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As one part of my job, I spend time working on science assessment at the state level. After recently participating in a benchmarking session, I began wondering if skills such as measuring, graphing which are taught in math are also taught and/or reinforced in science instruction. Would you be willing to share what happens in your classroom on this topic? Kathy

I was thinking about this just the other day...when we study gases in third grade, we talk about air pressure. One of the demos I do is the "Breaking the Stick"--meter stick, about half hanging off a table, the half on the table covered with ONE sheet of newspaper. Quick hard blow on the hanging off end and the stick snaps--the single piece of newspaper holds the other end down. How? Air pressure. And then I have to talk to my students about 14.7 pounds per square inch--Area. Some of my third grade students sort of understand the idea, but I do have to take plenty of time to discuss square inches and area. Then we try to figure out how much air pressure is pushing down on the paper, and that involves figuring out how many square inches there are in a sheet of paper. Their ability varies year to year and even section to section. They work in groups of four students, and I have some groups who measure and multiply, I have some girls who measure, mark, count across and down, and multiply, and then I even have groups that measure, mark, and draw all the one inch squares and then count them, one by one. So, all that is to ask--how do you explain 14.7 pounds per square inch if they don't really understand area?

Hi Kathy, It is interesting that you mention this. Yes, there are specific math skills that can be incorporated into most science activities: measuring, collecting data, creating graphic displays, etc. Students may get introduced to these process skills in science first. Since math (like reading) is very structured, students may have learned to add 3 + 4 and not know how to use a ruler or meter stick. Science class takes the mathematical abstract and gives it a real purpose. Of course, like Amy mentioned, they may not have learned about area yet (in math class) when we have to teach them about psi! So we become math and science teachers simultaneously...

Hi Kathy,

Since math is the language of science, it makes perfect sense that mathematical concepts are also taught and reinforced in science. As the STEM initiatives become more mainstream, I think we will see an increased emphasis on integrating math and science in elementary classrooms. NSTA press has an excellent series of books that provide activities linking math and science. The books are broken down by grade level with one book for K-4 classrooms and another book for 5-8 classrooms. The books are excellent resources full of hands-on learning experiences that emphasize the links between math and science.

Yes, I use an inquiry-based science program which incorporates measuring and graphing qu9ite frequently. Students are more confident to use graphs and measuring in math when we have already done it in our science inquiries.

Susan, I think that the integration of math and science skills is critical to science instruction. :-)I love hearing that this is happening. Could you give a specific example so all could get an idea of what you mean? Thanks Kathy

As a third-grade teacher, I always try to use integrated approaches of math in conjunction with science instruction. Since school just started for me (in Hawaii), I'm about to start a common campus bird survey data collection. I teach my students about estimation and surveying data collection over a large area (our recess field). Students identify and learn how to tally the zebra doves, mynah birds, golden plover (kolea), and cardinals. They then use that data to construct pictographs, vertical or horizontal graphs. Later in the year, when I teach my student simple machine concepts, students use metric units to measure distances rolled for the cars that they construct, or force exerted on lifted objects with a spring/force gauge. This year I was thinking that "leap year" could coincide with construction of catapults for distance. I wholeheartedly agree that math and science need to be taught and reinforced together. I'm going to explore more of the STEM options that were suggested.

When teaching volumes of regularly shaped containers, way back in early '80s, I used to involve children in measuring volumes of liquids by using plastic measuring cylinders, calibrated mugs or empty tetra-pack containers (with volumes marked on them). After measuring the volume, they would apply appropriate mathematical relationships to verify what they measured. Children liked the activities very much. I agree fully with Carolyn when she says, "There are specific math skills that can be incorporated into most science activities: measuring, collecting data, creating graphic displays, etc. Students may get introduced to these process skills in science first. Since math (like reading) is very structured, students may have learned to add 3 + 4 and not know how to use a ruler or meter stick." One way in which examples like 3+4 can easily be handled is to use number lines in math classes themselves. I used to give actual meter sticks to my students when working with number lines. In some elementary school science syllabuses like those in India, when "skeletal system" is introduced, cylindrical shape of our bones is mentioned. Textbooks which follow the syllabus do not usually go beyond "Our bones are cylindrical in shape as they need to be tough". What I used to do in such situations is to involve children in a simple science activity as follows: Each child takes an A4 sheet of paper and tries to support a pen or pencil on the paper. Obviously they can't. Then I ask them to roll the paper, tie the roll with a thread, make the roll stand on the tabletop and place the pen on the roll. Children get amused that the same paper works now in supporting the pen. Hence, they understand the toughness associated with cylindrical shape. Then I explain the mathematics behind the above concept by showing an example of cross-sectional views of different shapes such as a square, rectangle and circle with the same perimeter (for example, 44 cm). Then I ask them to calculate the cross sectional distance between any two symmetrically opposite points in each cross-sectional shape. After some work and after some discussions, they realize that the cross-sectional distance in the circular shape is the largest (14 cm), which is the circle's diameter. This makes them believe that cylindrical shape (the cross-section of which is a circle) is the sturdiest. Now it is easy for them to know why bones in our bodies and pillars in old buildings are cylindrical in shape.

Lori, I am curious what science curriculum you use for your simple machines unit? I also teach third grade in Hawaii and am always for ideas! Thanks for all the ideas for math/science connections. I think it is much for meaningful when the students can apply the math in a cross-curricular way.

Hi Shawna, I don't use a formal curriculum for science. My grade went for the trade-book and leveled reader approach to science instruction as my complex wanted a more inquiry-based approach to science. I'll get back to you on the series of leveled readers that my students use, but here's a sampling of what I do for my simple machines units. Keep in mind, these simple machine units all require either mass measurements (especially pulley) or metric measures for distance, height, etc.: Lori 1) Levers: creating a balance with a pencil, ruler, and paperclips (very low-tech). I've also tried washers for more consistency. This usually transitions to catapults in trying to experiment with farthest distance (not height) for flying a paperclip (spread out into a "V" shape). I ALWAYS have my students measure in metric units for science. It's actually a lot easier for them and in keeping with what most of the international community does. My science methods instructor said that if you could use a long-enough 2' x 4' and hollow-tile (or something like that), that you could have your STUDENTS lift you, too. I'm not that brave with my third-graders. 2) Inclined plane: I have my students construct various types using folders, blocks, cardboard, etc. We use difference heights (they don't understand grade of incline) when we roll cars they made down the slope. 3) Wedge: I try to get a large refrigerator box and students "wedge" race across our campus field. I have a large pressboard that I use as the non-wedge. Only once has the non-wedge won, but that runner was the tallest, fastest, and strongest girl in my class. You could also pull a styrofoam block cut first as a rectangle, then into a wedge through a long pan (those big plastic tubs from Big Name super value stores) We actually have timed the trials as a measurement component. 4) Screw: This one is tricky, but I have refurbished desks with bolts that constantly fall out, the students spend the first half of the year helping to re-screw in the bolt to their desks and are pros by quarter 3. I also take a scalene right triangle, with the hypotenuse colored with a half-inch band and have them wrap the height around their pencil. They can visually "see" the transition from inclined plane to screw. 5)Wheel & Axle: students create their own three-wheeled or four-wheeled car out of floral foam, dowel, and wheels I got from same Big Name value store. I took a course where the instructor encouraged the opportunity to actually build wheel and axles, but you need a lot of parent help (which I don't get). The students roll down the inclined plane for distance (metric). 6) Pulley: I use fishing sinkers or washers so students can take the mass, sewing spools with dowels, twine/string to have students create their own pulleys. We have used a triple-beam balance to take the mass of commercial items the students wanted to lift. Here's a Web Site my students like to visit once they've learned about the 6 simple machines: Ed Heads (interactive Web site) http://www.edheads.org/activities/simple-machines/

In science students need to know math to understand the science lessons to do the experiments and showing their results. I teach fifth grade and one of the benchmarks is to "Identify the variables in the scientific investigation and recognize the importance of controlling variables in scientific experiments". This past week I did a science lab of dropping water on a penny and counting how many drops it takes until the water slips over and a variable we change was using 50% water and 50% soap. The students did both the water, water and soap lab four times and then computed the average. In their results I had students make a double bar graph with all four trials and the average. The students had to know how to count, add up the results, what an average is, divide, label the x and y axis, make a scale for the graph and make a double bar graph. Using math in science is just a great way for students see that math is everywhere and also help some students to understand a concept better they may have been having hard time with.

Hi again everyone! In our district we have noticed vast inconsistencies in our students ability to do math in science. I have had years where my seventh grade students struggled to use a triple beam balance because of problems with simple addition and concepts such as volume and density befuddle them more often than not. They simply do not have a grasp of basic math skills (addition/subtraction/multiplication/division/fractions/decimals) and we do not have time to go back and teach them at the middle level. Our sixth grade teachers started abandoning their curriculum for the first semester and tried teaching these skills, but it's seems nearly impossible to get them to stop drawing arrays for simple multiplication that they should know by heart. If a student has to come out of a more complex problem to draw a diagram or set up a convoluted lattice multiplication problem - the more complex problem is lost to them by the time they're finished. Our district strongly supports what some people call "fuzzy math" - programs such as Everyday Math - and I can't help but wonder if this isn't part of the problem. I would like to hear elementary teachers' thoughts on this. Does your district use programs such as these? Do you see them as helpful to your students? Have you talked to teachers in the middle grades and high school to see how they view students' math skills since these types of programs gained in popularity? I can't believe I am starting to sing the praises of rote memorization...wonders will never cease. Looking forward to your comments! Kendra

Hi Kendra, I never thought I would be encouraging memorization either, but it is amazing what kids don't have when they get to high school. As a math teacher part of the time (sometimes more math than science) I have noticed that kids go straight to the calculator, and need formulas to figure things out. One thing that I have found students lacking is the concept of factoring. So many math problems would be no problem if kids were able to do some mental math and factor problems. For instance, the problem 90/15 looks hard to do mentally, but if you factor out a 3, it becomes 30/5, which should be no problem. So much of it is simply mental gymnastics, which come partially from memorization, but also from repeated use (sans calculator) and an understanding of the underlying concepts. I do spend many evenings helping kids who are enrolled in Everyday Math learn how to do the problems with real math. I have to say I am also disappointed, and when they get to the higher grades they have not mastered a lot of the concepts that they need to handle measurement and dimensional analysis. Just my two cents.

Being in Hawaii, we have the unique opportunity to be part of ONE school district. In terms of mathematics instruction, complexes (the High-school that middle-school and elementary feeds into) may have more influence as to what instructional practices might drive curriculum selection. I'm fortunate to be teaching at a school which has maintained adequate yearly progress in terms of NCLB. With that freedom comes the ability to have each school dictate curricular practices. Currently, my school has adopted an integrated approach to math instruction: we're using the skeletal structure of "Singapore math"-based instructional sequences, coupled with problem-solving tasks (real-life/somewhat like Everyday Math), and rote practice. I like the Singapore-Math sequence because it builds upon number sense which is key to science principles of measurement. Students still do not know what a reasonable estimation customary or otherwise of lengths. Ex.: I think my car is 12 yards long or my house is 1 meter tall. I think students need a balance between structured instruction involving rote memorization (because knowing the times table will help with other aspects of math) and problem-solving-based activities. Application needs to be practiced, but cannot be achieved without the tools at their disposal.

Hi, I'm a kindergarten teacher in Hawaii and last year started a small garden outside my front door of the classroom. I was able to teach measurement by measuring our seedlings each day, we graphed how many days seeds took to germinate, and once we harvested our veggies we cooked them which required them to follow a recipe using measurement. They loved working in the garden and I noticed many of them measuring eachother's plants and comparing their data. This started as a service learning project where we grew food to share with others, and really it branched into so many different lessons and integrated throughout the curriculum. If you don't have a plot to start the garden, I sent home a note asking for cracked plastic baby pools (the ones you store under the house because you don't know what to do with them) which I drilled holes in and planted herbs in.

Jennifer Rahn said, [i]Hi Kendra, I never thought I would be encouraging memorization either, but it is amazing what kids don't have when they get to high school. As a math teacher part of the time (sometimes more math than science) I have noticed that kids go straight to the calculator, and need formulas to figure things out. One thing that I have found students lacking is the concept of factoring. So many math problems would be no problem if kids were able to do some mental math and factor problems. For instance, the problem 90/15 looks hard to do mentally, but if you factor out a 3, it becomes 30/5, which should be no problem. So much of it is simply mental gymnastics, which come partially from memorization, but also from repeated use (sans calculator) and an understanding of the underlying concepts. I do spend many evenings helping kids who are enrolled in Everyday Math learn how to do the problems with real math. I have to say I am also disappointed, and when they get to the higher grades they have not mastered a lot of the concepts that they need to handle measurement and dimensional analysis. Just my two cents.[/i] Jennifer, I couldn't agree more. I was shocked to find that the Everyday Mathematics program calls for students in the first grade to use a calculator for basic math (under the premise that if they do this enough time they'll memorize it naturally - it sounds good but it just doesn't seem to be happening in reality). By the time they're in middle school they have no number sense. I think this problem is compounded by some of program's methods, such as the lattice multiplication I mentioned earlier. Lattice multiplication allows students to make errors while computing and still manage to get a correct answer in some situations. If they're making mistakes and don't even know it, how can they have a solid conceptual understanding? I think this leads to the problem another teacher mentioned about the lack of reasonable estimation skills. I've seen middle school students come up with answers that are wildly impossible and have no idea their answer doesn't make sense. You also make an excellent point about factoring and the inability to do "mental gymnastics." I remember groaning my way through mathematical memorization - I must have written my multiplication tables 500 times during elementary school, plus flashcards and mental drills. But by the time I reached high school, I had no problem tackling the harder math and science classes. It just feels like we're short-changing our kids. Here's where I think we could take a cue from China - they're elementary levels focus solely on basic mathematics skills until they are as fluent and flexible as possible. I'll be glad when this trend comes full circle and we can get back to "real math" as you put it. I simply couldn't agree more, Kendra

Kendra, I would agree that there really is not much need for a calculator before algebra. There are so many ways to learn from doing long division, fractions as fractions and not decimals, and learning to recognize number patterns. As a dinosaur, I didn't have a calculator until I reached grad school, but even then could calculate solutions faster in my brain than most of the class did on the calculators. It got to the point where the teacher would provide the problem, look to me for the answer, and a second classmate to confirm. But it was all simple math. I also thought it interesting that you brought up China and their approach to early mathematics. My daughter had a roommate last year (Chinese) who routinely studied by carefully copying notes that were already impeccable by most standards. Being curious, and also a tech aficionado, I asked why she didn't type them into the computer to start with, since they would then be easier to manipulate, organize, and modify. Her answer was simple; writing the notes helped her learn. Apparently, there has been a great deal of research into the linkage between the act of writing and that of learning the contents. She benefited from the kinesthetic value of rewriting notes before exams. There is a substantial body of research that seems to validate the importance of handwriting, and that there seem to be links between writing and other systems of symbols, i.e., mathematics.

In my opinion, the memorization of facts is necessary for students to be really proficient at higher level math and science classes and really to be successful in everyday life. When I was teaching physics at the high school level, I was astounded by the number of students who were unable to do simple addition, subtraction, multiplication, and division in their heads. Calculators have become the "standard tool". On the contrary, when I brought this up to my dad, he asked me how many students in my high school math class knew had to use a slide rule. There was one. It was me. My dad taught me to use the slide rule "because you won't always have a calculator". The point was well taken. In a society that is trending toward more and more technology everyday, we are moving away from memorizing basic arithmetic facts. As a teacher, I see this as a breakdown. Because students do not know their math facts cold, they have to "think about" the answer or "plug and chug" to find the answer. This, in-turn, distracts the student from the problem solving aspect of math. Additionally, I have been very surprised by the number of people who are unable to do simple math (like 20% of a check or figure out the price per unit at the grocery store) in their head. In addition to memorizing math facts (addition, subtraction, multiplication, and division), I also think it is important to commit things like 180 deg in a triangle, 360 deg in a circle, 90 deg in a right angle, the equations for area of a rectangle, triangle, circle, pi=3.14, etc. to memory. Although many districts are moving away from it, I still think that memorizing math facts in the elementary grades is the most effective way of preparing students to be successful as they move into the upper grades. I have attached a journal article to includes research on the importance of memorization of math facts in terms of student achievement.

Attachments

Achievement_in_Math_and_Memory_Work.pdf (0.47 Mb)

We just were sent to a training to find out how to incorporate math and science. How timely after I had posted on this thread. A lot of good ideas were given such as: Using a shadow stick to measure the shadow of the sun at each half hour interval during the day. Adding tape could be used for the measurement to create a bar graph. Students could then show the data in two different forms (perhaps a table and their own bar graph) and then students could link the science concepts to the sun and the earth. We did run into some problems such as a half hour block that was surprisingly sunny in Hawaii. These "problems" could be turned into math problems where students could guess the missing data based on the patterns in the data chart. We also some hands on activities that used the "field of vision" lesson from a NSTA science book. The students looked through an index card with a circle cut out with a diameter of different centimeters. They charted how far they could see on a ruler (the specifics are slightly complicated so respond if you are interested). Then they tried to continue the pattern with other numbers. This could relate to life science for animal adaptations and why they might have unique eyes. I think math and science go great together! It is just a matter of having the resources and time to figure out how to find the best match!

I believe that an effective science classroom needs to be integrating an array of other skills and courses in order to be fully engaging those students who are being taught. In the learning process, it has been shown through research that students will remember a concept easier and apply that concept more frequently when they are able to make connections and draw upon experiences with those concepts. Science is a key subject in order to begin forming student's minds from linear thinking to unconfined thinking. By unconfined, I mean that they are not constrained to just learning science in a single way. Rather, they are able to learn science through a variety of other subjects, such as math for instance. When teaching basic mathematical skills, such as addition or subtraction, it is extremely hard for students to grasp these abstract concepts because they have nothing in their lives that they are seemingly able to compare it to. In science, we give students the tools necessary to form a connective idea which will allow them to easily recall the information better, and gives them a real-life experience to connect with in order to draw information from. Using the addition and subtraction example, students are able to see the real life application of its use in both measuring and graphing. Now, instead of having a broad idea, they are looking at its real world use, and can apply that knowledge later on down the road. For instance in my college level science class we learned some progressive new styles in executing inquiry based learning while integrating core standards across a curriculum. The experiment titled "Mini Metric Olympics" (Found at www.nclark.net/mini-metrics.pdf) is a lesson designed to engage students in the fields of science, math and language arts. The students learn the importance of estimation and measuring, while learning about metric conversions. As the students learn about the metric system, they achieve an accurate representation of how the metric system compares to standard U.S imperial units. Students measure with such items as a ruler, meter stick, liter measuring set, and scales, among other items. As a participant in the classroom to this experiment, I was directly put into the shoes of those students I will be one day teaching this to. I am a grown college student and from participating I can honestly say that students will be able to grasp concepts with ease because of the interest it generates and natural curiosities it feeds on. Rather than students following linear directions, they are able to do things their own way, and come up with interesting results. For instance the "straw throw" was particularly frustrating for some, and easy for others, because of the way you threw the straw. It seemed that the harder you threw the straw, the shorter the throw would end up. The more finesse and touch you put on the straw, the further it went. With a room full of college students, there must have been 3 different conclusions as to why this was, all of which had validity and proof behind the argument. This simple experiment drew upon our curiosity and drove us to look deeper for an answer. Along the way, we used math skills in measuring and converting metric units to imperial, and also language arts as we recorded in our own words what the results yielded, and orally presented that information. Ultimately, using science as a means to incorporate multiple subjects should be applauded, and needs to be used more in the everyday classroom.

Hi Shawna, You mention the 'field of vision' lesson from an NSTA book; the lesson sounds intriguing and I would love to learn more about it. Is it possible for you to give us a reference for the lesson; your students must gain a different insight into quantifying their world with this lesson. Thanks so much for sharing. ~patty

There are a number of issues, in my opinion, with the curriculum and the way it assessed. LIFE DOES NOT HAPPEN IN Math time, reading time, science time, etc. Math is life -- it's skills are in every facet of your day. Science is life -- you can not live without it. You may not think about the skills, but the processes are interlinked, overlapping, and inseparable. In my class I let learning dictate the direction of instruction. I try to make two points: how "this" applies/changes in different situations or subjects and how they may see it again (in the testing world, in another subject, in another grade, in the real word. A point last week came up with producers and consumers --- what are they? (We were talking economics not science)So I took the time to explain in the "science world". Map, graphs,charts... when do you teach them? They show up on all subjects of state testing.

Hi, All,

These NSTA Press resources by John Eichinger have been mentioned a few times, so I thought I'd post the links to make them easier to peruse:
Activities Linking Science With Math, K-4
Activities Linking Science With Math, 5-8
Determining the Size and Shape of the Blind Spot (field of vision activity)

Claire

Kendra,

As I reread this thread, I focused on a quote from you:
they're elementary levels focus solely on basic mathematics skills until they are as fluent and flexible as possible. I'll be glad when this trend comes full circle and we can get back to 'real math' as you put it.

I think you will be getting your wish with the implementation of the Common Core in Mathematics. There are shifts that are occurring so K-5 is focusing on numbers and operations. If students become experts in the mathematical practices as welll as the content it will be much better for mathematics as well as science.

Kathy