When thinking about working out at the gym, for the optimal work out it's important to work on cardio for a time, work on flexibility for a time, & work on strengthening our arms, legs and core for a time. One may even engage in interval training where one does very short shots of each of these, with rest in between. Interval training is defined as:
Why interval training is effective? Interval training is a great way to hammer out a quick workout, and it's extremely effective for transforming your physique. By incorporating intense periods of work with short recovery segments, interval training helps you give maximum intensity while still maintaining your exercise form.
By now you are probably wondering what all of this has to do with the teaching of mathematics? The same thing that happens to our bodies with distributed practice (exercise) happens to our brains when we space the learning over time. Each time we are exposed to an idea or concept, we are able to build upon our previous learning. In education, this is referred to as spaced learning, distributed practice or spiraled curriculum. There is an overwhelming body of research that supports the benefits of spiraling the learning versus massed learning.
When I was last a math student in the Rochester Public Schools, and in my early career of being a teacher of math in the Rochester Public Schools, the common and accepted practice for teaching was called “massing”. We would teach a mathematical concept or algorithm for an entire unit, take an assessment, record a score and move on to the next concept. This practice may be difficult for some teachers to let go of because they felt they gained some level of success. Sometimes as teachers, we feel if we teach something really well until the students in our class “know it”, then we have ensured that our students have achieved success. The concern lies in that they may “know it” for the moment, but research tell us they may not retain it for the long run.
One way to think about it in our lives is this. How many passwords does a person need to keep track of these days? Which passwords are easiest to remember? The passwords that have a personal connection and/or are used most frequently. Think of a password that was assigned and/or one that may only use a couple of times a year. How hard is it to retrieve that password? It can be frustrating when one struggles to remember it because it was known at one time, but hasn’t been accessed enough times or recently enough. Spiraling helps learners make connections over time, which creates more robust pathways for recalling information (CEMSE)
The positive effect of spaced learning (spiraling curriculum) has been documented in the literature since 1885. John Hattie listed it as having the 12th most positive effect on learning on a list of over 100 strategies in his book Visible Learning (Sticky learning). We now know that distributed practice in our core instruction is the way that most students will learn, retain and apply learning to new situations. Spiraling leads to better long-term mastery of facts, skills and concepts (Center for Elementary Mathematics and Science Education).
So how does this connect back to the gym workout? If an individual worked on one part of their training for 3 weeks, moved to another part of training for 3 weeks and yet another part of training for another week, their whole physique would transform at different rates-gaining in one area, losing in another. If the desire is to transform the whole physique, as mentioned at the beginning of this blog, it would be important to work on all parts simultaneously to ensure that the whole body is in better shape. That’s what we are trying to achieve with students. It's important to work on all areas of mathematics and continuously build upon prior learning.
This post brought to you by Ann Miller, K-8 Math Specialist
There is no sugar coating it, implementing anything new, including new curriculum, in the first few years can be a challenging and stressful time for teachers. Statistics tell us that if you have been teaching for at least three years you have probably been a part of a new curriculum implementation. So, whether you are implementing a new idea, a new approach or a new curriculum, here are some tips to help you along as you begin this journey.
1. Approach it with a Growth Mindset
If we chose to approach a challenge as an opportunity to improve our instruction and have a greater impact on student learning that, in the end, is what is most likely to happen. A collective belief of an entire staff in their ability to positively affect students is called Collective Teacher Efficacy (CTE). In his most recent publication, John Hattie cites Collect Teacher Efficacy as having the greatest affect size or positive impact on student success. Individual belief is good, a common shared belief is even better. Believe you can achieve, and you will. Believe you will fail, and you will.
"We all do better when we all do better." – Sen. Paul Wellstone
2. Be Up for the Challenge
Researchers from the University of Texas at Austin’s’ Research and Development Center for Teacher Education tells us that “real and meaningful change takes time and always comes with challenges. Build in space for setbacks. Anticipate obstacles and meet them with a cool head. One of the most difficult aspects of adopting new curriculum (or anything new for that matter) and instituting real change is the fear of failure that comes with it. Understand there is room for failure as long as there is a commitment to learning from it.” Give yourself permission to try something and know if it does not work as anticipated, you can reset and try approaching it a different way.
"To create a new standard, you have to be up for that
challenge and really enjoy it." -Shigeru Miyamoto
3. Be kind to yourself
Celebrate the success as you go along. Don’t be afraid to say, “This is going well!” and share that success with colleagues. On the flip side, don’t be too discouraged when something doesn’t go well. It is all part of the process. Remember there is a great deal of work to be done in this process, but do not give up that important “me and/or family time”. This is what energizes us to sustain the effort in the long run.
"If I am not good to myself, how can I expect anyone else to be good to me." - Maya D’Angelo
4. Don’t work too hard on the unimportant things
Sometimes we can get caught up in the “bells and whistles” and spend too much time on the unimportant things like fancy bulletin boards. In her blog, Nancy Flanagan reminds us, “The most important thing you can do before schools starts is think about the curriculum and the kids you are teaching” Keep your focus on best instructional practices. Your time is precious, as you do your unit and daily planning ask yourself, “What is it I want my students to learn today and what is most effective way to get there?” Remember, cute worksheets do not develop conceptual understanding.
"You have to work hard to get your thinking clean to make it simple." -Steve Jobs
5. Don’t be afraid to let some things go
Change is the opportunity for a fresh start. Try new things. Rejuvenate. It is OK to let the old files go. (Even if it is your favorite). Change is difficult for many reasons. Sometimes it is because we believe we are losing something of value. Some teachers may share these sentiments: “I liked the old curriculum, it worked for me” or “I have spent a great deal of time developing resources for (insert initiative here), now I have to start over”. Or it might be that we fear that we will not be able to adapt to something new… again. Stepping out of our comfort zone is how we grow and improve.
"Let it go. Let it go." – Elsa, Disney’s Frozen
6. Give it time
Rome wasn’t built in a day. Research tells us it takes years to effectively implement a new curriculum. It can take just as long to implement other aspects of change. There is definitely a learning curve to this process. Take it one day at a time with your eye on the goal of increasing student learning.
"Patience is a key element of success." - Bill Gates
7. Know that You Are Not Alone
We can no longer teach in isolation. There is so much value in collaboration. There are many people who want to support you and to see you succeed in this endeavor. Your colleagues may be experiencing the same feelings of uncertainty and frustration as they work to make changes and try new things. Be sure to reach out and share successes and concerns. We can all learn from each other.
"The smartest person in the room, is the room." – David Weinberger
8. Take advantage of all the possible professional develop you can
In order to effectively do anything new, you need some degree of learning to occur. Take advantage of all the possible staff development opportunities you can that are offered right within your own district. The more you know about the content area, concepts being taught and best instructional practices the more success you will have in increasing your students’ learning. Look for courses to support your learning on the RPS PDexpress.
In regards to the new elementary math curriculum, you may want to organize a cohort that uses the Curriculum’s Teachers’ Edition as a Book Study for CEU’s. This gives you the opportunity to study and have professional dialogue as you “unwrap” your new curriculum together. The Office of Curriculum and Instruction will be offering as much math support and training as it possibly can. Please contact us with questions, concerns and ideas as to how we can best support your learning.
"The most effective teachers actively seek to improve their own teaching." - John Hattie
9. Have confidence in the leg-work that others have already done
Whether you are trying a new behavior plan, a new method of grading, or a new curriculum, likely you chose it because there was research to show that it was effective and produced great results. Whether you did the research or you read someone else’s research, believe and trust that of all the choices out there, this one rose to the top as being worthy of replication.
In regards to the new elementary math curriculum, trust that “great care” was given in the development and selection of this curriculum. You may or may not have been a part of the articulation or curriculum adoption process. However, if you are a staff member in the Rochester Public School system, you need to know that many of your colleagues spent a great deal of time reviewing data, current best practices in instruction and content as part of a process to select this new curriculum. Every step of this process focused on what is best for our students. Believe that the articulation committee made the best decisions possible in the selection of this curriculum.
"Confidence is contagious. So is lack of confidence." – Vince Lombardi
Finally, the best tip of all – believe in yourself. The biggest difference between successful people and unsuccessful people is not intelligence, opportunity, or resources. It is the belief that they can make their goals happen. We all deal with vulnerability, uncertainty, and failure. Some people trust that if we move forward anyway, then we will figure it out. If you do not believe that it has possible to make new things work, then it is hard to make any progress. It does not matter how good the ideas are, nothing will work for you if you do not believe in it. And more importantly, nothing will work if you don't believe in yourself.
"YOU GOT THIS!!!!" - The office of Curriculum and Instruction
The journey may not be easy. You will not always be successful on your first attempt. You may love some things you are trying and dislike others. You may soar high and then crash but you will soar again; Higher, father and faster than you could ever imagine.
This post brought to you by Julie Ace, Elementary Implementation Associate
Minnesota standards require us to teach about the indigenous people to our state. From that point, it is our responsibility to ensure that what we are teaching is accurate. Minnesota state standards require that our students encounter different teachings about Dakota and Ojibwe people throughout their K-12 experience. Learning about Indigenous People and the history of our area before America’s colonization is fundamental to understanding the relationships between people and place. We cannot truly understand the dynamics of our area if we do not include a long and multi-perspective history. Teaching accurately about Indigenous People benefits not just our Native students, but also all students.
In my short time working for the school district, I have noticed there is never enough time in a day to teach all the things that need to be taught and there is an ever-present desire to find new resources. I have also noted the increasing number of blogs and information hubs, such as Pinterest, that have easy ready to use ideas.
Unfortunately, by using these resources, what ends up happening is an overload of information that often times isn’t well researched or vetted through any credible sources. Inadvertently, this can lead to activities that perpetuate stereotypes, keep Native Americans in the past, and demote native culture to cute crafts.
Something we want to work to avoid is only exposing students to historical views of Native Americans. Today there are 572 federally recognized tribes, 11 of which are located in our state. We want students to understand the sacrifice these tribes have made at the benefit of our country, as well as learn about tribes that have called Minnesota home for 100s and thousands of years to help build well-rounded learners.
An example of how we can begin to do that is to help students make connections and understand the differences between the various Native tribes. Many people know southwest Indians use adobe dwellings to stay cool, but let’s not stop there. We should build on understanding that each tribe has its own traditions, clothing, types of dwellings, etc. dependent on the region they inhabited. It is important to learn about tribes from around the country, but Minnesota state standards require us to place an emphasis on learning about our tribes here in Minnesota.
As educators, we can be better equipped to teach our students about Indigenous people by taking advantage of events and professional learning opportunities provided by various education associations and societies. Here are some of the great upcoming opportunities, most of which happen on an annual or even more frequent basis.
As we approach summer and think about professional development in our upcoming year, I encourage everyone to consider one of these amazing opportunities. Let us all strive to teach Native American content in the humanizing manner with which we teach all other subjects. As always, I am here to help in whatever way I can.
Don’t you sometimes wish that students could just see inside your head and understand exactly what you are thinking? That may be every teacher’s dream. If someone would invent a tool that allowed students to see inside our heads, they would become a millionaire! Unfortunately, this invention hasn’t been created yet, so we need to find a way for students to “see” what we are thinking through strategic teaching methods. Marcia Dove and Andrea Honigsfeld call this idea “making thinking visible” in their newest book Co-Teaching for English Learners: A Guide to Collaborative Planning, Instruction, Assessment, and Reflection. In their book, they give several strategies for making thinking visible for students so that they can begin to magically see inside our teacher heads to increase reading and writing skills.
Think Alouds are one way that makes thinking visible for students. It seems so simple. Just talk about what you are already thinking. Yet it is extremely powerful for students. Teachers can model their thinking by making text-to-text, text-to-self, and text-to-world connections. Check out this video to see a Think Aloud in action:
A Write Aloud provides a scaffold for students to guide them through the process of writing. Teachers can model a piece of writing so students can see the steps and procedures in the writing process. Throughout the process, the teacher explains verbally what he or she is thinking. The teacher can talk about why they selected a particular vocabulary word, phrase, transition word, or structure. Write alouds can be done with one teacher, or in a co-teaching partnership. In a co-teaching partnership, one teacher can do a think aloud while the other teacher takes notes or writes out what the other teacher is thinking in a structured format (or with a graphic organizer). Another idea is to have one teacher think aloud and write out what they are thinking, and then the other teacher performs a separate think aloud to show the differences in their writing and thinking processes. If you have a paraprofessional, it would be helpful to give them a frame for the think aloud so they can assist and/or provide other think aloud strategies.
A Scaffolded Comprehend Aloud is another version of a Think Aloud. While think alouds support different reading and writing strategies, Dove and Henigsfeld believe that scaffolded comprehend alouds “make thinking visible about processing and analyzing the language of complex readings at the word, sentence, and text level” (pg. 85). Dove and Henigsfeld provide the table below with different sentence starters (pg. 85-86). Each content area, and grade level, may have to adapt these, but this list can provide a start to using think alouds and/or scaffolded comprehend alouds.
Think Alouds, Write Alouds, and Scaffolded Comprehend Alouds are three great strategies to make our thinking visible to students. They provide a way for students to see inside our heads, model good reading and writing strategies, and allow students to use critical-thinking skills.
If you would be interested in trying any of these out with students, reach out to an instructional coach, or I would be happy to come out and model them beside you.
This post brought to you by Katie Miller, K-12 EL Implementation Associate
Dove, M.G., & Honigsfeld, A. (2018). Co-teaching for English learners: a guide to collaborative planning, instruction, assessment, and reflection. Thousand Oaks, CA: Corwin, A SAGE Company.
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
During this past year, many of you at your sites and within your PLC’s have worked very hard to identify the most important or prioritized learnings for your specific grade level. Prioritized Learning is the learning that has been identified as most essential to a particular grade level or course and for which significant time and resources are devoted to ensure mastery. To identify priority learnings we used the five key areas, asking ourselves; does this learning have:
After work was completed within site PLC’s, representatives from each RPS Elementary site in the content areas of English Language Arts and Math came together as a collaborative effort to construct the prioritized learning for each grade level and content area. (insert working Prioritized Learnings) Once the prioritized learnings were identified, teachers again went back to sites and PLC teams to begin the task of building proficiency scales for each priority learning. The proficiency scale will indicate specific information about what student achievement looks like, ranging from no knowledge to in-depth knowledge.
Within the Rochester Public School District it was determined that a three point proficiency scale indicating proficient, partially proficient and not proficient would best rate and communicate information regarding student performance.
In the next couple months, elementary site representatives will come together again to collaborate in the building of District Proficiency Scales for each prioritized learning in the content areas of English Language Arts and Math at each grade level.
Each grade and content area collaborative team will work to be sure each proficiency scale includes the fundamentals, specific word choice, and clarity allowing PLC teams to have the ability to asses, or build multiple common formative assessments based on the content of the proficiency scale.
A great deal of RPS effort, time and resources have been dedicated to this endeavor, WHY??
To answer this question, we need to look at both the reality and the research. The reality is stated best by Larry Ainsworth, “So many standards, so little time……” Statistics provided by Dr. Doug Reeves, founder of Creative Leadership Solutions, tell us that on average a student spends 13,000 hours in school from Kindergarten through grade 12, however if all standards were taught with the same length and depth it would take over 15,000 hours, time we just do not have. Because of the overwhelming number of standards, many of us may feel we have been taking the approach Ainsworth calls “Spray and pray” to try to cover all we feel is expected. When this happens,
Research tells us that the most effective schools focus on: simplicity, clarity and priority. (Schmoker, 2011). This research is also evident in the success of 90/90/90 schools (90% free and reduced price lunch, 90% minority, 90% achievement). These schools have focused on academic achievement by clearly identifying priorities.
For more answers to Prioritized Learning Frequently Asked Questions and the research that supports these efforts, please watch the RPS Prioritized Learning video below and read the Frequently Asked Questions responses.
This initiative is intended to be a collaborative effort to improve teaching and learning within our district, with our experts, classroom teachers, having the strongest and most important voice in the room. Another key thing to keep in mind is that prioritized learning, proficiency scales and common formative assessments are living documents with future opportunities for continuous improvement. As we continue to grow and improve, so will our work in this area.
This post brought to you by Julie Ace, Elementary Implementation Associate
Best Practices/ Tom W. Many Ed.D. and Ted Horrell Ed.D www.tespa.org
Allowing for student choice is about creating learners that are inspired, embrace creativity, and take ownership of their learning. Allowing for student choice is acknowledging and embracing the idea that in order to grow passionate and invested learners, we as teachers need to give our students the opportunity to have choice and voice throughout their day. Here are some meaningful and easy ways to incorporate student choice in your classroom that ensures you are meeting student needs, while allowing them the flexibility to do it in their own way.
Think about how you can incorporate time into your day when students are able to have unstructured innovation time. How often in your classroom do students get to work on projects that they are passionate about? Not only is this a great way to learn about your students but it allows them to create something that they are passionate about and grow their love of learning on a topic that interests them. After all, don’t we want to grow students that are curious and have a passion for lifelong learning? Don’t forget to let students study, research and build on topics of their choosing!
This is one of the more popular and perhaps easiest ways teachers can incorporate more choice. Choice boards allows the teacher to ensure that the tasks students are choosing meet the standard for the day but allows a student the flexibility to show their learning in different ways. Choice boards can be used in many different ways. If you typically provide students with how you expect them to complete a specific learning target, consider providing them with a choice board. You will immediately see their interest and engagement level rise because they now have the opportunity to complete a task in a way that is interesting to them. You both win!
There are many great tools online that allow for students flexibility and can fit in with everyday lessons.
When asking students in the classroom to collaborate on a project or reflection sheet, consider allowing them to collaborate over Google or on a Prezi. You will be surprised by how quickly your students will pick up on these technology tools even if you don’t feel like an “expert” using the tool yet. Don’t let your lack of comfort with technology hold your students back. If they can demonstrate the knowledge on how to use the tool, given them the flexibility to do so!
Do you have students in your classroom who could teach a topic to another student? Instead of always using a traditional peer tutor, ask your students if they would be willing to create a short video tutorial and pair your older and younger students together. If you aren’t partnered with another classroom, find a topic that your students are an “expert” at and allow them to create a video to help other students in the classroom when they have questions. This allows students to review a certain topic on an iPad or computer at their own pace.
Create Opportunities for Student to Give You Feedback:
Student choice leads to more student voice! Don’t be scared to ask your students for feedback after a lesson or unit. Taking the time to allow them to reflect on how the lesson went not only allows them time to reflect on their own learning, but allows you to find out how you could change in the future to be more effective. Creating a “Teacher Report Card” like the one below lets student know that you are open to feedback as well and wanting to ensure that you are meeting their needs.
Remember that when you provide your students with choices, they feel heard and their learning in turn feels more valuable. Students who have choice and voice in their classroom are engaged and take more ownership in their learning. If as you reflect on your own teaching style you find that you don’t allow for student autonomy in your classroom, try incorporating some of these ideas into your room and you will see a difference in the level of engagement and excitement in your students.
This post brought to you by Kate Palmquist, APOSA overseeing Elementary Curriculum and Instructional Coaching
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
Consider the following statements (which my teachers taught me and I have taught to my students). For each one, decide whether or not the statement is TRUE or FALSE. I encourage you to write down your answers.
If you suspect that each and every one of these statements is false (or at least not ENTIRELY true), you are correct. In their article, “13 Rules That Expire” (Teaching Children Mathematics, NCTM, August, 2014), the authors challenge us to rethink common “tips” and “tricks” that we often use with students to learn a procedure. Our intentions are good. Perhaps they are the same tricks we were taught. Unfortunately, these tricks and tips often “expire” and aren’t always true. The result is that we leave students with partial understanding of the mathematics and misconceptions that we “hope” someone will correct later. We also leave students with the idea that math is about a “mysterious series of tricks and tips to memorize rather than big concepts that relate to one another.”
The authors go on to give examples of why the statements are simply not always true.
Here are a few of their examples.
1) When you multiply a number by ten, just add a zero to the end of the number.
Does this rule always work? Consider: 0.25 x 10 = 0.250 Not so much.
2) Use keywords to solve word problems.
This approach often leads students to pull out the numbers and do the operation that the key word suggests, rather than focus on what is happening in the story. When students see “altogether,” they may think they always add. But what about this story: There were 9 dogs in the yard. Some more dogs came and altogether there were 18 dogs. How many dogs came? (You’d probably subtract to get the answer.) Or perhaps this one: I had 3 boxes of crayons with 8 crayons in each box. How many crayons do I have altogether? (Most people would multiply.)
3) You cannot take a bigger number from a smaller number.
Image the temperature is 10° and it drops 15 degrees. In this case, 10-15 can (and does) happen and the result is -5°. Even from young ages, we can start looking at a number line with negative numbers. Students often think that subtraction only means “take away,” but they also need to understand that subtraction can be the distance between two numbers on a number line.
14) The equal sign means Find the answer or Write the answer.
Students often believe that the equal sign means “the answer comes next” instead of understanding it as “is the same as” which is a relation between the two sides. When they think that, they will struggle with equations such as:
4 = 4 (They will say this is false because there isn’t an operation.)
8 = 3 + 5 (They will say it is false because it’s backwards.)
Every time we use statements that are not entirely true or tricks that are not grounded in conceptual understanding, we hinder student learning in the long run. This article is great food-for-thought for all teachers of mathematics!
The whole article (with discussion of all 13 statements) can be found here.
This post brought to you by Carol Lucido, the K-8 District Math Coordinator
13 Rules That Expire by Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty (Teaching Children Mathematics, NCTM, August, 2014)
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.
Enjoy our Blog!
Members of the Elementary C&I team post useful tools, tips, and tricks on a weekly basis to help you help students.