn’t waste her time. Time for me to learn her strengths rather than assume she needs her weaknesses healed. I never had enough time with any of my kids (is there ever enough?). Don’t assume I’m preaching some pollyanna, feel good, pie in the sky, silver bullet, quick fix. Until we teachers can teach the policy makers and tax payers that we need more time we can expect more of the same [see: Responsibility or Status Quo]. Until we can convince all stakeholders that we need to be able to judge which tests are right for our students we can expect more standardized tests.
Testing is necessary or testing is a wast of time? Standardized tests or your own constructed response tests? Portfolios with projects or Standardized test scores? Teach facts or concepts?
Either/or is not the question. It is a false dichotomy.