I cannot tell you how many times I have heard people say “I am not good at math”. This is from students, parents, friends, and colleagues, many if not all, I believe to have normal to well above average intelligence. On the flip side, no one really freely admits, “ I can’t read, or comprehend text well.” Why is that? Why is it so easy to admit we don’t understand or like math? Don’t get me wrong, there are many people out there that love math and are making great strides in mathematical thinking. But for many of us, something went wrong and math is not our “thing”.
We have a name for this propensity for not liking math, it is called, "Math Phobia” and it is at epidemic proportions. Math phobia is actually defined in a medical dictionary as a feeling of tension, apprehension or fear about one’s ability to do math, which subsequently interferes with the performance thereof.
This phobia is present everywhere in our society and has prompted an entire industry of memes and graphic T-shirts that promote the idea that math is hard and scary. (Underlying message, so it’s ok not to be good at it or to even try.) When we believe something to be too difficult to master, this attitude stops us from focusing on the problem we are trying to solve.
So what went wrong, why do so many lack confidence in our math skills?
Research suggests that for many of us it was the way we were taught. Math was taught to most strictly through the study of arithmetic and computation. We were led to believe math was a list of rules and specific algorithms that could only be memorized and procedures done specific ways to get to the one correct answer. You were considered smart if you could compute quickly. Thinking about math this way is boring, stressful and/or unproductive. In his article, Why Do Students Fear Math, Pradeep Kumar states;
Another reason that many people feel they are not good at math is that they were lead to believe you are either born to be good at math or you were not. The truth is that we are not predestined to be good or bad at math, although the attitude that you are a math person or you are not continues to prevail. Stanford University Professor Jo Boaler says,
How does our own attitude about math affect how we teach math and more importantly, how does it impact our student's success rates?
Research suggests that parents and teachers with anxiety about algebra and equations transmit those feelings to their children and students, who then perform worse on math. Math anxiety has been recognized as an impediment to math achievement. As teachers, our attitude and confidence with math skills have a direct impact on our student's achievement rates in math.
In a recent study, Boaler and her fellow researchers recruited 40 5th-grade teachers from the Central Valley to take a 12-hour online math course she and her team created. The course, “How to Learn Math for Teachers,” covers perceptions about math, how anyone — with enough practice — can develop the brain skills to understand complex math problems, and how math is used in everyday life. The course also covers basic math concepts, such as number patterns and reasoning, and offers tips for teaching those concepts.
When commenting about the impact of the Stanford study, published in the journal Education Sciences, Jo Boaler said,
For our students to do well in math, many of us need to change our own attitudes and understanding of mathematical concepts and ideas.
Changing perceptions and skill sets is difficult. Where do we begin? The first step is to adopt a growth mindset. A growth mindset is based on the belief that your basic qualities are things you can cultivate through your efforts. If you have not read it already, I highly recommend you read Mindset: The New Psychology of Success by Carol S. Dweck, Ph.d. This philosophy has been a game changer for many. (This one, in my opinion, is also worth a second look even if you have already read it).
About a decade later, Dweck’s Stanford University colleague Jo Boaler piggy-backed off these ideas and applied it to mathematics. Mathematical Mindsets was published in 2016 applying advanced neurological research to how students best learn mathematical concepts. This book sparked an international resurgence in mathematical best practices. This is a must read for any teacher of mathematics. In it, Jo Boaler explores the power of mistakes and struggle, the concept that there are creativity and beauty in mathematics, (A concept I did not get at any time during my math education), the importance of developing flexibility with numbers and how mathematics is a path to equity.
When I first read Mathematical Mindsets, the greatest take away for me was there are creativity and beauty in math. What?!?! As a recovering mathophob myself, I was led to believe math was all about speed and (this one is from my dad who would sit with me as I cried through my math homework) you only get the right answer if you have a sharp pencil. In the book, you are introduced to Maryam Mirzakhani, the first woman to win the Fields Medal (equivalent to the Nobel Prize for Mathematics). If you have not heard of her before, her amazing and tragic story is worth looking up. Born in Iran, Maryam was a mathematician at Stanford who studied hyperbolic surfaces and who had in 2016 produced what has been called the “theory of the decade”. Surprisingly, Mirzakhani described herself as a "slow" mathematician, saying that "you have to spend some energy and effort to see the beauty of math." To solve problems, Mirzakhani would draw doodles on sheets of paper and write mathematical formulas around the drawings. Her daughter described her mother's work as "painting". In Mathematical Mindsets Maryam is quoted as saying:
For many of us, math was taught strictly through the study of arithmetic and computation. The reality is that mathematics is so much more than that. We need to make the study of mathematics more meaningful and engaging for the next generation. We need to take that leap of faith and believe that even as adults we have the ability to learn more about math concepts and with a growth mindset promote positive attitudes towards the discovery of math for ourselves and the future generations we serve. Be the teacher that promotes this T-shirt.
This post brought to you by Julie Ace, Elementary Implementation Associate
Best Way to Change Scores is to Change Teachers Attitudes
Challenging Myths About Learning
Jo Boaler Ted Talk: How you can be good at math and other surprising facts about learning.
(2008) Foundations for Success: The Final Report of the National Mathematics Advisory Panel, National Mathematics Advisory Panel (U.S. Department of Education, Washington, DC).
St.Myers, Andrew; Carey, Bjorn (15 July 2017). "Maryam Mirzakhani, Stanford mathematician and Fields Medal winner, dies". Stanford News. Retrieved 17 July 2017
Jacobson, Howard (29 July 2017). "The world has lost a great artist in mathematician Maryam Mirzakhani". The Guardian. Retrieved 21 October 2017.
The Llama Llama books are favorites in our house. I’m fairly certain we own every one ever written and have read each of them no less than a dozen times each. The other night my daughter and I were reading Llama Llama Mad At Mama. In case you aren’t familiar with the story, let me bring you up to speed. Llama and mama have to spend the day running a bunch of errands and Llama is not pleased with the plan. One of their errands is a trip to the grocery store. As mama is shopping, Llama is getting increasingly agitated until he escalates to the point where he totally loses control; Llama throws things, knocks things over, kicks his feet, yells and eventually begins to cry. When we reached this point in the book, I turned to my daughter and asked her how she thought Llama was feeling. She answered me then turned to me and said, “Mom, how do you think MAMA LLAMA was feeling here? I know Llama is very upset but mama must be too! I bet she is embarrassed by his choices. I think she also might be worried that something is really wrong with Llama. But I also know she is mad because look at her face! Poor Mama Llama!” WOW! This mama was incredibly proud! Like I said before, we have read this book at least a dozen times and this was the first time she keyed into how Mama Llama was feeling. Her reflection that night got me thinking about the power of using characters in literature to teach social-emotional learning.
Social-emotional learning is such a big topic in education right now that this month's entire edition of Educational Leadership is dedicated to this topic. Everyone is talking about the importance of teaching these kinds of lessons in school. Yet I know that as a classroom teacher, I would have been hard-pressed to add one more thing into the learning day! With so many expectations already on our proverbial plates, how can we do even one more thing? However, teaching social-emotional learning through literature doesn’t add a new expectation to teachers’ already jam-packed curriculum - it can easily be incorporated into reading routines already in place. Here are some ways to begin building in this type of learning with the system you already have set up.
Read It & Reap
When reading a book with students, take the time to make connections between what students read, their personal values, and the world around them. In the last decade or so there has been a shift away from doing this with kids. This happened greatly in part because of the increase in the weight being placed on standardized tests. Our goals for student learning became much more academic focused. “If a question wasn’t text dependent, then it wasn’t a good/necessary question. We stopped asking anything (or nearly anything) where the inference couldn’t be drawn directly from the text.” (N. Boyles) Certainly we need to dig deeply into the texts we read for academic reasons, however, go back to those same books you have previously read and revisit them. “This time, ask questions related to social-emotional problem solving to begin discussions that raise students awareness and encourage them to rethink their own responses to challenging situations.” (N. Boyles) Having these types of discussions may actually take you into the Common Core’s comprehension standards that are sometimes overlooked (author’s craft, purpose & point of view, use of illustrations) and deeper levels of Webb’s depth of knowledge system.
There are numerous aspects to social-emotional learning. Instead of trying to hit them all, be selective and target 4-5 over the course of the year. Here are 5 that have been identified by the Collaborative for Academic, Social, and Emotional Learning because each competency can be addressed through several related focus areas:
Notice the first two are centered on the individual and the final three address interaction among individuals. This progression makes complete sense; how can a student manage their relationships with others until they are able to identify and manage their own feelings and self-perceptions?
Use A New Lens
Many of the books we choose to read with students could target a multitude of the skills listed above all in one text. However, discussing all of them will likely overwhelm students (and likely you as well) and you may miss your intended target. Instead of using a text to discuss various SEL categories, select one skill so students are able to think deeply about specific issues. This can be done with many books - even books that weren’t specifically written with teaching SEL in mind. However, there are many authors out there who have written books around the different areas of SEL learning. Here are some lists that may help guide additional book selections:
25 Best Kids Books to Teach Social-Emotional Skills
50 Must Have Picture Books to Teach Social-Emotional Skills
Hearts and Minds: Picture Books That Strengthen Social-Emotional Learning
Social-Emotional Learning Diverse Book List for Grade PreK-8
As I reflect back on reading with my daughter the other night and her reaction to the text, it reaffirms for me how much children learn through books and the characters they meet there. Though Llama Llama is a favorite in our house (and my daughter has obviously connected with the characters and is learning a great deal about emotions) I recognize that it may not be the best fit for you and your students. Hopefully, though, you will be able to find other texts that you are already using, or perhaps a new one from a list, to try your hand at incorporating some intentional social-emotional learning within your classroom.
This post brought to you by Rebecca Mecikalski, Elementary Implementation Associate
Recently I was asked about an article that I had shared awhile back so I am sharing it again. The focus is around the things we can do in our classrooms to help our students be more successful in regards to mathematics.
The ultimate goal of mathematics is to produce students who can think mathematically and solve
If that is truly the ultimate goal, we have to teach as though we believe it. We have to maximize every
opportunity for students to think deeply, to create their own solutions, to build/write/draw/talk about their thinking! Students learn important mathematical concepts THROUGH problem solving. This is a mind shift away from the idea that we teach math concepts procedurally first and only then can they do problem solving.
Quotes from Principles to Action: Ensuring Mathematical Success for All, NCTM (2014)
Here are some different ways we can change our practices to be more effective.
We think we are being helpful, but are we handicapping them for later?
We used to help students identify words like “altogether” and “in all” in story problems and we said these meant to do a particular operation. I clearly remember posting lists of these words under various operations. My intentions were good and I had seen it done by others. Now, I know there is strong evidence that this practice may actually hinder students’ comprehension of the story! Why?
1. Now we know that when the emphasis is on the “key words” themselves, students tend to find the numbers and just do the operation without thinking about the overall story in the problem.
2. These words can be present in a story problem but not necessarily indicate a particular operation. For example,consider what operation you would use to solve the following problems that contain the word “altogether”:
3. Standardized tests often make a point to avoid these key phrases. When students become dependent on finding the key words and doing that operation, they no longer have a strategy for solving problems when the words aren’t there.
Even at the earliest grades, our focus needs to be on comprehension of the story and true problem solving. It is with good intention that we offer up tricks or shortcuts, but in the long run, these tend to expire and negatively impact student learning.
At every grade level we want to be sure that we are presenting students with practices that create a problem solving environment because that is where true learning and enduring understandings are taking place.
This post brought to you by Carol Lucido, the K-8 District Math Coordinator
How many times has a student pushed your buttons or tried to get into a power struggle with you? Low breathing and smiling keeps a teacher’s body and heart rate calm, which in turn keeps the students calm and prevents verbal challenges. So, do you want to build even better relationships with your students with an even greater focus on content?
It is essential, that as teachers, we give students fair and consistent boundaries, while at the same time, maintaining and preserving relationships. A majority of our students are motivated to learn and behave when we operate from a base of INFLUENCE instead of POWER.
In our work as ENVoY coaches, we have seen teachers consistently use Educational Non-Verbal Yardsticks (ENVoY) GEMS to build more meaningful relationships with all students, focus even more on content, and increase student independence.
Some may think using ENVoY means misbehavior is ignored but that is not the case. ENVoY is not void of discipline. It is more importantly, a set of solid culturally responsive routines used to influence students to increase their on-task independence. When discipline is needed, staff should utilize their building-wide processes and procedures.
According to ENVoY’s author, Michael Grinder, adults who systematically utilize the full range of nonverbal management skills reinforce consistent and fair parameters with all students, regardless of unique learning styles or cultural backgrounds.
Think of it like this: If you purposely tried to use words mostly for content and relationships, and used non-verbal signs, gestures, or signals to manage behavior/transitions, how would that impact your classroom? Coaches can help you identify the balance and art of managing behaviors by influence rather than power.
These practices are not only for classrooms, but media centers, hallways, gyms, computer labs, special education rooms, and main offices can also feel the positive impact of ENVoY.
ENVoy strategies- are identified by 4 phases of teaching and include the following GEMS:
Getting Attention: Freeze Body, Above Pause Whisper
Teaching: Raise Your Hand/Speak Out
Transition to Seat Work: Exit Directions, M.I.T.S. (Most Important Twenty Seconds)
Seatwork: Off/Neutral /On, Influence Approach
Below are some ideas and examples of how teachers tailor ENVoY fit their personal teaching style:
Above (said 2 levels above that of the group) Pause (for silence and attention) Whisper (to begin the content)
The value of the routine affords any guest teacher the opportunity to gather students efficiently with their own Above Pause Whisper as well.
Exit Directions (visual list of what students Need, Do, When, How, and Then)
ENVoY recommends routines for students to manage their own learning. After group instruction, teachers go through Exit Directions then allow students a moment to process, ask questions for clarification, then move into work time. The teacher can use the visuals to NONVERBALLY direct students who may need additional help getting started. Exit Directions also ease transitions for students and adults entering the room at various times. They quickly read what the class is working on and are able to begin with minimal direction/distraction.
Silent Select (written names for student selection)
ENVoY recommends silent select for least disturbance when requesting students from classrooms. Support teachers could write students names on whiteboards or have printed lists and smile and stand silently at the door.
Developing ENVoY routines and management strategies help students feel safe and experience structure and expectations that support their learning. Contact an ENVoY Resident Coach to increase your ENVoY capacity!
This post brought to you by Paula Kuisle, Instructional/ENVoY Coach, Elton Hills Elementary
and Angie Ellsworth, Behavior/ENVoY Coach, Pinewood Elementary
Feel free to connect with Paula via her email or Angie via her email
Remember the days you spent hours creating beautiful lesson plans (for imaginary students!) only to be reviewed and assessed by college professors who perhaps have never taught in a k-12 setting? While we may have moved away from writing lesson plans that include the detail necessary to earn passing grades, formal lesson planning may be an exercise worth revisiting.
Examining a traditional lesson plan template forces us to consider who our students are as learners, the learning objective of each lesson, what mastery of that objective will look like, and the materials needed to engage our learners by differentiating for their needs. Your overall instructional plan will also include interventions and extensions for those who fall below or far exceed the learning target.
That’s a lot to plan for, and for some, our pedagogical tool boxes are just full enough to carry us through the instructional phase; however, mindfulness about the desired learning results and evidence of learning should not be overlooked as we plan. Through John Hattie’s extensive research on student achievement published in Visible Learning (2009), we know that there are some educational practices that are more impactful than others. He found, “effective teachers set appropriately challenging goals and then structure situations so that students can reach these goals.” Being mindful about what we want our students to know and be able to do as a result of the learning experience and determining what that learning looks like is what Hattie termed “teacher clarity.” Teacher clarity ranked in the top 10 or over 100 positive influences on student learning that Hattie studied. He further defined teacher clarity as “organization, explanation, examples and guided practice, and assessment of student learning,” which brings us back to the lesson plan.
The process of creating a narrow focus for learning when lesson planning—writing it down and determining what success looks like—is one of the most effective things we can do as teachers. Making the learning visible for our students, offering precise clarity about what they are learning and what it should look like when they have learned it, matters. When we consider that framework, creating meaningful and engaging learning experiences becomes more targeted.
Identifying academic learning targets for each lesson as part of more formalized lesson planning will help us problem solve the “what ifs...” What if students appear bored? What if they struggle so much they give up? What if they get through the learning experience in half the time I had planned? What if they just don’t get it? What if…
What if my lesson plan included:
You might be thinking: “Won’t this take a lot of time to plan? I teach many grade levels or different content within the same grade—I am not sure I have time.” Determining the learning objective and success criteria are often already embedded in curriculum; making a purposeful plan to share them with students in a meaningful way may take time. Most classrooms post daily learning objectives already; taking those visuals a step further to include what success looks like may be the first step you could take to make the learning more visible.
Planning instruction that engages students, increases student voice, includes instructional dialogue, and is differentiated takes time; however, you do not need to reinvent the wheel. Many instructional strategies work well within many different content areas and for various ages and can be used in rotation. See what works for you and your students. Knowing what it looks like when they have met your objective, though, is an important piece of the plan.
This post brought to you by Kari Kolling-Anderson, Instructional Coach, Gibbs Elementary
Feel free to follow Kari on Twitter @KollingAnderson, to call her at 507-328-4122, or to connect with her via email
Hattie, John. Visible Learning: A Synthesis of Over 800 Meta-Analyses Relating to Achievement; Routledge, 2009.
Getting students to talk more seems like a very simple task. Students talk all the time, right?! Sometimes, it’s hard to get them to stop talking! The question is: are students using social language or academic language? Our goal should be to increase academic talk in our classrooms, while encouraging students to continue to develop their social language. Seems easy right? Not always true, as I have discovered in my teaching experiences.
Here is an example of a lesson that I learned a lot from:
Interaction is a key component of SIOP (Sheltered Instruction Observation Promotional). We often say we want students to talk more and teachers to talk less. However, before we can expect students to interact and use academic language, we first need to teach them the procedures and routines to do so. The error I made was I wanted students to use the academic language, but I had not taught them how to do so in the Turn and Talk.
So, here are some eight steps to help you not make the same mistake by instead creating an environment that teaches students how to build the skills needed to interact with one another and to use academic language (Echevarría and Short).
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Teach students how to listen to each other.
If we want students to talk, we need to teach them also how to listen. What does listening to each other look like? Model for students what active listening looks like. Have students practice listening skills using social conversations first (i.e. tell each other about their favorite TV show) and then move into more content-rich conversations.
| 2 |
Teach students how to respectfully speak to one another.
What types of respectful words or phrases do you hear (I agree with you because…, I don't know that I can agree with you, and here's why...)? Provide sentence frames and model how to use them. Hang them up or write them on the board for students as a reference or to keep in a journal.
| 3 |
Align the conversation to lesson objectives.
Make sure students know the goal of the lesson. That way they know if their academic conversations are on-topic or on-target. If they are not on-topic, remind them of the target or objective to help get them back on track.
| 4 |
Pose questions that prompt high-quality discussions.
If you want students to increase their academic language, then make sure questions lend themselves to higher-order thinking skills. Questions should make students think, clarify, predict, or explain. A question such as “Tell your partner one fact about the Gettysburg Address” could be changed to “What do you think the reaction of the crowd was after President Lincoln gave the Gettysburg Address and why would he have reacted that way?”
| 5 |
Teach students to ask questions or expand their thinking.
Students often need to be taught how to keep a conversation going. Put question and sentence frames around the room that expand discussions, such as Tell me more about …, Why do you think… I heard you say…, That made me think of …, Do you think that …, or That idea connects to the story by …. These frames allow students to build on each other’s thoughts and create engaging conversations.
| 6 |
Link oral discussion to reading and writing.
Academic speaking and listening are deeply tied to reading and writing. Student discussions that are linked to text bring forth deeper academic discussions.
| 7 |
Set reasonable time limits.
Think about how long it will take students to talk to each other. Don’t let a turn and talk that lasts 1-2 minutes turn into 10 minutes. This creates wasted academic time and often leads to off-task behavior.
| 8 |
Hold students accountable for their talk.
Let students know that you are listening to them. Walk around and listen to what they are saying. Have a clipboard and write down what students say. Them, when the class is brought back together, talk about the great conversations you heard. Provide examples and discuss why these conversations were so powerful. This will motivate students moving forward because they know you are listening and sharing out their examples and ideas.
Consider using all of these eight steps to take your classroom conversations to the next level. I know they certainly helped my students.
If you would like to study these ideas future, consider reading the article "Student Interaction Gone Awry" by Jana Echevarría, and/or watching the Teaching Channel video "Talk Moves in Academic Discussions". Both provide great ideas on how to help students interact.
And, of course, feel free to connect with me directly. I would love to help you increase the academic talk in your classroom.
This post brought to you by Katie Miller, K-12 EL Implementation Associate
During the Back-to-School staff development days, the vast majority of our elementary and secondary math teachers attended a training on the 8 research-based mathematics instructional practices from NCTM. Participants had amazing conversations about how to make math learning more powerful for all of our students. The million dollar question now is… NOW WHAT? How does this impact my classroom?
It can be daunting to make sweeping changes to your instruction all at one time. Don’t let that deter you – just start somewhere. Here are some first steps you might try!
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Get to know your students as math learners
Pose some questions and ask students to discuss, write, or even draw a picture about their answers…
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Establish positive norms for your classroom and revisit them often
Communicate ideas such as those suggested by Jo Boaler in Mathematics Mindsets:
| 3 |
As you begin to plan lessons, try to enhance the use of the 8 instructional practices.
Even small changes can have a great impact. As one math teacher shared in the August training, “I started by just having kids talk more and explain their thinking…and it made all the difference!”
Here are a some things to consider (again, from Jo Boaler, Mathematics Mindsets):
Finally, don't forget to give yourself and your students time to grow into these new practices!
This post brought to you by Carol Lucido, the K-8 District Math Coordinator
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