Top 10 Activities to Process the Common Core Standards

Gearing up for the Common Core is both exciting, yet can be overwhelming.  This Top Ten List of activities are designed as different ways to process the Math Common Core Standards.  They could be used in a whole group setting, small group, professional learning communities, or for individual learners.  The Ten Activities are linked to more detailed information. I hope you find some of these helpful in your district.

Cognitively Guided Instruction = Engaging Students

As I was reading Steve Wyckoff's blog about creating students who are passionate, inspired, and remarkable, I thought, wow, Steve should have been tagging along with me the past couple of weeks.

I have been visiting kindergarten through third grade math classrooms.  Yes, I said math classrooms.  You may be wondering what planet I've been visiting.  These are classrooms where the primary focus is on problem solving using the Cognitively Guided Instruction approach.  CGI is a constructivist research-based strategy, which allows young children the opportunity to explore and discover how numbers work together to develop true number sense. 

Top 8 Strategies For Using Math Manipulatives

#1  From day one, set ground rules for using manipualtives.  Talk about the similarities and differences between using manipualtives for play and for using them as math tools.

#2 Talk with students about how manipulative helps them to learn math concepts.

#3 Discuss etiquette when using manipulatives if you need more green triangles, how do you go about getting more.  Interfering with another's work is not acceptable.

#4 Set up a system for storing materials and familiarize students with it.  Some teachers designate and label a place for the manipulatives.  Others use zip-lock bags and portion out the manipulatives for each student, pair, or group. 

#5 Give students time to explore with manipulatives when introducing a new tool.  After children have explored a material, ask what they've discovered and record observations on a chart.

#6 Post class charts about manipulative tools.  It sends the message that you value manipulatives, but also helps them to learn materials names and how to spell them.  This also reminds students of all the possible tools available to them.

#7  Write about the use of manipulatives.  Manipulatives provide a concrete objects for students to describe.

#8 Let parents work with manipulatives, it is important for them to understand why using manipulatives is helpful in learning math. 

Two Steps For Developing Communication in the Classroom

This week I have been thinking more and more about how to get the message of the importance of communication between student to student and students to teacher is critical if we want to create great problem solvers who have great reasoning skills.   I just read an article in a NCTM journal by a fourth grade teacher and I love her quote: "Communication is not a passing fad!  It belongs in the very heart of every math classroom."  So how do we make it the heart of every classroom? 

Do You Scare Easy?

In the Guided Math book Laney Sammons gives scary statistics from the US Department of Education from 2008.  Are you ready for this?  Maybe you should sit down, take a deep breath, and prepare yourself to be terrified.

 OK, here it goes:

 78% of Americans over 18 cannot compute interest paid on a loan.  That would explain the state our country is in!  LOL 

71% of American over 18 cannot determine miles per gallon on a trip. 

This is the one that really gets me - 58% cannot calculate a 10% tip.  We're not talking a 15% tip, but a simple 10%.  WOW.

 I have been working with my husband on weekends to build  a new home. What  I've come to realize very quickly and sheepishly,   I am good at book math, but not so good at real-world math.  In fact, as a teacher, I thought I knew what real-world math was, but I didn't have a very good clue.  I think all educators should take a month or more sabbatical,  go out into the real-world (different careers), and not just watch what real workers do, but actually roll up their sleeves and do the work.  I believe until this happens, we will not be able to make a dent in changing our mathematical education in this country.  

We designed our first lesson to talk about the difference between an inch and a cm, and then were going to have them measure various items in both to make sure they did know the difference.  As the lesson began, each teacher watched his or her designated child diligently.  Then, all of a sudden, as many children came to the document camera to show how they measured an item, a light bulb came on for us educators.  See we thought the reason the students were missing the test items had to do with them just reading the last number on the ruler.  In Kansas students have to read a broken ruler.  So if they show a pencil starting at the 4

" line and ending at the 10" line, then students have to state it is 6".  We all thoughts many students would say the pencil is 10".  Boy were we surprised when they stated "seven inches".  Seven inches, really, show us how.  One by one students would come to the document camera and measure each object. This is when we had the ahha!  Students did not understand the concept of an inch.  They were counting the lines on the ruler, not the space in between the lines.  All the teachers in the room, including myself, couldn't wait to get out of the room.  Now we know how to fix this misconception.

Our second lesson, after being revised, made us realize we need to clarify students' concept of an inch.  I believe this is what happens when we move to a procedure or skill before a concept is deepened and understood completely.  This time we started with the one-inch square tiles.  Making sure students understood, by measuring with their ruler that yes it is an inch.  Measuring objects with the square tiles, then laying a broken ruler on the object, made students question their own understanding. 

True learning took place that day, not just with students but with also many great educators. 

Active Engagement Is CRUCIAL

We can no longer afford to have math as a passive subject.  The days of the teacher modeling a couple procedural problems to students memorizing meaningless steps needs to be replaced immediately.   This means that the textbook is a resource and guide but NOT the lessons.  We need to allow students time to explore,  discover, and make conjectures and generalizations about mathematical concepts.   As one teacher from the grant stated, "One must truly understand the whys behind procedures for true learning."  Another teacher wrote, "A deep understanding of math is critical to future success."

Use of Math Tools

Research from RTI or MTSS in Kansas states clearly that CRAapproach promotes strong understanding.  As students are learning new concepts they should begin with a Concrete experience.  This hands-on experience may include manipulatives or other concrete tools.  Teachers should then, as students are ready, move them to a representation of the concept.  This could be with the use of a graphic organizer or drawing a picture.  The teacher is waiting and facilitating discussion to then move the student to the abstract representation of the concept.  All students move through this CRA approach at different times.  It takes a skilled teacher to move each child through this approach on each new concept.    Representation is one of five process standards that NCTM encourages for deeper understanding.

Comparing of Different Strategies

There is more than one way to skin a cat.  I remember my mother telling me this as I grew up.  Real mathematicians know that there is more than one way to solve a problem.  There may be more or less efficient strategies, but there is more than one strategy.  Often times the “traditional” strategy is rote learned with little to no understanding.  If students explore and discover strategies or algorithms that works, it is important for them to share and compare their strategies with others.  These strategies often make more sense and can be very efficient.  Teachers from the MSP grant share the following that they would like to remember: “Have students discover rules/ procedures that way they will remember.” “There are different ways of processing information.” “Students who can explain why a procedure works are going to be more successful.”

Questioning and Risk Free Environment

Is it not amazing that when we ask someone a question about their answer,  we automatically assume our answer must be wrong?  This is true of young children and adults.  This stigma of questioning must be changed if we plan on making risk free learning environments.  As teachers we must be retrained in our questioning ability.  Questions such as “How did you know to …” , “Why did you choose to ….”  Open questions, which require more than one word answers, are great tools for all educators.  I’ve worked with educators for more than twenty one years and I have yet to find an educator who feels competent in asking higher level reflective questions.  It is only when we understand that having the “right” answer is NOT the goal of a math lesson or classroom will we be able to create the atmosphere of a risk free environment.  Some quotes from teachers: “Be patient with students who don’t understand math.” “Create a safe learning environment.” “It’s ok to try something new.” “The classroom environment must be inviting and welcoming.” “Ask more open-ended generic questions to get students thinking.”

Problem Solving

When in the real-world do you ever encounter a worksheet of naked number problems?  If you have, outside of a school setting, please let me know.  Math is everywhere in the real-world, but it is always within a context.  Usually we don’t have all the information we may need to solve the problem, often we have too much or unnecessary information.  Problem solving needs to be a goal.  NCTM refers to problem solving as a process standard.  The how we should be teaching mathematics.  Remember back to when you were in math class.  We always did the first thirty naked number problems and then we had two problems at the bottom of the page that the teacher would often allow us to skip. If you didn’t get to skip them, it was pretty clear that you just needed to find the numbers in the problem and do the same computational procedure as the first thirty problems.  This fear of story problems needs to stop.  As early as Kindergarten, students should have problem solving in math daily.  Yes,  I said daily.  Cognitively Guided Instruction is the BEST math instructional strategy and philosophy that I have ever been exposed to.  You need to check it out.

Developing Communication and Shared Thinking

 Communication is a process skill according to NCTM.  In other words, a student communicating with each other and with the teacher is critical to  their mathematical learning.  Many teachers feel that they don’t have the time to allow students to communicate or they may be afraid students will not be discussing mathematics.  If the math students don’t require them to be actively engaged, then it is very possible the conversation will not be around the problem.  It is important that active engagement is infused into your classroom climate.  Communicating verbally is one way for students to process information.  A few teacher reminders: “Faster is not always better.” “Remember to make students prove why and explain their answer.” “It takes time to develop deep understanding.” “Students need various amounts of time to process.”

I always love the quote, “The one who does the talking, does the learning.”  No wonder I got so smart when I taught the same lesson three times through each day when I was departmentalized.

Connection to the Real-World

Why do I need to know this?  If I had a dime for every time I heard this from my sixth graders I would be sitting on a beach today instead of writing this blog.  LOL!  My husband and I are currently building a home.  We are our own general contractors.  My husband owns a heating and air-conditioning company where he has worked for over 25 years.  As we were digging the basement we needed to level the land, make it the same depth, and making our basement square.  I came to a real self-realization that rainy day. I’m really good at book math and not so good at real-world math.  In fact, I’m not sure I really no what real-world math is.  I believe as teachers, we live in a “book math” world.  We try to make connections, but these connections are only as good as what we know.  In other words, we don’t know what we don’t know.  My solution: I think every teacher, specifically middle school and high school, needs to take a sabbatical and go into the real-world, roll up their sleeves, and do the work.  It is only in this way, that we will truly begin to understand the mathematical demands of the world. Teachers from the MSP grant remind me: “Bringing in real-life situations truly gives a need and desire to work with numbers.” “Help students develop their own real world problems.”

Estimation and Using Mental Math

This area of mathematics is one that many teachers dread, and maybe even skip in their textbook.  Why? I think it is because textbooks attempt to proceduralize estimation by teaching rounding, or some other procedural method.  In order to really be able to do mental math or estimate one must have number sense and a strong working knowledge of the concept.  For example:  One may use mental math to solve the problem 3,459 + 998 by adding one thousand to 3,459 and then subtracting two.  This requires the person to know the relationship between 998 and 1,000.  If students don’t have a great enough number sense, which requires a lot of opportunity to work with this size of numbers, they only know a computational procedure.  If I were to ask you to estimate what 7 1/8 divided by 6/8, if you don’t have a strong conceptual understanding of division and fractions, you would not be able to give me a close estimate.  Most teachers can not give a close estimate themselves.  Students need to learn conceptually before they move into a procedure.  If we don’t allow this time, estimation and mental math is an unattainable.

Schema Based Instruction

This is the understanding that story problems have different underlying mathematical structures.  This allows students to organize types of problems and therefore organize different strategies appropriate to the problem.  Thomas Carpenter, researcher of Cognitively Guided Instruction, organizes story problems into fourteen different categories.  For more information, check out Cognitively Guided Instruction.

Writing and Reflecting on Learning –

Metacognition is a hot new term in education. Basically it is the thinking about our thinking.  It is important for a person to set goals, and analyze how closely they have reached their goals.  It is also important for  a student to be reflective on what they know, what they may be confused about, and what they don’t know.  It is only when we can look into a mirror to evaluate and reflect on our own learning process, will we be able to move forward in our learning.  More and more teachers are beginning to use reasoning books with their students.

Top 10 Instructional Strategies to Retool Your Classroom

The past four years I have been involved with a Math and Science Partnership grant.  One strong component of this grant is the intensive two week professional learning that all participants must attend.  Two purposes are always a strong component of this grant.  One teachers need to engage in high levels of mathematics to improve their content knowledge and to explore and reflect on their instructional strategies.  Ten instructional strategies tend to emerge every year.   If we could re-tool every math classroom with these strategies, I have no doubt that the United States would become the strongest country on the globe.

#1  Active Engagement

#2  Use of Math Tools

#3 Comparing of Different Strategies/Algorithms

#4 Questioning and Risk Free Environment

#5 Problem Solving

#6 Communication

#7 Connection to the Real-World

#8 Estimation and Using Mental Math   

#9 Schema Based Instruction

#10 Writing and Reflecting on Learning

Rote Counting - Foundational Skill of Number Sense

Rote counting is a foundational skill of number sense.  Unfortunately most kids only learn how to skip count by 2's, 5's, and 10's starting with the first multiple. 

What is Number Sense and How Do I Get It For My Students?

What is number sense?  I hear from school to school, teacher to teacher that kids don't have number sense or know their basic facts.  I've often wondered, not knowing the basic facts, is it the problem or the symptom of a greater problem.   I've come to the conclusion that not knowing the basic facts is a much deeper problem of not having strong number sense.  So what is number sense?

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My last blog was titled What is Number Sense? How Can I Get It For My Students?