Archive for November, 2011

Common Core Math Standards (And What Science Education Can Learn From Them!)

November 28th, 2011

Skipping steps in science education and what we can learn from math standards

In math education, no one would dream of asking students to calculate the area under a curve before they have learned to count! Second grade classes do not solve for x before learning simple numeric relationships like greater than, less than, and equal to, or how to add, subtract, divide, and multiply numbers. This is because there is a nearly universal understanding in education that mathematics is built one concept upon another.

There is an accepted basic sequence in the presentation and practice of math concepts. This sequence is based on the premise that to truly understand a concept, you must first understand the basis by which that concept has arisen. For example, the number 2 does not mean much without understanding the number 1, or that 1+1=2. We can relate any concept to the top of a stairwell, and each step leading up to it as the necessary steps to get to the top, or the final concept. If you skip a step, you might get to the top faster, but you won’t fully understand the concept.

Likewise, when transferring from one school district or even state to another, students are likely to encounter similar math concepts from school to school at various levels.

One of the interesting and regrettable aspects of past practice for science education is how our long-time experience with the conceptual sequence nature of mathematics is typically not applied in the science curriculum. Consider, for example, the following list of activities that may be considered as part of the science curriculum in many schools in the country:

  • A first grade class visits a local pond.
  • A second grade class anticipates the hatching of a cocoon into a butterfly in a nylon cage.
  • One third grade class grows seeds in plastic cups, while another, in the same school, traces the outline of students on wide rolls of “butcher” paper for subsequent labeling of body parts.
  • A fourth grade class has an aquarium or hamster in the back of the room.
  • A fifth grade class makes models of the solar system out of marbles and ping-pong balls.
  • A local park ranger speaks to a group of sixth grade students about water pollution and its effect on animals.

Are these activities scientific? Of course they are. The problem is that, without a clear progression of science concepts,the science education experience that results from a hodgepodge of activities like these is likely to be a patchwork of interesting memories without deep meaning. The beauty of science is in understanding the interrelations between such diverse topics. Recognition of such relationships requires a scientific conceptual base, one that involves a sequence that logically builds upon itself.

Now, let’s return to the list above and make two other important observations. First, with the exception of the model of the solar system activity, all of the topics are drawn from the life sciences. There is a conspicuous absence of physical sciences – chemistry and physics. Second, there is little use of math in conducting the activities. This is not always the case, but it is the typical case. What a shame. Science is the perfect vehicle to add application and purpose to math! Let’s just consider two aspects of basic mathematics here: Numbers and Counting and Numeric Relationships.

Numbers and Counting

In math, we learn to count. We learn that 5 comes after 2 and before 7. We also learn that each numeral may be used to represent the number of things. 10 fingers, 2 hands,  and 1 nose.

In science, most all numbers require units. For example, nothing weighs 57. No place exists 500 from where I am standing. Without units, numbers in science are nearly meaningless. Someone may weigh 57 kg (kilograms). Chicago may be 500 km (kilometers) from where I am standing. As we will discuss in our next blog on Common Core Standards: English Language Arts, we use units associated with numbers all the time in common language as well. Consider the list in the previous paragraph again: 10 fingers, 2 hands, and 1 nose.

Numeric Relationships

In math, we learn that 5 is greater than 2 and less than 7 (5 > 2 and 5 < 7). We can then conclude, with no additional data, that since 5 is greater than 2 and less than 7, then 2 must be less than 7 as well. Numeric operations contribute immensely to the relationship between numbers. Even though both 5 and 2 are each less than 7, if we add them together (5+2) they are equal to 7 (5 + 2 = 7).

In science, the relationship between different numbers gives us interesting properties such as motion, density, and concentration. If a person moves 7 m (meters) in 14 s (seconds), they have a speed of 7 m/14 s or 0.5 m/s.

A block with a mass of 0.8 kg and a volume of 1 m3 (cubic meter) has a density of 0.8 kg/1 m3 and will likely float on water. On the other hand, a much smaller block with a mass of only 0.4 kg and a volume of only 0.1 m3 has a density of 4.0 kg/1 m3 and will sink like a stone (note: density = mass/volume).

Missing the Boat

Speaking of floating and sinking, the simple fact is that we miss the boat and lose a tremendous tool for teaching math concepts and skills when we do not directly relate them to the science curriculum.

This is particularly true if we have the opportunity to present a 100% hands-on, experiential science curriculum like LabLearner. Students in a lab collect data all the time. Some of the data is descriptive (colors, smells, sounds, etc.). We will discuss the impact of the science curriculum on descriptive language in our next blog.

On the other hand, much of the data collected in a science lab concerns size, weight, speed, temperature, time, and other quantifiable parameters. All of these forms of data necessitate numbers, units, and calculations. Performing the mathematic calculations required to solve problems from the science lab not only provides repeated practice of math skills, but also allows students to get a sense of the importance and practical applications of math as a whole. Science lab captivates and intrigues students with interesting occurrences and challenges them to explain what happens, and to predict what will happen next. However, without math, they are helpless! They require math to make sense of their data.

Teaching Science in Progressing Steps: It Makes Sense!

I don’t know how many times in hundreds of classroom observations we have seen students literally demand to know how to do the math required to explain their experimental results if they do not currently have the specific skills to do so. For example, I recall a fifth grade student who was growing frustrated trying to measure the distance around a wheel with only a meter stick. As he turned the wheel, he tried to “bend” the meter stick around it, but kept loosing the exact spot. He walked up to his teacher and said, “We can easily measure the distance across the wheel with the meter stick. Surely there must be some way to use this number to get the distance around the wheel! This is ridiculous!” His lab partners agreed. The teacher seized the moment, explaining that C = (pi)d (circumference = 3.14 x diameter). Her students jumped months ahead in math, thanked her, and went back to their experiment.

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What’s The Point Of Creating New Standards?

November 21st, 2011

Why do we need new academic standards? According to The Opportunity Equation group, there were several reasons for states to join the Common Core State Standards (CCSS) initiative back in 2009:

“For states, there are many good arguments for adopting the Common Core State Standards: Common standards* provide clarity about what students are expected to learn in mathematics and English language arts; they help teachers zero in on the most important knowledge and skills; they establish shared goals among students, parents, and teachers; they help states and districts assess the effectiveness of schools and classrooms and give all students an equal opportunity for high achievement.”

*Author’s Note: That is, as opposed to standards developed and adopted by each individual state as in the 1990s. The “Common” of the CCSS therefore reflects that they are intended to serve as a much more universal, national core of academic guidelines. A common core of standards that is much more consistent from state to state.

If we consider the quote above, one might ask, outside of the “common” element of the CCSS, couldn’t this mission have been realized using existing national and state academic standards? Zeroing in on the “most important knowledge and skills” for example, may have been achieved by streamlining and consolidating bulky 1990s standards. Establishing “shared goals among students, parents, and teachers” is a question of communication and commitment and, at least on the surface, would seem potentially independent of whether we were considering 1990s’ or 2000s’ standards. And as to helping states and districts to “access the effectiveness of schools and classrooms”, the 1990s rendition of standards had more than enough high-stakes, standardized tests to do this, perhaps too many!

So let’s repeat the original question – why do we need new academic standards? Surely there must be one overarching reason. One answer that would make real sense. Namely, that the 1990s academic standards did not work well enough (by what criteria?) in terms of student achievement and success. No outcome in education can or should trump student achievement. So the question must become, what is wrong with our current standards, many of which are barely a decade old and were developed by countless hours of work from Nobel laureate scientists, teachers, politicians, and state and federal departments of education – much the same group that is working on the new standards?

Are we really sure that the reason that the last version of academic standards didn’t work because they were written poorly or missed the point? Could be. However, if we do not consider alternative explanations of why the 1990s standards were so inferior as to deserve retooling, we run the risk of failing again with a new set of standards. It would seem that the most obvious place to look is at the educational system itself. How well-trained in scientific thinking are our practicing complement of K-12 teachers, for example. It is difficult to teach something that we don’t know well ourselves. This question may be acutely critical for our K-5 elementary school teachers. Of the hundreds of elementary teachers we have worked with over the years, nearly none went into elementary education because they wanted to teach science!

If teacher training is an issue that could impact the success of the CCSS initiative, what are we planning on doing to reverse the situation as quickly as possible? And what about preservice student teachers? Are we confident that the next generation will be better prepared to confidently handle the science content required to train their students to think scientifically? What about science supplies and equipment? Do our schools have facilities for serious hands-on science instruction, and again, are our teachers prepared to teach in this unfamiliar style?

The final point is simply that, if previous standards failed, even in part, due to our system of education, then we must address the relevant issues with the same intensity and intelligence that we are devoting to new standards. If not, CCSS will likely fare no better than the standards we seek to replace. CCSS will fail as well.

But, there is good news!

Perhaps the main reason that the last generation of national and state standards did not succeed as we would have liked is because they were never given the chance. Perhaps we went wrong from the very beginning. Perhaps we did not spend enough time educating our professional teaching staff and administrators to understand the point of the 1990s standards.

Instead, teachers did what they have always done – they did the best they could with the information they were given. What should have been eureka!! moments turned out instead to be pages of bullet-point standards. Instead of debating the best pedagogical strategies to accomplish an inspiring and noble mission, to make their students the best they can be, they were handed a pile of standardized tests and a warning.

The good news is that almost everyone in education has recently witnessed how not to improve the system. How not to inspire. How not to teach. Moving forward, the key will be to build a team consisting of teachers, principals, parents, and students. The key will be to articulate a clear plan to that team so that they not only know what they are supposed to do, but why they are doing it and why it matters!

Note to readers: In the coming weeks Dr. Verner will delve into specific standards (math, language arts and science). You can expect a detailed discussion on math standards next week!

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How Does YOUR Mind Process Information?

November 16th, 2011

Dr. Verner recently spoke with teachers and principals at the Diocesan Education Institute in Arlington, VA about the Information Processing Model and how our minds work. Click the link below to follow his presentation and take fun tests to see firsthand how you process information (you can test your students as well)! Click here to learn about the Information Processing Model.

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Influencing What Your Students Remember

November 8th, 2011

If you’re a teacher you know that a student’s mind can wander during the course of a lesson or class. You also know that you want to get as much information into their brain while you have their attention. You might think that different students are focused and/or will lose their attention at different times. While there are certainly individual differences, studies suggest that there are common patterns shown by all students.

The Serial Positions test, one of the most reproducible cognitive tests known, demonstrates that there are absolute times when your class is likely to be at their most attentive, and also when the class is most likely to lose focus. Clearly, we want to get as much important information to them during their peaks of attention!

In the Serial Positions test, subjects are shown a series of words for 2 seconds each. They are told to try to remember as many of the words as possible after the list is presented. When the test is scored, the results are consistent with the graph below:

Serial Positions Effect (Click to enlarge)

Psychologists and cognitive neuroscientists interpret these results to indicate that in a “learning session” students remember most of what is presented at the beginning and end of the session, with very little recall of what is presented in the middle of the learning session.

The initial level of high recall is usually attributed to the “Primacy” effect. That is, students tend to focus and process information early in a learning session. This could be for various reasons. For example, it may be because the brain is preparing for new information and is therefore paying extreme attention to the initial moments of a session. This attention and information processing then wanes as the session progresses.  The student gets tired of thinking.

The upward level of retention following the trough of low retention is usually ascribed to as the “Recency” effect. This elevated level of recall is generally thought to be due to the notion of short-term memory. That is, whatever was presented last in the learning session would be remembered simply because it remains in short-term memory and is not replaced with new information.

These results suggest that we may want to begin the learning session with a straightforward statement of what we wish to teach during the upcoming learning session and end the session with a review of the most important information.

We should be careful not to overload the information given between the Primacy and Recency effect.  Increasing the “amount’ of information included in a learning session simply increases the amount of information that is forgotten and does little to increase the amount of information that is remembered! In the graph below, you can see the same Primacy and Recency effect, regardless of how long the list is:

Serial Positions Effect: Length of List (Click to enlarge)

How does this relate to Block Scheduling where a typical class period is 60 or 90 minutes? It’s likely that cognitive gain can be realized by breaking up any learning session into smaller “bites”. That is, while a longer learning session may produce a trough of retention, breaking a 60 or 90 minute period into three learning “sections” of 20 or 30 minutes each may reduce low recall times and increase time spent in Primacy and Recency states.

Share your thoughts! How can we break extended learning sessions into smaller bites that students perceive as separate events? I would love to hear about approaches you take in your own classrooms that might be related to the research we have discussed here. Please share by commenting below!

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