Core Proposition #3
Teachers are responsible for managing and monitoring student learning.
Element A: Teachers call on multiple methods to meet their goals.
Artifacts: Technology Innovations for Education, PhET Interactive Simulations Website.
Event: Using technology to engage students when writing and graphing linear equations.
Description: During the Linear Equations Unit in Algebra I, students learn about slope, slope-intercept form and writing equations in slope-intercept form. This happens over several days, but on one particular day I had the students use an interactive website called PhET Interactive Simulations to enhance their understanding. By this time, students had seen slope on previous days, and now had learned graphing lines in slope-intercept form this class period. This game had students look at graphs and alter the equation (either the slope or y – intercept) to fit the graph. It also had students look at an equation and alter a graph to fit the equation. The students were given about 15 minutes to play the games that kept track of their score, kept time if they chose to be timed, and gave them instant feedback. If students missed a question it gave them the opportunity to correct their mistake and if they missed it a second time, it showed them the correct answer and explained why. Students were quick to get to the website to try this game. They were all playing. I had a lot of students announcing their score and asking questions to their neighbors and/or myself. There were also questions that showed the equation in point-slope form, which we had not covered in class yet. Students were asking questions about this new form. I took the time to speak one-on-one with students about this new form and also have a quick whole-class discussion.
Analysis: This past year was my first time trying out this interactive website. I am always up for trying new things, especially technology, to engage my students because I know how beneficial it is. High quality mathematics education includes the Principles for School Mathematics such as the Technology Principle. The Technology Principle states that “technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning” (NCTM, 2000, p. 24). In fact, I use an abundance of technology in my classroom including, but not limited to, videos, You-Tube, interactive websites, textbook resources, Smartboard Software, and graphing calculator investigations. My Technology Innovations for Education paper lists and describes some of the resources I use. Even since writing this paper, I have incorporated more technology in my classroom including the PhET Interactive Simulations. The PhET Interactive Simulation is just one example of how technology can be used to generate exploratory mathematical environments. Learning happens when students ask the “What if…” questions, and students’ success in mathematics is related to their ability to ask good questions and to raise interesting conjectures based on them (Cole, 1995).
This activity was successful for several reasons. First, this activity was non-threatening for the students. They were able to play, make mistakes, and learn from their mistakes. They had the opportunity to choose a level, ranging from 1 to 6, and then they had time for multiple attempts. Second, students asked the desirable “What if…” questions previously described. When students saw the equations written in point-slope form, they were eager to learn what numbers represented what characteristics of the line. “What if the equation looks like this?” They were learning material from the technology before it was even taught in class. It acted as a head start for the kids. Third, the activity acted as a great visual to make the necessary connections for the students. Cole (1995) states that technology enriches the range and quality of investigations by providing a means of viewing mathematical ideas from multiple perspectives. This activity gave another perspective. With a click of a button students were able to see how the characteristics of the equation changed the appearance of the line. Fourth, the students were given immediate feedback. If they were correct, they were given a check mark and smiley face. If they were incorrect, they had the opportunity to fix their mistake. If they were incorrect a second time, the program showed them the correct answer with a little explanation. The students were able to know why they missed the question and use the information on the next question or on a future game. The technology acted as another teacher because it assisted with feedback. How convenient!
Reflection: I was happy with my first attempt at using this interactivity with my Algebra I students. All of the students were engaged and asking questions. I really liked how the students could choose their levels, the immediate feedback, and how my students were asking questions. My favorite result from this activity was their curiosity about point-slope form (a future concept). What I plan on doing in the future is to allow my students the 15 minutes at the end of the class period to practice slope and slope-intercept form as I did this first time. However, I want to also have the students play again at the beginning of the class period were I teach point-slope form. This would review slope and slope-intercept form, but also be a great introduction for point-slope form. I could take examples from the game and teach from them. The students would be able to see how the form works and be able to be involved in the learning process.
Description: During the Linear Equations Unit in Algebra I, students learn about slope, slope-intercept form and writing equations in slope-intercept form. This happens over several days, but on one particular day I had the students use an interactive website called PhET Interactive Simulations to enhance their understanding. By this time, students had seen slope on previous days, and now had learned graphing lines in slope-intercept form this class period. This game had students look at graphs and alter the equation (either the slope or y – intercept) to fit the graph. It also had students look at an equation and alter a graph to fit the equation. The students were given about 15 minutes to play the games that kept track of their score, kept time if they chose to be timed, and gave them instant feedback. If students missed a question it gave them the opportunity to correct their mistake and if they missed it a second time, it showed them the correct answer and explained why. Students were quick to get to the website to try this game. They were all playing. I had a lot of students announcing their score and asking questions to their neighbors and/or myself. There were also questions that showed the equation in point-slope form, which we had not covered in class yet. Students were asking questions about this new form. I took the time to speak one-on-one with students about this new form and also have a quick whole-class discussion.
Analysis: This past year was my first time trying out this interactive website. I am always up for trying new things, especially technology, to engage my students because I know how beneficial it is. High quality mathematics education includes the Principles for School Mathematics such as the Technology Principle. The Technology Principle states that “technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning” (NCTM, 2000, p. 24). In fact, I use an abundance of technology in my classroom including, but not limited to, videos, You-Tube, interactive websites, textbook resources, Smartboard Software, and graphing calculator investigations. My Technology Innovations for Education paper lists and describes some of the resources I use. Even since writing this paper, I have incorporated more technology in my classroom including the PhET Interactive Simulations. The PhET Interactive Simulation is just one example of how technology can be used to generate exploratory mathematical environments. Learning happens when students ask the “What if…” questions, and students’ success in mathematics is related to their ability to ask good questions and to raise interesting conjectures based on them (Cole, 1995).
This activity was successful for several reasons. First, this activity was non-threatening for the students. They were able to play, make mistakes, and learn from their mistakes. They had the opportunity to choose a level, ranging from 1 to 6, and then they had time for multiple attempts. Second, students asked the desirable “What if…” questions previously described. When students saw the equations written in point-slope form, they were eager to learn what numbers represented what characteristics of the line. “What if the equation looks like this?” They were learning material from the technology before it was even taught in class. It acted as a head start for the kids. Third, the activity acted as a great visual to make the necessary connections for the students. Cole (1995) states that technology enriches the range and quality of investigations by providing a means of viewing mathematical ideas from multiple perspectives. This activity gave another perspective. With a click of a button students were able to see how the characteristics of the equation changed the appearance of the line. Fourth, the students were given immediate feedback. If they were correct, they were given a check mark and smiley face. If they were incorrect, they had the opportunity to fix their mistake. If they were incorrect a second time, the program showed them the correct answer with a little explanation. The students were able to know why they missed the question and use the information on the next question or on a future game. The technology acted as another teacher because it assisted with feedback. How convenient!
Reflection: I was happy with my first attempt at using this interactivity with my Algebra I students. All of the students were engaged and asking questions. I really liked how the students could choose their levels, the immediate feedback, and how my students were asking questions. My favorite result from this activity was their curiosity about point-slope form (a future concept). What I plan on doing in the future is to allow my students the 15 minutes at the end of the class period to practice slope and slope-intercept form as I did this first time. However, I want to also have the students play again at the beginning of the class period were I teach point-slope form. This would review slope and slope-intercept form, but also be a great introduction for point-slope form. I could take examples from the game and teach from them. The students would be able to see how the form works and be able to be involved in the learning process.
Element B: Teachers orchestrate learning in group settings.
Artifact: PIES PowerPoint
Event: Students practice solving equations using the Kagan activity Fan-N-Pick
Description: My Algebra I students have spent about a week on solving equations thus far. At first, students learned when solving an equation they must do the same thing to one side of the equation as the other to keep it balanced. Students also learned inverse operations and how to solve one-step, two-step, and multi-step equations. Multi-step equations include distributing and combining like terms. On this particular day, students are adding to their solving equations repertoire how to solve variables on both sides equations. I start the lesson by showing examples and having the students work them out with me. Then I prepare the class for a Kagan cooperative learning activity called Fan-N-Pick to practice solving all the types of equations we have learned so far, including the new “variables on both sides” equations. I first model the activity with 3 volunteer students and explain my expectations. When the students are clear on the activity, I group my students in to groups of 4 based on the people in their vicinity. Students then move to their groups, picking up the appropriate materials and Fan-N-Pick cards on the way.
During the activity, all students have a dry-erase board, dry-erase marker, and eraser. At the beginning of each “round” one student fans the pre-made equation cards made by me. The student to the left of the “fanner” picks a card without looking. The “picker” is the “Expert” of this round. The “picker” writes the equation on his or her white-board and the other three students solve that equation on their own white-board. As each student solves the equation they turn their white-boards to the “picker” and has him or her check their answers. If the student is incorrect, the picker/expert helps the student by looking though the work and finding any mistakes. Once all three students have been checked off and/or helped the process starts over again. This time the “picker” is now the “fanner” and the jobs of the students rotate for the duration of the activity.
Analysis: This particular time using Fan-N-Pick was successful. In fact, every time I incorporate this Kagan activity in to my lesson I find it to be successful. Kagan cooperative learning activities are unique because they encompass four principles referred to as PIES (Positive Interdependence, Individual Accountability, Equal Participation, and Simultaneous Interaction. It is the implementation of PIES that distinguishes cooperative learning from group work (Kagan & Kagan, 2009). My PIES PowerPoint is a reference for myself and any teacher planning to orchestrate learning in group settings. It gives the positive outcomes of PIES and reminds us why to use PIES, what it stands for, and what questions you should ask yourself about an activity when having students work in groups to maximize learning. Once we understand PIES and how to implement the principles, we are prepared to unleash the full potential of cooperative learning.
This Kagan structure was successful because it satisfied all of the principles used in PIES. Positive Interdependence (P) means that outcomes go up and down together and that no one can do the task alone. Therefore, students work as a team and work toward the same goal. Students helped, encouraged, and tutored each other because they knew that the task could not be completed without everyone’s involvement. Kagan and Kagan (2009) state that Individual Accountability (I) has three characteristics: the performance is done without help, someone witnesses the performance, and the performance is required. During this Fan-N-Pick each student had to preform because they were given a white board to show his or her work. It would be obvious and awkward if a student chose not to participate. The other three students in the group witnessed each student work independently and helped only when needed. Equal Participation (E) is obtained because the students took turns during the Fan-N-Pick and rotated duties. Simultaneous Interaction (S) means that a high percent of students are actively engaged at once. During this Fan-N-Pick every student was engaged during the problems. Three students were solving while one student was monitoring, helping, and checking.
Reflection: I will continue to use Kagan cooperative learning structures like Fan-N-Pick because of the high percentage of “on task time” for each student and the amount of help that each student receives. I will also continue to ask myself if my activities incorporate the principles of PIES because of the positive outcomes. Not only are students engaged, get help, and learn, but they enjoy the structures as well. I often hear comments “Class is already over?” and “Can we just finish the last one or two?!” It makes me laugh to myself how the students are begging to do more math. What can be better than that!?
In addition, I will also continue to model and explain each activity beforehand to make sure it is understood and runs smoothly. Even when a structure is effective, it can play out terribly if it is not explained and/or set up properly. As for grouping students, I will continue to group students either using Popsicle sticks or by proximity. With four students, even when it is random with Popsicle sticks, there is always a stronger student with a lower student. If I group students based off of who they sit by, there will be a variety of levels because I make my seating charts based off of student levels.
Description: My Algebra I students have spent about a week on solving equations thus far. At first, students learned when solving an equation they must do the same thing to one side of the equation as the other to keep it balanced. Students also learned inverse operations and how to solve one-step, two-step, and multi-step equations. Multi-step equations include distributing and combining like terms. On this particular day, students are adding to their solving equations repertoire how to solve variables on both sides equations. I start the lesson by showing examples and having the students work them out with me. Then I prepare the class for a Kagan cooperative learning activity called Fan-N-Pick to practice solving all the types of equations we have learned so far, including the new “variables on both sides” equations. I first model the activity with 3 volunteer students and explain my expectations. When the students are clear on the activity, I group my students in to groups of 4 based on the people in their vicinity. Students then move to their groups, picking up the appropriate materials and Fan-N-Pick cards on the way.
During the activity, all students have a dry-erase board, dry-erase marker, and eraser. At the beginning of each “round” one student fans the pre-made equation cards made by me. The student to the left of the “fanner” picks a card without looking. The “picker” is the “Expert” of this round. The “picker” writes the equation on his or her white-board and the other three students solve that equation on their own white-board. As each student solves the equation they turn their white-boards to the “picker” and has him or her check their answers. If the student is incorrect, the picker/expert helps the student by looking though the work and finding any mistakes. Once all three students have been checked off and/or helped the process starts over again. This time the “picker” is now the “fanner” and the jobs of the students rotate for the duration of the activity.
Analysis: This particular time using Fan-N-Pick was successful. In fact, every time I incorporate this Kagan activity in to my lesson I find it to be successful. Kagan cooperative learning activities are unique because they encompass four principles referred to as PIES (Positive Interdependence, Individual Accountability, Equal Participation, and Simultaneous Interaction. It is the implementation of PIES that distinguishes cooperative learning from group work (Kagan & Kagan, 2009). My PIES PowerPoint is a reference for myself and any teacher planning to orchestrate learning in group settings. It gives the positive outcomes of PIES and reminds us why to use PIES, what it stands for, and what questions you should ask yourself about an activity when having students work in groups to maximize learning. Once we understand PIES and how to implement the principles, we are prepared to unleash the full potential of cooperative learning.
This Kagan structure was successful because it satisfied all of the principles used in PIES. Positive Interdependence (P) means that outcomes go up and down together and that no one can do the task alone. Therefore, students work as a team and work toward the same goal. Students helped, encouraged, and tutored each other because they knew that the task could not be completed without everyone’s involvement. Kagan and Kagan (2009) state that Individual Accountability (I) has three characteristics: the performance is done without help, someone witnesses the performance, and the performance is required. During this Fan-N-Pick each student had to preform because they were given a white board to show his or her work. It would be obvious and awkward if a student chose not to participate. The other three students in the group witnessed each student work independently and helped only when needed. Equal Participation (E) is obtained because the students took turns during the Fan-N-Pick and rotated duties. Simultaneous Interaction (S) means that a high percent of students are actively engaged at once. During this Fan-N-Pick every student was engaged during the problems. Three students were solving while one student was monitoring, helping, and checking.
Reflection: I will continue to use Kagan cooperative learning structures like Fan-N-Pick because of the high percentage of “on task time” for each student and the amount of help that each student receives. I will also continue to ask myself if my activities incorporate the principles of PIES because of the positive outcomes. Not only are students engaged, get help, and learn, but they enjoy the structures as well. I often hear comments “Class is already over?” and “Can we just finish the last one or two?!” It makes me laugh to myself how the students are begging to do more math. What can be better than that!?
In addition, I will also continue to model and explain each activity beforehand to make sure it is understood and runs smoothly. Even when a structure is effective, it can play out terribly if it is not explained and/or set up properly. As for grouping students, I will continue to group students either using Popsicle sticks or by proximity. With four students, even when it is random with Popsicle sticks, there is always a stronger student with a lower student. If I group students based off of who they sit by, there will be a variety of levels because I make my seating charts based off of student levels.
Element C: Teachers place a premium on student engagement.
Artifact: Thematic Unit
Event: A Kagan structure during one lesson in a thematic unit for an Algebra I class.
Description: The objective for one lesson during a polynomial and factoring unit is for students to factor trinomials in the form x2 + bx + c. I begin the day by motivating students and arousing interest with a guessing game. I ask the students to find two numbers that multiply to equal 15 and add to equal 8. I then ask the students to find two numbers that multiply to equal negative 30 and add to give negative 1. This gets them thinking similarly to how they will need to think when factoring trinomials. After I introduce them to vocabulary and show them some examples we move on to a Kagan structure to practice this factor method called Inside – Outside Circle. Materials used during Inside-Outside Circle include a note card with a trinomial on the front and the factored answer on the back, a dry erase board, dry erase marker, and an eraser. I assign students to be a part of the inside circle that faces out and then others to the outside circle facing in. The inside circle quizzes the outside circle. The outside circle writes the factored answer on the white boards and shows the inside circle. The inside circle either praises or helps, depending on the answer shown. The inside circle does not, however, just tell the outside circle the answer. Once students are finished, they stand back to back to show me they are finished. Once the whole class is finished I have one of the circles rotate a certain number of spots to repeat the process. The inside and outside circle will alternate who quizzes and who answers. This process repeats until I feel the students have had sufficient practice.
Analysis: Kagan structures are extremely effective and simple to use in any lesson. In fact, the Kagan structure described above was just one structure used in a thematic unit over polynomials and factoring. Each lesson in this thematic unit includes a Kagan structure, and all of the structures help produce student gains such as boosting academic achievement, closing achievement gaps, improving student relations, promoting thinking skills, and creating a more kind and caring school community. Not to mention, students are always engaged during each Kagan strategy. Kagan and Kagan (2009) state that there is far more engagement and retention of meaningful experiences; the content is processed in episodic memory, not just semantic memory. From the Inside – Outside Circle activity, particularly, students are up out of their seat, easily monitored, have a specific role, and are either expected to answer or help at all times. The use of manipulatives such as the index cards and response boards and the interaction between students also keep the students focused and engaged. Furthermore, students are taking turns (Equal Participation) and half the classroom is talking at once instead of one at a time (Simultaneous Interaction). Because the PIES principles Equal Participation and Simultaneous Interaction are built in to the structure, the structure optimizes classroom engagement (Kagan & Kagan, 2009).
Reflection: Inside-Outside Circle is a Kagan structure that I don’t do as frequently as others but I am happy with how this structure allowed my students to practice factoring trinomials in the form x2+ bx + c. Ever since I started teaching one of my goals while planning every lesson has been to make every student accountable and to give them the opportunity to participate and see how they can do it even when they originally thought they couldn’t. I love when students find that confidence. Kagan structures are so easy to implement and the planning has already been done for me! I just have to know the structure and put it in to place. Student engagement, and all of the other positive benefits, then just come naturally.
Description: The objective for one lesson during a polynomial and factoring unit is for students to factor trinomials in the form x2 + bx + c. I begin the day by motivating students and arousing interest with a guessing game. I ask the students to find two numbers that multiply to equal 15 and add to equal 8. I then ask the students to find two numbers that multiply to equal negative 30 and add to give negative 1. This gets them thinking similarly to how they will need to think when factoring trinomials. After I introduce them to vocabulary and show them some examples we move on to a Kagan structure to practice this factor method called Inside – Outside Circle. Materials used during Inside-Outside Circle include a note card with a trinomial on the front and the factored answer on the back, a dry erase board, dry erase marker, and an eraser. I assign students to be a part of the inside circle that faces out and then others to the outside circle facing in. The inside circle quizzes the outside circle. The outside circle writes the factored answer on the white boards and shows the inside circle. The inside circle either praises or helps, depending on the answer shown. The inside circle does not, however, just tell the outside circle the answer. Once students are finished, they stand back to back to show me they are finished. Once the whole class is finished I have one of the circles rotate a certain number of spots to repeat the process. The inside and outside circle will alternate who quizzes and who answers. This process repeats until I feel the students have had sufficient practice.
Analysis: Kagan structures are extremely effective and simple to use in any lesson. In fact, the Kagan structure described above was just one structure used in a thematic unit over polynomials and factoring. Each lesson in this thematic unit includes a Kagan structure, and all of the structures help produce student gains such as boosting academic achievement, closing achievement gaps, improving student relations, promoting thinking skills, and creating a more kind and caring school community. Not to mention, students are always engaged during each Kagan strategy. Kagan and Kagan (2009) state that there is far more engagement and retention of meaningful experiences; the content is processed in episodic memory, not just semantic memory. From the Inside – Outside Circle activity, particularly, students are up out of their seat, easily monitored, have a specific role, and are either expected to answer or help at all times. The use of manipulatives such as the index cards and response boards and the interaction between students also keep the students focused and engaged. Furthermore, students are taking turns (Equal Participation) and half the classroom is talking at once instead of one at a time (Simultaneous Interaction). Because the PIES principles Equal Participation and Simultaneous Interaction are built in to the structure, the structure optimizes classroom engagement (Kagan & Kagan, 2009).
Reflection: Inside-Outside Circle is a Kagan structure that I don’t do as frequently as others but I am happy with how this structure allowed my students to practice factoring trinomials in the form x2+ bx + c. Ever since I started teaching one of my goals while planning every lesson has been to make every student accountable and to give them the opportunity to participate and see how they can do it even when they originally thought they couldn’t. I love when students find that confidence. Kagan structures are so easy to implement and the planning has already been done for me! I just have to know the structure and put it in to place. Student engagement, and all of the other positive benefits, then just come naturally.
Element D: Teachers regularly assess student progress.
Artifact: PowerSchool link located on school's home page
Event: The use of formative assessments and feedback in my classroom.
Description: In my classroom I regularly assess student progress. I use an abundance of formative assessments such as teacher observation, student work, self-reporting, technology, and peer assessment. Teacher observation includes noticing the number of students volunteering to answer a question. For instance, if I ask students to tell me the first step in solving a problem and no students raise their hands, then I need to revisit step #1. If I have a lot of hands in the air, then I know that the information was received well. I also spend a lot of time observing how students are doing during cooperative learning activities. An example of student work being used as formative assessment is response boards. Students are able to show their understanding of a concept quickly and simultaneously while working independently. A way that students self-report in my classroom is using their hands. I can have them give me a thumbs up, thumbs down, or somewhere in the middle to check for confidence and understanding. Also, I can have them show me a number somewhere from 1 to 10 as a quick assessment. Technology assessments include clickers, a program called Kahoot, and even texting in answers. Peer assessment is used during cooperative learning activities. Every now and then I give my students a partner quiz.
Summative assessments are used in my classroom as well. Chapter tests are given at the end of every chapter and a final exam is given at the end of each semester. Summative assessments take place a lot less than formative assessments in my class. It is not that summative assessments are unimportant, but if a course is irremediably bad or students are not understanding the material, this fact should become evident during the formative evaluations mentioned above. Because of formative assessments, a course can be abandoned on the basis of such data, and ultimately, courses can almost always be improved (Posner & Rudnitsky, 2005).
It is important to note that assessments aren’t useful without the results being communicated with the students and parents promptly and accurately. During formative assessments I give students feedback individually and to the class as a whole. It can take place through body language such as head nods or a thumbs up, verbal praise, and written feedback. Summative assessments have feedback as well. I use written feedback on the chapter tests, verbal feedback with individual students during tutorials, and a documentation of grades using an online gradebook referred to as PowerSchool. Students and parents can access grades and written commentaries by going to the school’s home page.
Analysis: Cole (1995) states that various modes of assessment yield critical and useful information to inform and shape tools and methods that promise to improve academic achievement. With these formative assessments, I am able to make adjustments to my instruction and/or give feedback to my students immediately. Not always do teachers’ lesson plans work out exactly the way they were thought to go. Sometimes students already know information and need to be challenged more to hold interest. On the other hand, sometimes students aren’t picking up on a concept as quickly as a teacher planned and more instruction and practice needs to be devoted to the concept. Without formative assessment, a teacher will not know either case. The teacher should be aware of student progress long before the summative assessment. My formative assessments allow for me to know my students’ progress during each lesson.
Among the most important practices an effective teacher engages in is letting students know about their behavioral and academic progress and success (Sprick, 2006). Therefore it is essential that I give students positive feedback on their successes and constructive feedback on their misunderstandings in a variety of ways. Students know what they need to fix when I give feedback such as “Show each step in solving the equation. Showing the step of dividing each side by 5 may have prevented your calculation error.” Students know what I expect and what to continue with feedback such as “Your ability to show me both ways to factor the polynomial tell me you understand what characteristics to look for when factoring.” Instead of just saying “good job” students know what exactly they did right or wrong.
An extremely beneficial source of feedback for my parents and students is PowerSchool. Sprick (2006) states that feedback should be accurate, feedback should be specific and descriptive, and feedback should be contingent. PowerSchool not only shows grades for assignments, tests, and quizzes as soon as I enter them, but it allows me to write detailed and individual commentaries. While percentage grades are important, I believe comments about a student’s character are just as important, if not more. It is the commentaries where I report on how the student is behaving in class, how the student treats me as the teacher and his or her classmates, and what specifically the student is doing well with or needs to improve upon.
Reflection: My classroom is an environment where formative assessment continually takes place and feedback is given all of the time and in a variety of ways. I am very happy with the timely feedback my students receive and I am confident that students know how they are progressing throughout the unit. Even though students and parents are “in the know” I want to continue to find ways to be in contact with them and give them updates on their progress.
Description: In my classroom I regularly assess student progress. I use an abundance of formative assessments such as teacher observation, student work, self-reporting, technology, and peer assessment. Teacher observation includes noticing the number of students volunteering to answer a question. For instance, if I ask students to tell me the first step in solving a problem and no students raise their hands, then I need to revisit step #1. If I have a lot of hands in the air, then I know that the information was received well. I also spend a lot of time observing how students are doing during cooperative learning activities. An example of student work being used as formative assessment is response boards. Students are able to show their understanding of a concept quickly and simultaneously while working independently. A way that students self-report in my classroom is using their hands. I can have them give me a thumbs up, thumbs down, or somewhere in the middle to check for confidence and understanding. Also, I can have them show me a number somewhere from 1 to 10 as a quick assessment. Technology assessments include clickers, a program called Kahoot, and even texting in answers. Peer assessment is used during cooperative learning activities. Every now and then I give my students a partner quiz.
Summative assessments are used in my classroom as well. Chapter tests are given at the end of every chapter and a final exam is given at the end of each semester. Summative assessments take place a lot less than formative assessments in my class. It is not that summative assessments are unimportant, but if a course is irremediably bad or students are not understanding the material, this fact should become evident during the formative evaluations mentioned above. Because of formative assessments, a course can be abandoned on the basis of such data, and ultimately, courses can almost always be improved (Posner & Rudnitsky, 2005).
It is important to note that assessments aren’t useful without the results being communicated with the students and parents promptly and accurately. During formative assessments I give students feedback individually and to the class as a whole. It can take place through body language such as head nods or a thumbs up, verbal praise, and written feedback. Summative assessments have feedback as well. I use written feedback on the chapter tests, verbal feedback with individual students during tutorials, and a documentation of grades using an online gradebook referred to as PowerSchool. Students and parents can access grades and written commentaries by going to the school’s home page.
Analysis: Cole (1995) states that various modes of assessment yield critical and useful information to inform and shape tools and methods that promise to improve academic achievement. With these formative assessments, I am able to make adjustments to my instruction and/or give feedback to my students immediately. Not always do teachers’ lesson plans work out exactly the way they were thought to go. Sometimes students already know information and need to be challenged more to hold interest. On the other hand, sometimes students aren’t picking up on a concept as quickly as a teacher planned and more instruction and practice needs to be devoted to the concept. Without formative assessment, a teacher will not know either case. The teacher should be aware of student progress long before the summative assessment. My formative assessments allow for me to know my students’ progress during each lesson.
Among the most important practices an effective teacher engages in is letting students know about their behavioral and academic progress and success (Sprick, 2006). Therefore it is essential that I give students positive feedback on their successes and constructive feedback on their misunderstandings in a variety of ways. Students know what they need to fix when I give feedback such as “Show each step in solving the equation. Showing the step of dividing each side by 5 may have prevented your calculation error.” Students know what I expect and what to continue with feedback such as “Your ability to show me both ways to factor the polynomial tell me you understand what characteristics to look for when factoring.” Instead of just saying “good job” students know what exactly they did right or wrong.
An extremely beneficial source of feedback for my parents and students is PowerSchool. Sprick (2006) states that feedback should be accurate, feedback should be specific and descriptive, and feedback should be contingent. PowerSchool not only shows grades for assignments, tests, and quizzes as soon as I enter them, but it allows me to write detailed and individual commentaries. While percentage grades are important, I believe comments about a student’s character are just as important, if not more. It is the commentaries where I report on how the student is behaving in class, how the student treats me as the teacher and his or her classmates, and what specifically the student is doing well with or needs to improve upon.
Reflection: My classroom is an environment where formative assessment continually takes place and feedback is given all of the time and in a variety of ways. I am very happy with the timely feedback my students receive and I am confident that students know how they are progressing throughout the unit. Even though students and parents are “in the know” I want to continue to find ways to be in contact with them and give them updates on their progress.
Element E: Teachers are mindful of their principal objectives.
Artifacts: Instructional Design Package
Event: An Algebra I Unit on Solving Equations
Description: With each activity, lesson, unit, and course I have a purpose for doing it. It doesn’t just happen. It takes a lot of thought and planning, and then reflection upon, and sometimes that reflections results in adjusting of the plan. The term instructional design refers to the systematic and reflective process of translating principles of learning and instruction into plans for instructional materials, activites, information resources, and evaluation (Smith & Ragan, 2005). My Instructional Design Package for Chapter 2 in Algebra I is an example of how I plan a unit with a learning context analysis, a learner analysis, a learning task analysis, learning objectives, an instructional strategy development, and a learner assessment.
Analysis: When I start a course or unit I start with what I want and expect my students to learn, just as I did with Chapter 2’s Solving Equations. These are called Intended Learning Outcomes (ILOs). The ILOs are important in later steps of course planning – in organizing the course into units, in selecting general teaching strategies, and in planning an evaluation strategy (Posner & Rudnitsky, 2005). Throughout my entire unit, I am doing everything based off of my principle objectives. For example, in Chapter 5 of my Instructional Design Package, I give specific strategies used in a lesson to help students solve one-step equations. First, I catch their attention and arouse their interest. Next, I teach them “how” to solve a one-step equation and “why” it works. Last, I give the students an opportunity to practice and give immediate feedback to give the students the confidence to continue and/or fix their mistakes. With all of this said and done, the learning objective should be obtainable.
Reflection: The systematic planning needed prior to implementation and the reflection that should occur afterward are well informed, guided, and organized by instructional design principles and processes (Smith & Ragan, 2005). By following instructional design principles and processes I know that my instructional plan was successful. If at any point, it was not, instructional design would allow for me to make changes. That is the beauty of it. It forces a teacher to think through every aspect of an instructional plan and allows for opportunity for reflection and improvement.
Description: With each activity, lesson, unit, and course I have a purpose for doing it. It doesn’t just happen. It takes a lot of thought and planning, and then reflection upon, and sometimes that reflections results in adjusting of the plan. The term instructional design refers to the systematic and reflective process of translating principles of learning and instruction into plans for instructional materials, activites, information resources, and evaluation (Smith & Ragan, 2005). My Instructional Design Package for Chapter 2 in Algebra I is an example of how I plan a unit with a learning context analysis, a learner analysis, a learning task analysis, learning objectives, an instructional strategy development, and a learner assessment.
Analysis: When I start a course or unit I start with what I want and expect my students to learn, just as I did with Chapter 2’s Solving Equations. These are called Intended Learning Outcomes (ILOs). The ILOs are important in later steps of course planning – in organizing the course into units, in selecting general teaching strategies, and in planning an evaluation strategy (Posner & Rudnitsky, 2005). Throughout my entire unit, I am doing everything based off of my principle objectives. For example, in Chapter 5 of my Instructional Design Package, I give specific strategies used in a lesson to help students solve one-step equations. First, I catch their attention and arouse their interest. Next, I teach them “how” to solve a one-step equation and “why” it works. Last, I give the students an opportunity to practice and give immediate feedback to give the students the confidence to continue and/or fix their mistakes. With all of this said and done, the learning objective should be obtainable.
Reflection: The systematic planning needed prior to implementation and the reflection that should occur afterward are well informed, guided, and organized by instructional design principles and processes (Smith & Ragan, 2005). By following instructional design principles and processes I know that my instructional plan was successful. If at any point, it was not, instructional design would allow for me to make changes. That is the beauty of it. It forces a teacher to think through every aspect of an instructional plan and allows for opportunity for reflection and improvement.
My Goals:
1) To continue to use technology in the classroom and find the most current activities to use in my classroom. This includes collaborating with other teachers to see if they know of any great interactivities or ways to use technology.
2) To use Kagan cooperative learning activities whenever appropriate to maximize student engagement.
3) To continue to use a variety of formative assessment.
4) To continue to manage my time to allow for prompt feedback on assignments and assessments.
5) To follow the successful instructional design process with all of my courses.
1) To continue to use technology in the classroom and find the most current activities to use in my classroom. This includes collaborating with other teachers to see if they know of any great interactivities or ways to use technology.
2) To use Kagan cooperative learning activities whenever appropriate to maximize student engagement.
3) To continue to use a variety of formative assessment.
4) To continue to manage my time to allow for prompt feedback on assignments and assessments.
5) To follow the successful instructional design process with all of my courses.
References
Cole, R. (1995). Educating everybody’s children: Diverse learning strategies for diverse learners. Alexandria, VA: ASCD.
Kagan, M. & Kagan, S. (2009). Kagan cooperative learning. San Clemente, CA: Kagan Publishing.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
Posner, G.J. & Rudnitsky, A.N. (2005). Course design: A guide to curriculum development for teachers (7th Edition). Allyn and Bacon: Boston.
Smith, P. L. & Ragan, T. J. (2005). Instructional Design. Hoboken, NJ: John Wiley & Sons, Inc.
Sprick, R.S. (2006). Discipline in the secondary classroom: A positive approach to behavior management. (2nd edition). San Francisco, CA: Jossey – Bass.
University of Colorado Boulder. (2015). PhET Interactive Simulations. Retrieved from http://phet.colorado.edu
Wichita Collegiate School. (2015). PowerSchool. Pearson Education, Inc. Retrieved from https://wcsks.powerschool.com/public/home.html
Cole, R. (1995). Educating everybody’s children: Diverse learning strategies for diverse learners. Alexandria, VA: ASCD.
Kagan, M. & Kagan, S. (2009). Kagan cooperative learning. San Clemente, CA: Kagan Publishing.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
Posner, G.J. & Rudnitsky, A.N. (2005). Course design: A guide to curriculum development for teachers (7th Edition). Allyn and Bacon: Boston.
Smith, P. L. & Ragan, T. J. (2005). Instructional Design. Hoboken, NJ: John Wiley & Sons, Inc.
Sprick, R.S. (2006). Discipline in the secondary classroom: A positive approach to behavior management. (2nd edition). San Francisco, CA: Jossey – Bass.
University of Colorado Boulder. (2015). PhET Interactive Simulations. Retrieved from http://phet.colorado.edu
Wichita Collegiate School. (2015). PowerSchool. Pearson Education, Inc. Retrieved from https://wcsks.powerschool.com/public/home.html