Teachers from Paine Primary gathered on June 25th in order to become familiar with the components of our new curriculum, Eureka Math. Teachers were given in-depth professional development during the morning session. The second portion of the day was devoted to collaboration with grade level planning partners to discuss implementation of Module 1.
The CCSS do a great job of building learning progressions through all K-12 grade levels so that each year students build on what they learned the year before and deepen those skills. One example is equations. In kindergarten through second grade, students use equations to represent addition and subtraction problems. This includes the decomposition of numbers in multiple ways (8 = 4+4 and 8 = 3+5), finding the missing number in an addition equation (3 + __ = 8), and writing equations from visual representations and word problems. In grades 3-5, these same ideas are extended to multiplication and division.
As students move into middle school, variables (x, y, z) are added to equations, and students use opposite operations to find the variable’s value. For example, students are asked to solve 3x + 4 = 8 for x. Students also learn equations in two variables where the result is a straight line graph (y = 3x - 2).
As students move through high school, their understanding of the concept of functions grows to include exponential (think money growing in your bank account), quadratic (functions that model the motion of an object being thrown in the air), and other types. This comprehension of math as it relates to real-world phenomena wouldn’t be possible without the basic understanding that the two sides of an equation are equal, which was established in elementary school.
2. Focusing not only on the how… but the why
I created this Wordle using the top 100 words in the CCSS math standards. The bigger the word, the more frequently it appears in the standards.
When this picture popped up, I was surprised at the sentence that emerged: “Understand problems using numbers and equations.” This is the foundation of the Common Core math standards. We want students to truly understand mathematics, not just be able to “do” it.
I also couldn’t help but notice the words that are not visible in this picture, such as do and compute. While there is a place in the standards for algorithms, such as putting numbers on top of one another and adding down, it’s not the focus. Other visible words that support the idea of understanding in this picture are explain, recognize, apply and represent. When students complete the progression of the standards, they will not just be able to do math but really understand it.
3. Developing 21st century skills
“Why can’t it just be done the way I learned?” is a question I hear often from parents regarding the CCSS. The fact is, our students aren’t growing up in the same world we did, and we owe it to them to prepare them for today’s society. Our students will likely be doing jobs that haven’t even been created yet!
So how do we prepare students for those jobs of the future? We teach them 21st-century skills such as problem solving, communication, and digital fluency. A colleague of mine, Rob Kriete, created an awesome visual representation of these skills for parents and teachers. The CCSS for math also include eight math practice standards (link is external) which are habits of mind embedded within the instruction of the content standards. These are not standards that can be checked off a list--like being able to solve an equation--but are skills to be developed across all grade levels. In these practice standards, students are asked to persevere in solving problems, construct arguments, critique others’ arguments, and use appropriate tools in problem-solving. Being able to do these things will prepare our students for success in college and careers--even the jobs that don’t exist yet.
Like I said before, no set of standards will ever be perfect. But I truly believe the CCSS for math are putting our students on the track for success in the world in which they live. That’s what we all want for our kids, right?
Lindsey Walborn is a high school math teacher in China Grove, NC, who has nine years of classroom experience and is working towards a M.Ed. in Curriculum and Instruction. She has been a math department chair and currently leads a learning community for teachers of Math 3. Lindsey is also a member of Center for Teaching Quality Collaboratory and works closely with Student Achievement Partners
Does this image look familiar? If you have walked the halls of Paine Primary you
have passed by this décor. Have you ever thought about the math you
see all around? In this picture, do you see four squares that come together to
form a new shape? You also see a shape called a rhombus, which is a
simple quadrilateral with four sides having the same length. Could
this image also be of a tessellation, which consists of one or more geometric
shapes with no overlaps or gaps? Yes, it is! Math comes alive as we look
around.
Talk to your children or students about the math that you see,
no matter where you are. It is critical that children realize math is not an
isolated time during the school day. Math is part of every subject and
is inside and outside the doors of the classroom all around us.
Having your students sort out the dominoes needed for each of these games is part of their learning, so be sure to let them do the "work" of finding the dominoes they'll be using! For the first level, they'll need to sort dominoes with dots that total one to six. They will then put one domino on each of the petals of their flower. Players take turns rolling one die and then looking for a domino that totals the number they rolled. If they have one, they remove that domino from their flower. Here, the player rolled a three and is removing a 2+1 domino.
If the player has no domino that totals the number, he misses that turn. The first player to remove all of the dominoes from his or her flower is the winner.
Level Two is played the same way, except that this time players will be rolling two dice and will need dominoes that total 2 through 12. Roll, add, and find a domino with the same sum. Here, the player has rolled a two and a six, and is removing a 4+4 domino.
10 Frame Fill—Provides children practice with recognizing additive “10 Families” (e.g., 1 and 9, 2 and 8, etc.).
Number Flash–Children practice seeing numbers in terms of the important benchmarks of 5, 10, and 20
Subitize Tree ($0.99 and worth it!) In this app, there is a picture of a large tree with a set of doors. The doors open up to reveal an object for a short period of time for students to subitize. Then the doors close and the student has to touch the correct number.
You might look ridiculous pacing around the restaurant trying to figure out how much each of your friends owes, but new psychology research suggests you’ll get the last laugh.
Thanks to a mechanism in the human brain that likes to pair related, abstract concepts, scientists have found a so-called “congruency effect” in studying how we think. Similar to the infamous Tetris effect, in which extended gameplay can make other parts of your life seem to be nothing but L-shaped blocks and elusive straight pieces, the research shows the brain has a preference for addition and subtraction based on walking left or right.
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Over the last decade, psychologists discovered the interesting fact that doing addition was much easier in an elevator that was going up, and subtraction in an elevator going down. They also found we tend to conceptualize larger numbers better when we’re moving to the right and smaller numbers when moving to the left. In the latest study, a team from the University of Bologna and the Italian National Research Council tested whether walking direction affected people’s ability to add or subtract.
To do this, they recruited 52 people to perform a task. Each participant received a number and was then told they’d be adding to it or subtracting from it later on. The investigators then told them to begin walking and to turn either right or left and begin doing the arithmetic. After being told a number and which operation to perform, subjects were instructed to walk either right or left. Those who walked right added better and those who walked left subtracted better.Anelli, et al.
The results showed people were far better at adding numbers when they turned right and subtracting numbers when they turned left. “Our finding complements and extends previous results revealing that the direction of body motions can influence not only number magnitude in a number generation task,” the researchers wrote, “but also the more complex process of calculations that leads to a numerical magnitude.”
In other words, moving in accordance with the math problem can help us sort out the problem better than sitting still. And it doesn’t seem to be just walking that gets the job done. Other research has shown the experience of passive movement helps all the same, which means if you need to calculate your expenses for the month, consider driving around the neighborhood and only making right turns. Or if you’re in the middle of a run and can’t remember how far you are from finishing, head left to subtract from your desired distance.
“The present findings confirm the existence of a connection among numbers, space, and motor processes, by showing the emergence of a congruency effect when subtractions and additions were calculated while moving also along a horizontal axis,” the team concluded.
The study isn’t the first to uphold the benefits of walking. A wealth of data suggests the simple act of putting one foot in front of the other can eliminate depressive symptoms, improve mood, lengthen your life, and reduce stress. Which is good news, if what’s stressing you out is math.
Source: Anelli F, Lugli L, Baroni G, Borghi A, Nicoletti R. Walking boosts your performance in making additions and subtractions. Frontiers in Psychology. 2014.
Chris Weller is a Senior Reporter at Medical Daily, where he covers brain health and other fun stuff.
