Currently, I am working on a unit on decimals. I know that I will be teaching sixth-graders how to add, subtract, multiply, and divide multi-digit decimals. Since these are my teaching objectives, I now must develop ways to test my students during and at the end of this unit.
I can give my students an assessment that doesn’t count for much (if any) of their grade, just to see if they are understanding how to apply basic arithmetic operations to decimals. Such an assessment is known as a formative assessment. An example of a formative assessment for multiplication of decimals is a multiple choice quiz that only focuses on placing the decimal in the right place in the answer. If I make the assessment reflect a real-world activity that involves the addition and multiplication of decimals then it would qualify as a performance-based formative assessment. I think it would be fun to assign my sixth-graders the task of pricing three gift items for a baby shower, a birthday party, or Mother’s/Father’s Day. Students would take photos of the items and their prices, total the prices, and then multiply the sum by the decimal .07 to calculate the sales tax. Students would make a poster, powerpoint or document showing the photos, the sum of the prices, the sales tax, and the final total.
Again, this assessment is only formative since it only involves addition and multiplication rather than all four operations. It cannot be used as a unit test. Tests that assess the mastery of math skills and count toward the student’s grade would be classified as a summative assessment. An example of a 20 problem summative test for this unit includes five problems for each operation involving multi-digit decimals. Now that I have these assessments, I am better prepared to develop lessons on decimals.
I am extremely grateful for the TEACH-NOW teacher certification program. In just a few months I have learned more than I dreamed I would. Each week is a new adventure. This week I learned about unpacking a standard and backward mapping. Wow!
I teach at a private school whose curriculum is not aligned with Common Core standards. Before I began the TEACH-NOW program, I became familiar with the Georgia Department of Education State Standards for Middle School Math. Honestly, I read them but they didn’t mean much to me. However, now that TEACH-NOW has explained it to me, unpacking the meaning of a standard is quite easy. A standard states something a student is expected to be able to do.
This standard has the following verbs: add, subtract, multiply, and divide. The object of all this action is the noun phrase “multi-digit decimals.” I now understand this standard. It needs at least four main lessons (one for each verb) designed to impart the four skills that will be assessed. For a fuller example of unpacking standards, see my video.
A standard is an example of backward planning. The standard is the goal that the teacher is pursuing for the students. Exams or projects will be used to demonstrate that the appropriate skills have been developed. The lessons and activities will help the students master the skills delineated by the standard. Standards are simple and powerful. For a fuller example of the Backward Planning process, see my previous blog.
What was I doing before I learned about unpacking standards and backward planning? I was lesson-focused. What lesson does the textbook say to teach next? What kind of problems does the textbook use? Based on the answers to these questions, I would teach the next lesson and make quizzes and tests like the textbook problems.
This approach isn’t bad, but it has a potential downside. The teacher may be unaware of the bigger picture (of sixth-grade math, for example) and may be teaching disjointed, seemingly unrelated lessons. State standards offer the teacher a map of concepts that a teacher can build lessons around. Yet, as far as I can tell, the state of Georgia has established a sixth-grade math curriculum that has planned every aspect of every lesson for every standard. Potentially, a teacher could be once again lesson-focused. However, the lessons always start with a list of state standards to which the wise teacher would do well to pay attention. With the goal (standard) firmly in mind, the teacher is more likely to help the student reach it.
Now that I understand unpacking standards and backward planning, I feel less like a glorified substitute teacher and more like a professional teacher. I have a long way to go, but I’m on my way!
I am still learning the ropes of teaching. I usually start with my textbooks, formulate lessons, and then design assessments. This is a blog on a better practice for creating lessons.
That better way to plan a lesson is to start with the end result in mind, a method known as backward mapping.. “Backward design, also called backward planning or backward mapping, is a process that educators use to design learning experiences and instructional techniques to achieve specific learning goals. Backward design begins with the objectives of a unit or course—what students are expected to learn and be able to do—and then proceeds ‘backward’ to create lessons that achieve those desired goals” (Backward Design Definition, 2013).
The first standard on which I am using this method is a Georgia State Standard for sixth-grade math. It is as follows:
It is easy to find the proficiencies this standard is designed around: adding, subtracting, multiplying, and dividing decimals. I will focus on three of these.
These proficiencies represent the ends that I am beginning with, the destinations I am seeking my students to reach. I will know they have reached these goals if they pass assessments of these skills. Two of my assessments are standard math tests. The first will test the first two proficiencies, Add/Subtract Decimals Test, and the second will test the third proficiency, Multiplying Decimals Test. The third assessment will test students ability to recall the rules associated with adding, subtracting, and multiplying decimals. For example, to add and subtract decimals you must align numbers by their decimals. To multiply decimals does not require decimal alignment, but instead one must count the total number of decimal places used in the problem and give the answer the same amount of decimal places. Students will express these rules and give sample problems through one of the following media: a video, a song/poem, or poster. Here is an example:
Having determined my standard, proficiencies, and assessments, I am ready to create my learning experiences that will move my students toward the goals.
Adding Decimals Lesson Outline
Whiteboard Lecture
Rules for Adding Multi-Digit Decimals
Demonstration of Algorithm for Adding Decimals
Mini-Whiteboard Challenge: students compete to get the right answer to 20 problems on their mini-white boards.
Homework: 10-problem worksheet and making 10 copies of the rules for adding decimals
Subtracting Decimals Lesson Outline
Video Lesson and Demonstration of Algorithm for Subtracting Decimals
Worksheet with 30 problems
Homework: None
Multiplying Decimals Lesson Outline
Whiteboard Lecture
Rules for Multiplying Multi-Digit Decimals
Demonstration of Algorithm for Multiplying Decimals
Large and mini-whiteboard challenge: All students work 12 problems, most on mini-whiteboards while taking turns solving problems on the main whiteboard.
Homework: 10-problem worksheet and making 10 copies of the rules for multiplying decimals
Backward planning makes sense. I look forward to developing these lessons further and implementing them this semester.
Reference
Backward Design Definition. (2013, December 13). Retrieved September 12, 2017, from http://edglossary.org/backward-design/
For me, a new teaching year has begun giving me opportunities to experiment with different methods for encouraging excellent academic behavior in my students. Last year, I simply posted on my class bulletin board a list of names of students who were maintaining an 85 or higher average. Students who are doing better this year than last year have been requesting that I post the list this year so they can finally see their names on it! ( And so I will have to do that.) But I have been trying new things. I divided each class into two to three teams with the highest two or three scoring students as team captains. The teams gain points from their quizzes and tests scores. After each test, the team with the most accumulated points gets ice cream at lunch. I am hoping teammates will encourage and help each other reach higher heights. Teams also can earn or lose points based on group classroom behavior. Team captains have special privileges such as permission to leave the class for bathroom or water fountain breaks, exemption from having to show their work on homework, and early dismissal if they have completed all their assignments. So far quiz and test scores are almost entirely in the A range which is a great improvement.
Another way that I am positively reinforcing behavior is taking photos and videos of students and including them in emails to all the parents. I recently took a photo of seventh-grade students who score 100 on a quiz and sent to all the parent. Beyond that, I try to praise neat work, perseverance, helpfulness, and self-control verbally. Last week, at an after school sports event on campus, I had to tell a student that he, as a middle school student, was not allowed to be at the event without his parent. I instructed him to wait in the late stay classroom until his parent arrived. The student left immediately and reported to the classroom. Last year, he would have responded very angrily to such redirection. So I made sure to tell him later that he responded well and that I was proud of him. I gave him no points or ice cream just well deserved praise.
For academic behavior that is unacceptable, I am traditional in my approach. I do not accept homework that is messy, or incomplete. I reward such work with a zero. The work of students who get C’s or lower on quizzes or tests is examined closely for clues to what is lacking in their understanding. Then, I take the student aside and reteach them. Concerned parents are reassured and given details of corrective steps I have taken. And of course, they are given a low grade which shows them they will have to work hard to get their overall grade to improve.
My method for curbing negative non-academic behavior has not changed. Students who talk while I am lecturing, who respond disrespectfully to me or another student, or engage in “horseplay”, receive a strike for each offense, written by their names on the whiteboard. Three strikes on one occasion lead to a private conversation with that student about his or her behavior. Three strikes on another occasion lead to a conversation with the student’s parent about the behavior. Three strikes on a third occasion lead to a discipline write-up and a meeting with the dean of students who determines the appropriate correction. Students who have had behavior issues last year are written up after the second occasion.
I generally do not use the three strikes method or disciplinary forms for misbehavior in the lunchroom, however. Students who are too loud, overly active, who pop bags, throw food, etc. usually get assigned cafeteria clean-up. If the behavior of an entire table is unacceptable, that table is moved near me for a week or more, so that I can more closely supervise them. These methods are very effective for curbing negative behavior in the classroom.
With each new year, there are opportunities to improve as a teacher. I am pleased so far with the improvements that I am seeing in my students’ behavior. Hopefully, you will see success in your corner of education as you experiment with new methods in the areas needing improvement.
In this blog, I will consider three classroom learning environments to determine how they contribute to high student performance. I will reflect on what I do to create a high-performance learning environment.
In this video, we see that the teacher, Donna Migdol of Oceanside School District, New York, has high academic expectations of her fifth-grade students. One would assume that a fifth-grade S.T.E.M. (Science, Technology, Engineering, and Math) teacher would believe her pupils were very capable. She gave them a group project (PBL), designing a styrofoam roller coaster that was both fun and safe.
Migdol communicates high confidence in her students during the chiming sessions. At the beginning of the week, each team selects a student to be their chimer. The chimer reflects on last week’s design difficulties. Then the rest of the students chime in with suggestions for solving those difficulties. Migdol doesn’t interject her solutions into the dialogue thus showing her confidence in the collaborative abilities of the students. Migdol uses the vocabulary of physics and expects the students to do likewise (e.g. potential energy, kinetic energy). And she gladly provides a very limited number of construction resources and plenty of constraints because scarcity and difficulty make students better problem solvers. In addition to all these, Migdol asks questions that require critical thinking on the students’ part.
Although behavioral expectations aren’t mentioned, clearly the teacher assumes that the students will be kept busy and out of trouble by immersion in this rigorous and fun group project. Collaboration is a norm of this class, and all follow procedures such as the procedure of taking notes on the computer simulation results and determining improvements for future success.
In the second video, we hear primary students reciting math tables and (possible) math rules. In his article, Kan Wei explains factors in Chinese math instruction that lead to high student performances. Basically, students are called on constantly to demonstrate the correct way for solving various math problems. Wei says that students develop and prove their answers to problems while standing in front of the whole class, take grade-level tests every two to three week, answer “why”, “how”, and “what if” questions, and strictly follow the proper mathematical formatting of answers. The pressure of high expectation is a norm of Chinese math students.
Video 3: Whole Brain Teaching Ridgewood High - The Basics
In this third video you can see a noisy but fun learning environment. Whole Brain Teaching incorporates movement, gestures, choral repetition, educational games and many other techniques in classroom instruction. As the name implies, this method’s goal is to stimulate as much of the brain as possible during a lesson, similar to the way video games engage the whole mind. The more the student is immersed in the subject while simultaneously being unaware of this, the more like play and less like work the educational process becomes. Boredom is not the norm for the method. Grabbing and keeping the students’ attention is the norm.
Reflection
As I compare the three learning environments, I see a similarity between the first two approaches. Both operate under the assumption that students are capable of demonstrating high levels of conceptual understanding. The first class does it by applying what they have learned to a project- or problem-based lesson. Students collaborate and are almost entirely dependent on each other to develop solutions. The second class is drilled to the point that each individual can demonstrate a high level of proficiency through various assessments. Teachers teach detailed lessons in both classrooms and expect a lot in return from their pupils.
I also see a similarity between the first and third environments. The third classroom operates under the following assumption: the degree to which students remain engaged in the learning environment is directly related to how interesting and stimulating the presentation is to the whole brain. I would say that the first environment shares this assumption because it incorporated the use of project- or problem-based learning activities. The Roller Coaster project (including the use of the computer simulation) is an incredibly interesting learning experience.
Summary
My approach to creating a high-performance learning environment more closely resembles the Chinese math approach. I work example math problems of increasing complexity on the whiteboard. I have students compete to solve problems at the front of the class. I also test them every two to three weeks. Because I do not give makeup work or extra credit assignments, my students know they have to pass my tests.
I do not drill my students repeatedly like in the Chinese math video, however. I should though! Students seem to quickly forget the rules for adding/subtracting/multiplying/dividing negative integers and other concepts. They need these concepts permanently etched in their brains, and the sooner the better.
Having said that, I would prefer my teaching style to become more like the first video. I want to give more engaging assessments like project- or problem-based lessons. A blend of rigor and fun seems better than what I currently do. Some of my students are turned off to my teaching style, but they would be more engaged if given a choice of projects to complete. Perhaps this would enable those students to meet the high expectations I have of them.
Before I became a math teacher, I wanted to work outside of the United States. To better prepare me for such work, I got a master's degree in intercultural studies. I am now discovering that cultural sensitivity is important in classrooms across America. What are some things a teacher can do to establish a positive classroom environment for students from diverse racial, ethnic, and cultural groups? I've included some ideas about this topic in this blog. According to Critical Practices for Anti-Bias Education (2016, p. 9), how you setup your classroom can help establish a positive environment for students from diverse backgrounds. Are decorations in the class reflective of different cultures? Do posters depict people from various ethnicities? Are desks isolated or grouped for student interaction? Can your students recognize anything in your room from their culture? In my class, I like to praise students with expressions from French, Portuguese, and Spanish. No, I am not fluent in any of these languages, but I do dabble. When introducing algebra, I like to emphasize that this was a great contribution from Arabic culture to the rest of the world. When I take a trip out of the U.S., I try to show my classes photos of my experiences. These are ways I try to promote diversity. Teachers can do things like find out students' favorite meals and holidays from their cultures and work these things into assignments or class activities. There are a lot of simple things that teachers can do as well to create a welcoming environment in their classrooms for all students. Teachers can encourage positive interactions. Greeting students at your classroom door promotes positive interaction. Having little conversations with students about their interests also goes along way, especially for those who may feel left out due their ethnicity or other perceived differences that they may have. Teachers can promote introductions. It is natural to allow students to introduce themselves at the beginning of the school year. A good activity for students is to group them based on some commonality (birth place, number of siblings, birth order, favorite subject, etc). Despite our ethnic, social, and economic differences, we really do have a lot in common. Teachers can also help prevent intimidation. Avoiding classroom confrontations helps the teacher/student relationship. Speaking privately to a student after class about his/her behavior is a good practice. Another good practice is for teachers to proactively send notes home about good behavior in class. "A teacher might discipline herself to make one phone call home per day about some student’s positive behavior" (Marzano, 2007, p. 139).
Preventing intimidation includes anti-bullying strategies. Bullies can single out students who are different from the other students. All students, especially those from diverse racial, ethnic, and cultural groups need their teacher's assistance to create a more sensitive classroom environment. Teachers need to be fully aware of their school's Anti-Bullying Policy and respond immediately to bullying in accordance with that policy. A teacher could proactively start the school year with a talk regarding the pain caused by words and actions intended put down others. Often bullies have been bullied. Allowing students to share their stories of being bullied can sensitize other students to the pain it inflicts. At that time the teacher could explain strategies for dealing with bullies and encourage bullied students not to remain silent.
This school year be aware that the more you establish a positive, welcoming environment in your classroom for students of diverse backgrounds, the better they will learn and the stronger your community will be. Celebrate diversity.
References
Critical Practices for Anti-bias Education. (2016). Retrieved
July 31, 2017, from
http://www.tolerance.org/critical-practices
Marzano,
R. J. (2010). The art and science of teaching: a comprehensive
framework for
effective instruction. Alexandria, Va:
Association for Supervision and Curriculum
Technology is constantly advancing and changing everything around us including education. In a few years, students will truly be learning all the time, everywhere. As I read online articles regarding teaching in the future, they made references to flipped classrooms, cloud-based learning, further gamification of education, augmented reality, virtual reality, and holograms. Imagine being able to take an immersive virtual tour of the Smithsonian Institute and being able to ask your virtual tour guide any question you want and get instant accurate answers? Technology will give us very rich personalized learning experiences anytime and everywhere so that students can learn more, faster, sooner and all OUTSIDE the classroom. Students can then come prepared to school to build and create things as well as to solve problems. Classroom time will be devoted almost entirely to hands-on, collaborative application of learning. Students can experiment, build with 3-D printers, and invent solutions to real problems. The classroom of tomorrow will be a high-tech vocational research experimentation laboratory.
As students learn more at younger ages, teachers of today who teach high school may only be qualified to teach middle school tomorrow. Teachers will have to take tech-heavy continuing education credits in order to keep developing the skills that their students are hoping to master. The saying “Those who can do; those who can’t teach” will cease to be said as teaching becomes doing. The future is exciting but demanding for teachers. Teachers will only survive if they continue to learn.
References
How Technology Will Shape Teaching in the Future. (n.d.). Retrieved June 26, 2017, from
