Timed Tests – Are they Helpful?

Before I get into how I really feel about timed tests, I must share my confessions. I started teaching 6th grade mathematics in the early 1990’s. My students did not know their multiplication facts. (I hear this comment still today from 3rd-12th grade teachers!) So I gave a timed multiplication test every Thursday. There were 34 problems on the test and each one was worth 3 points. So if you answered all of them correctly, you could earn a 102. The students would typically have anywhere from 2 to 3 minutes. I never told them how long I actually gave them, they were just told that they had 2 minutes. I did NOTHING between each Thursday to help my students develop an understanding of multiplication either. (It was not in my standards.) So week after week I had the same students scoring 102 and couldn’t wait for the next Thursday. I had another group of students scoring a 42 every week and they acted like they could have cared less about the test. Then there was the third group of students scoring between 78 and 90 each week. They walked into class each Thursday with sweaty hands and some even sick on their stomachs. And for the most part, no one moved out of the range of scores I just provided.

I began teaching in January that year and replaced a teacher who retired in December. She had the reputation of being a great disciplinarian. For you teachers reading this, you know what that means…she had all of the ‘hard to manage’ kids on her team. That may have been a good plan in the past, but placing a brand new teacher in the same position was not very kind. I was either writing students up or writing assignments for them while they were in In School Suspension (ISS). Our team kept getting notices from the ISS teacher stating that we weren’t sending enough to keep them busy. So if they had any ‘free’ time, the ISS teacher just assigned a page or two out of the dictionary for the students to copy. Ugh! Are you kidding me? So I decided if the students were going to copy something it would be something that would benefit me. : ) I began sending a sheet of written out multiplication facts and had my students copy that during their ‘free’ time.

It didn’t take long to discover that those students started scoring higher on their multiplication tests each Thursday. About that same time the parents of the ’42 group’ were calling and complaining. So I came up with an idea. For every complete set of multiplication facts a student turned in, he/she would earn up to 10 points to be added to their lowest multiplication test (a set consisted of the twos-twelves). No one could raise their score above a 100. That was reserved for those who correctly answered all 34 problems on the first try. Yes, scores began to rise dramatically.

I’ve read research that supports timed tests as long as you are doing something to help the students improve in between the tests. (I have an idea of the source of that information, but I’m afraid to put it here without being certain.) The scores should not ‘hurt’ the students’ grades and the student should be encouraged to better their score, not necessarily to score a 100. I’ve also read research that says if you hear, say, do and write something you are way more likely to remember it. So all I had done was add the ‘write’ component.

Although I experienced success with my methods at that time, I now question my motives. My main goal was for my students to learn their multiplication facts – and most of them did. But the students who had scores improve on the timed multiplication test did not improve their scores on anything else they completed for me. I was not teaching for understanding. I now realize that my motives were focused on short term goals and not what was best for the students in the long run.

Since my early years of teaching I’ve read more research – the kind that goes against timed test. http://joboaler.com/timed-tests-and-the-development-of-math-anxiety/ is a wonderful example of this and she even provides links to the research that supports her article. Timed tests can (and does in many cases) create or contribute to a hatred of mathematics. It took a while for this to sink in to my thick head because ‘I had seen the success in my own classroom’. Once I began thinking about the logic, my own beliefs started to change.

Timed ‘test’ does not have to exclusively mean a test; it could be the use of flashcards, or the class game ‘Around the World’. Consider the kids who already know their facts. Are they learning anything by using flash cards, playing “Around the World” or taking a timed test? This is just a waste of time for them.

Now consider the kids who simply do not know their facts. What will the timed tests, flash cards and playing ‘Around the World’ do for them? My guess is that they will act out, become angry, develop greater self helplessness in mathematics, and learn to ‘not care’. I’ve seen this happen. All of those outcomes are the only way many of those students know how to cope with disappointment, embarrassment, and frustration.

Next consider the kids who are middle of the road when it comes to knowing their facts. They know the basics but flounder when it comes to the 6, 7, 8’s. The ones they may know this week they don’t know next week and vice versa. They’re the ones who get all worked up over the timed tests, because right now they still care. During ‘Around the World’ they aren’t hearing the facts that are given by the other students, they are just sitting there praying for the teacher to call out an easy fact when it gets to them; or better yet, they’re praying for a fire drill or for class time to run out. Some of these students may learn more math facts as a result of the negative pressure, but others just begin to move into the frustrated, angry, depressed, “I don’t care anymore” category.

So let’s recap the scenario above regarding timed tests, flashcards, and ‘Around the World’. Who benefited? Only the few in the middle group who actually used the negative pressure to cause them to try harder. For everyone else it was a waste of time and more specifically even detrimental to many.

So am I saying that students should not learn their math facts? Of course not! I know that life mathematically is a whole lot easier if you know your addition and multiplication facts. But students should be learning their facts with understanding. For example, they can learn their facts through the use of Number Talks and Cognitively Guided Instruction.

Did I open a can of worms today?

Have YOU ever had an Intellectual Need?

Yesterday I had an intellectual need! I’m sure I have experienced this need before, but I wasn’t aware of what it was called. As a matter of fact, I have already spent 30 minutes trying to define it the way it was defined for me and I’m still typing and backspacing.

For the sake of time I am going to try to muddle through this. I apologize in advance to Dan Meyer because I know that there is no way I can type in several paragraphs all that I learned from his presentation yesterday. Have any of you ever struggled to motivate students to WANT to do mathematics? I’m just going to call you a liar if you say No. What are some reasons that students work in a mathematics class? Desire to earn a good grade, expectations from home, goals of academic scholarships, fear of the consequences,to make the teacher happy, just because…But what about ‘intellectual need’? Have you ever had students in your class want to ‘do mathematics’ simply because they ‘just have to know‘?

I can’t summarize for you who Dan Meyer is or all that he does. I can only point you to his site. http://blog.mrmeyer.com/ On the far right column you will see a link for Three-Act Math Tasks. If you don’t go and pull up and read at least one of these tasks (I recommend Soda Math), you won’t understand the following comments. We are not talking about typical text book problems.

One thing that I can do is summarize the ‘rules’ for generating intellectual need. These are my notes from yesterday.

1. We need to ask our students for estimates – privately and then publicly. Once all students write down their individual estimates and then share them publicly, they become invested in finding out the ‘answer’.

2. Delay the information, vocabulary, and knowledge a little bit. A problem was set up but no detailed information was provided. We were then asked to write down what we wanted/needed to know. In Soda Math we needed to know at least 4 measurements. However, Dan only provided 1 measurement. We were then told to estimate the remaining 3 measurements.

3. He kept us at the edge of our capabilities and provided extensions (sequels) as needed.

4. He recorded our thoughts and in particular highlighted the differences to create a controversy.

5. Asking students to prove or disprove statements they understand is very often full of intellectual need. Does this sound familiar? If it doesn’t how about these words – Construct viable arguments and critique the reasoning of others. Yep, straight from the Common Core Standards for Mathematical Practice.

6. As the instructor, Dan positioned himself as surprised by stuff he definitely wasn’t surprised by or acted as the bumbling know-it-all.

7. We were given huge numbers to force us to think beyond our small tools.

8. Unexpected or counterintuitive results makes people want to know why.

9. Everyone loves to be puzzled and unpuzzled.

I am still processing all that I experienced yesterday and will probably write again later as I wrap my mind around everything. I just didn’t want to delay getting the word out about this wonderful resource for mathematics teachers. Dan Meyer tasks are primarily for middle and high school content. However, he graciously directed us to additional sites: http://www.techsavvyed.net/archives/2352 provide video story problems for the primary grades. http://www.estimation180.com/ provides an estimation problem for every day of the school year. http://wyrmath.wordpress.com/ requires students to choose between two options and then justify their choices. http://wyrmath.wordpress.com/ is an additional site he shared. I just haven’t had the time to investigate it yet.

 

Clue Words? Please don’t!

Now I know that most all of us are familiar with clue words to solving word problems. We were either taught them, or we have taught them ourselves, or we have had children who came home with them in their math notebooks.

For example, the following words supposedly indicate addition: in all, together, altogether, total, both, etc.

But consider the following problem.

Max likes to collect marbles. For his birthday his grandparents gave him 100 more marbles. Now he has 567 marbles altogether. How many marbles did he have before his birthday?

According to the clue words a student should add the numbers in order to solve the problem. However, adding the numbers would not yield the correct answer, nor would it even make sense.

I am NOT saying that students should not understand the meanings of words. But the meanings of words can be taught and learned without being taught as a ‘clue’ for what operation someone should use to solve a word problem.

I have a personal experience to share. Several years ago I went to my niece’s and nephew’s school to facilitate a mathematics lesson in each of their classrooms. My nephew’s group of four were solving “Max has 39 cupcakes. 17 are chocolate and the rest are strawberry. How many strawberry cupcakes does Max have?” He was so excited as he called me over to his group and told me that there were 22 strawberry cupcakes. I asked him how they knew that. One of the students said “Well, we subtracted to find out how many were strawberry.” All of the sudden my  nephew said, “Oh no, we have it wrong. We were supposed to add”. Not showing any emotion I asked why he thought they should have added. He said, “Well, because it says ‘in all’ and it says on that poster over there (pointing to the wall) that ‘in all’ means to add.” I thought I would cry. When the students were thinking about the actual problem and making sense of the actual content they reasoned their way to a solution – the correct solution. Yet, when an operation was mentioned they immediately gave up reasoning and (in my translation) thought “Uh oh, we’re not supposed to pay attention to all of the content. It will confuse us. We need to use that helpful chart with the clue words that will help us to always get the right answer.”

I have often said that I do NOT believe that teachers walk into a classroom thinking “Oooh, I’m going to mess my kids’ up so badly today…” Teachers in general love children. Most if not all have a nurturing nature. We want to help our students. At times clue words have proven to be helpful. The problem is however, that only the most traditional word problems follow the ‘rule’ of the clue words. If I am standing in front of a classroom and creating a word problem ‘on my feet’ I am more likely to create problems where the end of an action is what is missing. Two amounts are put together and the student is asked to find the total. Or two things are separated and the students are asked to determine what is left. But there are many problem structures that we rarely provide for our students.

I would like to introduce all mathematics teachers to Cognitively Guided Instruction (CGI). http://cognitivelyguidedinstruction.com/index.html and http://www.promisingpractices.net/program.asp?programid=114 are two links where CGI is discussed in detail. To be honest I know nothing about either of these sites but they seem to provide the background information needed to get a good idea of CGI. The first site provides 4 ‘GOTTA HAVE’ books for all teachers of mathematics.

So, if you are a teacher of mathematics and you have a poster of clue words on your walls, please remove it immediately. Order and read the Children’s Mathematics: CGI book and then provide for your students opportunities to work with a variety of problem structures without ‘telling’ them how to solve the problems.

I realize that many of my posts may cause discomfort for some, clarity for some, confusion for some, and maybe even anger for others. Please feel free to contact me if you have any question regarding any of my posts. robynovrick@yahoo.com