Category Archives: Mathematics

Math Myths

Spring 2010 277Since so many teachers are fearful of math, I am going to start out by exploding some of the more common myths that prevent us from thinking mathematically and actually ENJOYING teaching it!

Myth 1: Math is about getting the one right answer. No matter what you experienced in math class this is not correct. Truth: Math is about finding an answer that everyone agrees on.

Myth 2: Math is about numbers. Numbers are one of many tools that mathematicians use to solve problems. They also use objects and symbols and words and pictures. So then what is math? Truth: Much of mathematical thinking is devoted to the search for patterns and and solutions to problems describing those discoveries in ways that others can understand.

Myth 3: Math is boring. Truth: Math when taught properly can be just as fun as the arts. In fact, when I asked my third grade classes to vote on their favorite subject, they always chose math. But then why wouldn’t they when we had a six foot blue frog who was the king of the kingdom of three, they got to use chopsticks in a paper ball race and earned wages making products for their class store that they then sold to raise enough money to go to the Syracuse Zoo.

So how do we combat those myths and teach math so kids love it?

Make it meaningful! Counting, adding, and filling in worksheets because the teacher tells you to is a surefire way to bore children to death. Instead, always give them a purpose for thinking mathematically. Some examples:

  • Counting and computing for a purpose:  If you are addressing a common core math standard such as this one for kindergarten: K.C.C.A.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects), don’t take it at face value and give the children a worksheet with a picture of 3 apples and a space for them to write the number 3. Instead, think of a reason why they might want to count something and record the number.  Bring in a basket of crackers for snack. Make a chart for them to write their name and the number of crackers between 3 and 6 they want for their snack. As they gain experience make it more challenging. Bring in two or three different types and have them record the number of each kind they want and the total which cannot be more that 8, for example. 
  • Buying and selling: The class store using play money is a tried-and-true method used by teachers for decades for getting children to practice adding, subtracting, and more. In addition to a store think of other places money is used and set up dramatic play centers such as restaurants, plant nurseries, even an art gallery where children can buy things from each other.
  • Earning money for a purpose: Even better is raising or collecting money for a real purpose like our trip to the zoo. One time our school collected pennies for charity and the classes had to come up with different ways to count the huge jars of pennies turned in.
  • Being mathematically curious: Math is about comparing things and finding patterns. Ask which is bigger/longer/more? How do you know? Invite children to find and make patterns: Look at the interesting pattern the blocks in this tower make? Can you make a tower using a different pattern?

DSC02111Make it ever present! Math doesn’t just have to happen at math time. Fill the classroom with tools and materials that support mathematical questioning.

  • Measure everything: Set up a measuring center and man it with rulers, tape measures, square centimeter cubes, interlocking pattern blocks, volume containers, and trundle wheels, balance scales, spring scales, step-on-scales, and gram masses, metric cylinders, measuring cups, and measuring spoons. If the tools are handy then it’s easy to say: Which is heavier? Which is longer? Which is further away?
  • Tracking time: Fill your room with clocks, stop watches and timers of all designs. And then constantly ask when children set out to do a task: How long do you think it will take? In my room I always had a timer table where children could just observe the different ways to mark time, make their own “clocks” using dripping water or grains of rice, and where they could get a child-friendly stop watch to time how fast their cars rolled or their crickets hid.
  • Calculate it: Set out calculators, cash registers, old fashioned adding machines with print out tape, abacuses, and more. And challenge them to find the sum or product, subtrahend or dividend.
  • Fill the shelves and counters with fascinating objects that invite touching, sorting and counting: Fill clear plastic bottles with buttons, bottle caps, beads, glass jewels, pebbles, sea shells, centimeter cubes, plastic bread ties, spools, screws, etc. Provide laminated Venn diagrams and graphing grids and explore, one bottle at a time.

Make it a group effort: Instead of competition to get the right answer, work together to figure out how many different ways you can find the answer or pool resources to solve problems together.

  • Be statisticians: Collect statistics about each other, projects, school happenings, and more, and create class graphs that make numbers and comparisons visual.
  • Come to agreement: If individuals get different answers, have them put their heads together and compare their methodologies. Work together until everyone agrees.

NOTE: There are many other myths about math. Here is a list of 12 others to check out: http://www.uaf.edu/deved/math/help-for-math-anxiety/12-math-myths/

Advertisements

Why The “A” in STEAM?

Lego HouseA  is for Arts

Since 2007 there has been an refocused awareness on the teaching of the STEM subjects – the sciences, technology, engineering, and mathematics – using hands-on, real life problems. However, this should not be done by eliminating the arts. They are an integral part of the sciences. Think of the importance of aesthetics and art in designing bridges and robots, drawing meaningful biology diagrams, imagining the universe, and in representing patterns in numbers.

STE[A]M goes beyond the 4 STEM subjects. The bracketed A stands for the arts. These include the fine arts, music, dance, drama, and literature. In STEAM education the focus is on nourishing children’s curiosity, imagination, and creativity by drawing on the arts in the context of exploring science, math, technology, and engineering projects. Well-designed STEAM activities teach children to become astute observers, designers, and creators, while introducing them to the critical thinking and decision making skills needed for successful STEM careers and for the enjoyment of life.

OR…

STEAM = Science & Technology

interpreted through Engineering & the Arts,

all based on Mathematical Principles 

In addition, the arts are a powerful learning tool: The University of Florida has created a graphic showing why the arts belong in STEM education:

University of Florida’s Online Master of Arts in Art Education

 

 

Measurement Lab: Observing Beets

beet4In this observation lab students are introduced to basic measuring tools: metric ruler, metric tape measure, balance scale and gram weights. The example lesson is drawn from a second grade class who have been presented with fresh beets to observe. However, this lesson can be done at any grade level using any type of engaging object that has measurable variability within a shared unity of appearance or form, such as apples, clam shells, corncobs, feathers, hot wheel cars, keys, leaves, lemons, nuts, seeds, pumpkins, rocks, worms, and so on. The lesson objects should be close to the same size. There should be one object for each child.

PROCEDURE

OBJECTIVES: Students will review using their senses to make observations. They will practice using measuring tools and saying and recording metric units of measure. This lesson meets these standards for Grade 2.

  • CCSS.Math.Content.2.MD.A.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
  • CCSS.Math.Content.2.MD.A.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
  • CCSS.Math.Content.2.MD.D.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems1 using information presented in a bar graph.
  • 2 PS-1-1 Plan and conduct an investigation to describe and classify different kinds of materials by their observable properties. [Clarification Statement: Observations could include color, texture, hardness, and flexibility. Patterns could include the similar properties that  different materials share.]

beet9PREPARATION

At stations around the room have set up a sensory observation table with hand lenses, a weigh station with scales and gram weights, a length stations with rulers, and a circumference table with tape measures. Have one large table where the objects can be laid out to form a physical graph on graph paper.

OBSERVE

WOW: Place chosen objects in front of the children and ask them to observe using the sensory observation lab procedure – first using their eyes, then their other senses. Elicit this observation by asking questions that draw on their memories of the sensory observation lab.

ASK QUESTIONS

Ask: Which one is the biggest? How do we know? Introduce the measuring tools. Demonstrate how to use each one to get an accurate measurement.beet10

MAKE PREDICTIONS

Next ask each child to select an object and predict its size. Record their predictions.

TEST

Their task is to go to each center to observe and measure the object.

beets1RECORD RESULTS

They are to record their results on their lab sheet. [Measurement Lab Sheet] After they have observed and measured their objects, they should place them on the graph paper from biggest to smallest.

COME TO A CONCLUSION

Discuss how they decided to order them. Did they use length, width, depth, mass,  circumference or use a combination? Does it make a difference? How does using the tools help them decide where to place them? Make bar graphs using the different ways to measure.

NEW QUESTIONS

Does the type of object affect how one measures it? Try measuring other objects.

Does it make a difference what unit of measurement is used? Try standard measures or make up your own units.

STEAM IT UP: INFUSE THE ARTS

Infuse the arts by showing students examples of scientists’ journals such as Nicky the Nature Detective and Journal of Inventions: Leonardo da Vinci and having children DSC03777draw detailed illustrations of their object in their journals using regular and colored pencil.

Sunflowers: A Science & Math Observation Lab

sunflower headScientists use their senses to observe and formulate questions.

In this lesson a first grade class observes sunflower heads.

WOW [Wonderful Object of Wonder]: 5 large sunflower heads and 1 sunflower still on its stem.

Objectives:  Children will name their senses and then use them to make observations and create questions (Linguistic, physical, cognitive, and creative development). Children will estimate the number of seeds in a flower head and then count them. They will estimate the height of the sunflower plant and measure it (Common Core: CCSS.Math.Content.1.NBT.A.1; CCSS.Math.Content.1.MD.A.2)

Presentation: Sit children in small groups and set a sunflower head before them. Ask the following questions and allow time for every child to share his or her ideas several times.

OBSERVATION

What can we observe about sunflowers?

…with our eyes

  • What colors do we see?
  • What shapes do we see?
  • How many do we see?

looking

“The seeds are striped.” “They’re white and black.” “And gray and brown.” “The leaves are green and brown.” “There are yellow things like cups where the seeds have fallen out.” “There are fuzzy things on the seeds.” “There’s thousands of seeds.”

…with our fingers

  • Is it wet, dry or both?
  • Is it hard, soft, smooth, bumpy or all of these?
  • Does it stay together or fall apart?

touching

“Feels hard and bumpy.” “Loose. the seeds are loose.” “The brown part on the outside falls apart.” “Ugh. This part is wet.” “I can put my finger through it.” “Feels curvy like a funny shape ball.”

…with our noses

  • Does it smell strong or not very much?
  • Does it smell like something you have smelled before?
  • Does it smell nice or yucky?

Smelling

“Smells like chocolate milk.” Like dirt.” “Tickles my nose.” “Smells fuzzy.” Smells like a rainy day.” “Smells like wet paper.” “Good. It smells good.” “I like how it smells.” “Yuck. I don’t think so.”

…with our ears

  • Without moving or touching it, does it make any noise?
  • Does it make a noise when you touch it?
  • When might it make noise?

listening

“I don’t hear anything.” “It’s quiet.”  “It’s just sitting there.””It crinkles when I touch it.” “It’s like dead.” “Sounds like paper.” “It would make noise in the wind, I think.”

ASK QUESTIONS

DSC03419Solicit questions: Next gather child-generated questions and list on board or chart paper.

  • Is it alive? (the seed)
  • How does it get so big from such a little seed?
  • How tall is it?
  • What are these little yellow and brown flower things?
  • How many seeds are there?
  • Do they blow over in the wind?
  • Can we plant them [the seeds] now?

how tallMAKE PREDICTIONS

Have children make predictions for each question

TEST

Together with the children devise tests and do research to find the answers to the children’s questions.

For example: Set up a center where the children can remove all the seeds from a sunflower head and count them. At another center put out the different measuring tools and the sunflower on its stalk to find out how tall it is. Provide cups and dirt and plant some of the seeds to find out if they are alive. Put out books about sunflowers and find information on the web.

RESULTS & CONCLUSIONS

After all children have had an opportunity to explore the centers, share what they have learned, have them share with the whole group.

NEW QUESTIONS

Find out what new questions they have and make a list.

DSC03405STEAM IT UP: INFUSE THE ARTS

  • Draw pictures of the sunflowersDSC03422
  • Make up a sunflower song or poem or story
  • Do a sunflower dance
  • Make sunflower seed pictures
  • Pantomime a sunflower seed growing into a sunflower plant

SUNFLOWER FACTS

  • The scientific name for a sunflower is Helianthus., which is Greek for Sun Flower.
  • They are one of the fastest growing plants.
  • The tallest sunflower was 25.6 feet tall.
  • The sunflower is native to North America and was used as food by the Native Americans.
  • Each sunflower head is made up of 1000 to 2000 flowers which turn into the seeds.
  • The sunflower is a heliotrope, which means it follows the sun as it crosses the sky each day.
  • Oil is made from black sunflower seeds. Snacks are made from white striped ones. You have to crush break open the outer shell to find the edible seed inside.

SUNFLOWER CHILDREN’S BOOKS

A Big Yellow Sunflower by Frances Barry

From Seed to Sunflower by Gerald Legg

Sunflower House by Eve Bunting

This is a Sunflower by Lola Schaefer

sunflower lift

Tools for Young Scientists

Tools for Young Scientists

Girl with magnifying glass

Here is a list of the basic tools children need to explore their world.

  • Their senses – eyes, ears, fingers, noses, and sometimes their mouths
  • Magnifying glasses
  • A scale
  • A timer
  • A ruler and/or a measuring tape
  • Access to nature and man-made objects
  • Their imaginations

Everything else is an extra.

So gather these up and get ready to explore the environment with your children.