I can’t begin to tell you the number of times I heard that question during my thirty-one years as a high school math teacher. I certainly know many more answers to that question than I did when I began my teaching career, but I am still learning more answers all the time. And it’s not just because I am consciously looking for them but because new answers are being created every day. I read an interesting report today by Laura Devany on a panel discussion that highlights the persistent nature of this question and its relevance to student motivation and implies that we are doing a better job than in the past but we still have a long way to go. http://www.eschoolnews.com/2015/01/13/us-change-math-893/2/
I remember serving as secretary of the Math Club in high school. There weren’t a large number of students in the club and certainly more males than females. As Devany reports in a quotation from Danica McKellar, one problem we still face are the stereotypes, although I think people like Bill and Melinda Gates, Mark Zuckerburg and Sheryl Sandberg are helping to move us forward. “Part of what we need to address is the culture of this country, and why this culture encourages kids to not want to excel, and to shy away from wanting to seem like a nerd,” McKellar said. “Breaking stereotypes is just as important as changing the way the content is presented.”
I agree, but as a consultant who spends time in math classrooms, we still have a long way to go in the way the content is presented. Even though when working with teachers I stress the importance of creating relevance for the student in every lesson, (Yes, those RED frames of reference), I still don’t see many real examples of mathematics “in context.” In defense of the teachers, I don’t know that we adequately prepare them to deliver those kinds of experiences. One year I was working with a group of lateral entry high school math and science teachers. Their experiences in business, manufacturing and the science laboratory gave them a level of expertise I never knew. I also remember the opportunity one year to tour the Dupont plant in our district and learn more about their needs in skills for their employees. I wish I had many more opportunities like those.
Certainly our world is demanding a workforce more skilled in creative problem-solving, analytical skills and technical applications of mathematics. The publishers are listening and teacher resources, both hardbound and digital contain many more examples and problems which require students to draw on a variety of skills and concepts than they did when I began teaching. However, based on my experiences with classroom teachers in the past few years, I’m not sure the teachers are given the professional development and time needed to incorporate these resources on a consistent basis. No one outside the field understands the complexity of the demands on teachers and the time required to prepare each day to meet those demands.
So I would love to know, how does your state or district support the constant growth of teachers in not only their instructional strategies but in keeping up to date with the world around us and it’s impact on our professional requirements? How do we help the politicians, who provide the funding and time needed, understand the constant investment required in professional growth?
The Back to School buzz filled the room. It was late July and the first day of pre-planning. As excitement bubbled in the room, all I could feel was panic. We had just been handed the requirements for developing an effective standard- based classroom. The terminology for our classroom structure had changed; however, as I read, “Warm-Up/Activating Strategy 10 mins, Teacher-Led Mini Lesson 10-15 mins, Student Led Work Session 20-25 mins, Closing/Summarizing Strategy 5-10 mins” all I could see were the TIMES attached to each. My mind was spinning and I vaguely remember hearing my administrator’s voice in the background saying that all components of the Standards-Based Classroom were necessary for effective instruction to occur. NO… that did not help the panic I was feeling. How would I make this happen? I have NEVER been a person of few words, and holding me to times was one way to cause me to feel boxed in and limited. However, I knew that this new structure was not a suggestion but an expectation.
As a result of my training in Bran Based Learning I always worked to create a non-threatening classroom environment. How would I incorporate these time frames and keep a non-sterile, safe and secure classroom structure? Let’s start with the “Warm Up.” During this time I had to take attendance and get class started. A friend gave me a set of CD’s by Gary Lamb that were for increasing brain activity. These songs were anywhere from 3-6 mins long and became the “timer” for beginning class. The music was playing as the students’ entered the room. They knew that they had until it went off to do their warm up, get their homework ready to check, and be ready for class to begin. It also served as a timer for ME. I had to take attendance and get myself ready before the music went off. Maximizing class time became a conscious effort for me and the students.
After all these years, I still have my timer!
I knew I could not play music throughout the entire class, although, I did use it often as a timer. I needed a timer that was not attached to my computer or sitting on my desk. If I was on the other side of the room and needed to give the students 3 mins to discuss something, I needed the time to start immediately. Therefore, I began my quest for a timer. The end result was a $1 timer, super glue, a clip and a lanyard. I made me a timer that could be attached to any lanyard… because the lanyards HAD TO MATCH WHAT I HAD ON! I would put this on first thing in the morning and wear it all day. As part of our Positive Behavior Intervention I timed my students going to the restroom. If they were able to complete the task in the allotted time they received a “Knight Buck.”
Timing became a gateway to more effective instruction. Initially I was astounded at the amount of time I gained by simply timing myself and my students throughout my instruction; 30 seconds meant 30 seconds, 5 minutes meant 5 minutes. The timer did not restrict my classroom environment; it made my classroom more effective and engaging. As a result, I had taken a major step toward effective standards-based instruction.
Teaching Florida’s assessed curriculum using cooperative learning structures, teaching vocabulary in context, asking higher order thinking questions, using Thinking Maps, and teaching students to summarize in writing or orally with partners were the five school-wide strategies we implemented when I was principal of Lake Alfred Elementary in Florida. These five school-wide strategies were the tools teachers used to ensure the academic success of our diverse, economically challenged students. Our students’ efforts and teacher effectiveness earned our school six consecutive A’s from 2004 through 2009.
Teacher effectiveness is directly related to student learning so it is imperative for school-based administrators to develop long range plans to systematically train, coach and monitor teacher implementation of their school-wide strategies.
First, identify strategies that increase student achievement based on educational research. Next, decide which strategies to implement and in what order after analyzing your student data and gathering feedback from your leadership team and teachers.
Once, you decide on your first strategy, schedule initial professional development for that specific strategy. This training should explain the strategy, model how to implement it, clarify why the strategy increases achievement and provide practice opportunities for teachers during the training sessions. After initial training, administrators need to follow-up, including coaching and monitoring teachers as they implement the strategy.
Prior to implementing our first strategy, my Assistant Principal and I walked through classrooms daily. We felt it was critical to first have effective teacher management of student behavior before implementing new instructional strategies. However, at that time we were not observing teacher instruction consistently. Once we implemented our first strategy, we began observing teachers presenting Florida’s tested curriculums using our new strategies. We continuously supported and monitored teacher implementation of our instructional expectations with daily walk-throughs during reading, math, writing, and science; scheduled and unscheduled mini-observations and weekly professional development sessions to refine teacher effectiveness. During weekly K-5th collaborative planning, grade level teams met with resource teachers to develop plans to teach Florida’s reading, math, writing, and science standards. We used lesson plan templates (below) developed in-house to ensure teacher implementation of our five school-wide strategies.
Remember, as you hire new teachers, you must provide them the initial training and follow-up for the school-wide strategies already in place. If you are fortunate to have certified trainers on your faculty for any or all of your school-wide strategies, you can provide new teacher training in-house. If not, you’ll have to arrange for new teachers to attend outside professional development for that particular school-wide strategy.
With the exception of one school year, we implemented only one new school-wide strategy or curriculum program (Math Wings and Write From the Beginning… And Beyond) a year. Consequently, our teachers had a year to be trained, coached, and monitored to become effective in implementing a new strategy or curriculum program before we began to implement another strategy or curriculum program. Our overall administrative strategy was to increase student achievement by doing a few things very well.
Eileen Castle (email@example.com) is an educational consultant and FSC Adjunct Faculty member. She is a former Polk County, FL principal and district office staff member.
“A ship is always safe at shore but that’s not what it’s built for.” Albert Einstein
I remember the first time I stood barefoot at the ocean’s shore with my grandmother. She asked me to stand still there for a bit and allow the tide to rush saltwater over my feet to the sand then back again to the ocean. As my feet covered with wet sand, it felt as if I they were being sucked down deeper with each wave that rolled in. They began to feel heavy, and as I tried to pull them up out of the sand, it was difficult to do so. My grandmother smiled at me as she observed my reaction to this initial experience of standing still at the ocean’s edge. While I felt safe and secure as my feet became firmly planted in the sand, I realized that the longer I stayed there, the harder it would be to move. As this calendar year ends and another is soon to begin, I am reminded of the metaphor for life that this experience represented.
As an educator, a business man, a father, husband, and friend, I have deliberately decided to pause to reflect on the resulting impact of allowing my feet to get stuck in the sand. Not only does this limit my ability to grow and adapt, but it limits my ability to view life from different vantage points. Lack of movement may lead to an increased aversion to risk as well. So what’s it going to take to lift my heavier-by-the-moment feet from the sand?
During these moments of reflection, risk-taking experiences I have had and things I have read about risk are rushing like the waves to the forefront of my thinking. I am especially reminded of a poem given to me by a fellow teacher at my hometown school where I taught a couple of decades ago.
To laugh is to risk appearing the fool.
To weep is to risk being called sentimental.
To reach out to another is to risk involvement.
To expose feelings is to risk showing your true self.
To place your ideas and dreams before the crowd is to risk being called naive.
To love is to risk not being loved in return.
To live is to risk dying.
To try is to risk failure.
But risks must be taken, because the greatest risk in life is to risk nothing.
The person who risks nothing, does nothing, has nothing, is nothing, and becomes nothing.
He may avoid suffering and sorrow, but he simply cannot learn, feel, change, grow or love.
Chained by his certitude, he is a slave; he has forfeited his freedom.
Only the person who risks is truly free.
More recently, as I prepared to deliver a key note address entitled, Education is Risky Business, I was intrigued by the work of Brian Tracy. In his book, GOALS!, he speaks of something he refers to as Intelligent Risk taking, a more reflective and refined approach to taking risks. Tracy states, “It is a fact that every great leap forward in human life begins with risk taking and a giant step of faith into the unknown. Men and women who achieve goals and accomplish wonderful things are invariably men and women of great faith in themselves and their abilities. The better you become at analyzing before taking risk, and then avoiding as much of the risk as possible, the more competent and more capable you will become, and the more successful you will be.”
Perhaps in addition to, or even instead of, the traditional New Year’s resolution, you could consider a thoughtful risk you plan to take in the New Year. When contemplating this thoughtful risk, take some time to think about the reasons for doing so and the positive impacts you hope will result. May the thoughtful risk you take bring you great joy and satisfaction personally and/or professionally!
A few months ago, I sent Kristi Bosworth (Consultant for Thinking Maps) a copy of the Flow Map I created for my students for solving 2-step equations. I made it sports themed because many of the students I teach love sports, so I knew it would be a big hit. This is the Flow Map that I created:
After a few conversations, we agreed that by pre-creating this Flow Map, I took more than I gave. I took away the thinking from the students and made a Thinking Map for note-taking. So, with the help from Kristi, I came up with a neat way to present this information that really maximized the students’ thinking.
Before I taught the lesson, I prepared the materials, such as cutting out each piece of the Flow Map. By the way, all the resources that I used for this lesson is at the end of the post. I opened the lesson by instructing students to get out paper and write down the problem on the board. From there, I told them that for each step we complete on the board, they must copy and explain the step.
After the entire problem was written, I had students read their work aloud. I made comments as they went, and I challenged the entire class to be more detailed with math vocabulary words to explain their steps.
We did this for 3 more problems. After the last problem, we had a vocabulary-rich conversation about cognitive and mathematical words. Students were able to pull out the math-focused and cognitive-focused vocabulary. With those words, the students were able to look at my focus wall with Thinking Maps and pick out the type of thinking and the corresponding Map that we were going to use that day.
Then, I divided them into groups and gave them an envelope filled with all the pieces of the Flow Map. The objective of this activity was to use the notes they just took to sequence the steps of a 2-step equation. They reviewed the 4 problems that we had completed on the board and noticed the similarities with the problems. They were engaged in the thinking instead of me giving it to them! Because of this, they sequenced their way through a 2-step equation.
There was a learning curve for all of my classes. The students who excelled were able to complete the process faster than my students who struggled. I was able to, however, work with certain groups who struggled in order to scaffold their thinking. After each group finished presenting, I had them explain their reasoning. If something was incorrect, which did happen often, I walked through their reasoning in order to reveal the missteps in their sequence.
To conclude this part of the activity, students were asked to write a paragraph explaining their Flow Map. I made it clear that I did not want a “first, you do this then you do this.” I wanted them to pick a problem and explain the steps with math-rich vocabulary. After they wrote their paragraph, I gave them a handout of the Flow Map and they were to use their work to complete it and glue it in their notebooks. We talked through each step and why the steps were needed to solve an equation.
To wrap up the lesson, I created a close reading activity. I gave them a problem and they worked through the Flow Map for each step.
Overall, I was thrilled with the outcome of this activity. Students were able to critically think through the process of how to solve a 2-step equation without just GIVING them the steps. This activity opened my eyes to the amount of thinking that I “rob” from my students because I am not giving them a chance to work through it. I was challenged to figure out how I can implement this strategy more in my class.
If you decide to use these resources in your classroom, leave a comment below. I would love to hear your thoughts.
My name is Tyler Thomas and I am currently a seventh grade teacher at Pepperell Middle School in Lindale, GA. I graduated with my undergraduate degree from Shorter University in the spring of 2013. I just completed my gifted endorsement and will be done with my Master’s degree from Piedmont College in summer of 2015. I am currently in my second year of teaching and I love what I do. You can find me on Twitter (TheTylerThomas3) or Instagram (tylerwthomas) where I post a lot of my experiences in my classroom, along with funny stories of everyday life!
I have heard people say the only things certain in life are death, taxes and change. But then you also hear people say, especially in education, “some things never change.” There is also a good amount of disagreement these days on the benefits of new state standards and the changes it is producing in education. In my experience most of those opposed to these changes are parents, politicians or citizens without a true understanding of what the new curriculum is all about. I have frequently heard: “If it was good enough for me to learn it the old way why do we need to change it now?” But what about life, society and the world today is the same as thirty years ago?
I remember when I started teaching at a high school in 1980 and they received the first computer to ever enter the building. I had NO idea what to do with it, but within five years was teaching programming classes. Today’s schools are becoming so technology dependent that students are encouraged to BYOD, Bring Your Own Device! When I started teaching you could graduate from high school with General Math 1; now you need the equivalent of Algebra 1 and 2, Geometry and another math above those. The world has changed, our expectations for students has changed and as a result, the way we teach has to change.
Several people have given me the link to the following video.
Dr. Raj Shah does a great job of explaining one way of answering this question about why the math curriculum has changed. This answer is part of a big picture that many people outside education do not understand. I also addressed this in an earlier blog. Here is the way I explained it.
After taking advantage of the Buy 2, Get 3 Free chicken breast special, I told my daughter she could come by and pick up a pack. She was having guests for dinner so was excited about the free meat (she lives on a 3rd year teacher salary). When she came to pick it up, she looked at the pack which was labeled 1.8 pounds and said, “So how many ounces is that?” Now this girl is 26 years old, scored high enough on her AP Statistics Exam her senior year to place out of math in college and made an A in high school chemistry under a very tough teacher. Really? She was in a hurry and not in the mood to be coached to the answer so I answered: “Well there are 16 ounces in a pound, 0.8 times 16 is 12.8 and 16 + 12. 8 would be 28.8 ounces.” “Ok, so that’s more than enough for 4 people,” she replied.
The next day as I was spending 7 hours driving, I started thinking about that conversation. Why is it so many people have trouble doing mental math, particularly like this case, multiplication. My high school students were always amazed when I could multiply problems faster in my head than they could turn on their calculator and type it in. After some pondering, I have a hypothesis. Students don’t understand that all multiplication is simply an application of the distributive property. I certainly didn’t understand that in elementary school. I knew how to line up a multiplication problem and “move over” a space on the second line, but I really didn’t know why. You see it’s that WHY that is our problem. For example, why can’t students remember that to divide by a fraction means to multiply by the reciprocal? Because they don’t really understand the relationship between multiplication and division. That’s not just the rule for dividing by a fraction, it’s the meaning of all division, to multiply by the reciprocal (the multiplicative inverse).
All this brings me back to the Common Core Standards for Mathematics. It is this type of conceptual understanding that the Common Core Standards are demanding of students. Students won’t memorize procedures that have no meaning to them and therefore will not be retained over time. Students will need to develop a deep mathematical understanding of the structure of mathematics, from kindergarten through college. If students grow up understanding that all multiplication of more than 1 digit times 1 digit is an application of the distributive property, then when they get to algebra they won’t need something called FOIL to tell them how to multiply (4x + 5)(2x – 3) and they won’t freak out when suddenly the problem changes to (3x + 4) (2x2 -5x + 2).
So teachers are you ready? When a student asks you WHY they do a math problem a certain way, the answer should not be, “Because that’s the rule.” I would love to hear some of those “WHY” questions you or your students struggle with answering. Who knows, maybe together we can grow a generation of mathematically literate citizens!
With the changing role of education, we’re all learning and exploring a variety of ways to meet the needs of 21st-Century Learners. There are three types of instructional strategies that have been used interchangeably but actually refer to different things: Personalization, Differentiation, and Individualization. So what really is the difference between these three strategies? Personalize Learning created an awesome resource to clarify and we couldn’t resist mapping it. Enjoy!
“It was the best of times, it was the worst of times.” You probably recognize these lines as the opening of Charles Dickens’ A Tale of Two Cities. They are also lines borrowed by Dr. David Sousa to introduce the first chapter of his book, The Leadership Brain. He explains that it is the best of times because “never have we known so much about how the human brain develops, grows, and learns… It is the worst of times in that never before have the public schools been asked to do so much for society.” He continues that schools not only teach children, they raise them. While teachers are charged with presenting their curriculum, they are also asked to counsel on drugs, sex, family problems, and personal relationships. The point that gets driven home is that in these times, managing is not enough, educational leaders become the key to helping school staffs balance their responsibilities and priorities successfully.
I would advance this scenario from the educational leaders position considering that it is the best of times because never before have we had the depth and selection of outstanding professional growth and development opportunities. Many of these, like Thinking Maps, are linked to current brain research and offer better knowledge and instructional strategies that can ultimately lead to student success. It is the worst of times because we work on an ever-changing landscape where the demand for increased student performance data is accompanied by decreasing financial resources.
Consequently, educational leaders are compelled to serve as instructional leaders working with staff and community to ensure relevant and rigorous learning opportunities for their students. Schools cannot focus solely on dispensing knowledge, but on developing students who can learn and adapt to the knowledge and skills they will need to succeed in the 21st century. At the same time ,leaders must function as full-fledged business managers overseeing the prudent application of available resources at a time when those resources continue to diminish.
In summary, let’s change the saying “managers tend to do things right while leaders do the right thing” to reflect the situation educational leaders find themselves in and say “managers tend to do things right while educational leaders do the right things right.” More than ever, our schools need strong leaders.
I love magazines during the holiday season. I start collecting them about the middle of October and pour over them nightly. I don’t want to read them on my iPad; I want to tear out recipes, cut out sayings, and put them on my refrigerator, turn down the corners of pages I want to show someone, and put tabs on pages with possible gift ideas. I try to recreate clever decorating ideas that generally look pretty sad but still I love the engagement.
So when I was flipping through the November Good Housekeeping and saw the title “A Husband Who Does the Dishes,” I couldn’t resist reading. The Multi-Flow Map below summarizes the key points of the article. I printed out this map and have it posted on my refrigerator as a reminder.
While I have a million things to be grateful for in my personal life, I am also very thankful for a professional life as an educational consultant that I love. So here are a few things I am truly grateful for:
Having the privilege to work with teachers who have devoted their lives to helping young people.
Sharing, creating, and thinking with all of the fantastic educators in our company who are truly focused on contributing to the profession we all love.
A job that allows me to stay connected to teaching and to share the critical and creative power of Thinking Maps.
Any day that I can spend with children, hearing about their maps, and seeing them think.
Have you started your list? Create your Circle Map brainstorming these things, or if you are really motivated, create a Tree Map classifying all your blessings into categories. Can’t wait to see your thinking.
Bringing new programs to enhance learning to a school is sometimes a difficult undertaking. This year my school decided to take on the integration of not one but two new programs; Kagan strategies and Thinking Maps. Teachers crave meaningful trainings that they can feel are easy enough to implement immediately and not anything additional they feel like they have to do. Let’s face it, teachers are very busy people.
I have worked with the Kagan trainer at our school and we created a variety of ways that we can easily incorporate the two programs while involving the teachers. By doing this they are practicing both programs and seeing how the two can be easily integrated into one lesson.
This past week we had a faculty PLC Thinking Map scavenger hunt. I asked each grade level for a list of maps we could find if we “searched” their rooms. I then created a list for each grade level that required them to visit the grade level below them and the grade level above them. They had to take pictures of the maps they found and write down the teacher’s room number they found it in. Although we all work in the same place, how often do teachers actually have the time to visit anyone else’s room? Never!
By doing this we accomplished many things. First, teachers were able to see vertical movement between grade levels. Second, teachers were able to gain multiple ideas that they could incorporate into their own classroom without meeting with individual teachers. Third, teachers that were initially hesitant saw value in what was happening in other classrooms and realized if they didn’t jump on board their students would soon be left behind. Finally, as a trainer it helped me to see where we still had come confusion, and what my next follow-up training should be.
Once all the teachers returned to the media center we incorporated our Kagan strategy. We used mix, pair, share and rotated three times. Teachers had out their phones, were sharing pictures, and “aha” moments they had during their hunt. It was such an easy way for them to share what they had seen and the entire process was completed in the time it takes to hold a regular PLC meeting.
Using the Kagan strategy to share gave teachers an additional idea for their classroom. How easy would it be to have students work on maps individually and then share what they discovered in a five minute mix, pair, share!
In the upcoming weeks we are incorporating Kagan into every Thinking Maps training we have including a timed, pair, share, a picking stickies (all write round robin), and line ups. Teachers left the training saying things like “this was a great idea”, or “I never thought I could use a Thinking Map and Kagan together”. Every time we leave feeling accomplished and that our time was not wasted. It’s an amazing experience to provide beneficial trainings to teachers that love to learn!
The attached photos are an example of a circle map exercise that was found in a first grade classroom, and a working picture of the teachers doing the mix, pair, share Kagan strategy to share what they found.
My name is Christian Luciano and I teach second grade at Three Oaks Elementary in Fort Myers, Florida. I am passionate about sharing my love of learning with others. I love Thinking Maps! I honestly dream ideas on how to extend thinking in my classroom through the use of Thinking Maps.