Lesson Plays

Earlier this week we had our final face-to-face class for this semester. We were instructed to create a ‘lesson play’ for a small section of a lesson that we had already created and submitted. This task was designed to encourage us to think about what students will say and the struggles that they may have during our lessons. In saying this, it was interesting to think about the conversations that will take place with students ahead of time. It was difficult to think of the issues that they will have, since every class is different. We included some disagreements and contrasting opinions that would generally occur in a mathematics classroom. We wanted to show some classroom management and think about how we would regain the order in our class if a discussion began. It was critical to ask the students the proper questions and dig deeper when this occurred. We asked for their reasoning, which in turn would deepen their understanding of the math skills that we are working with. In general, ‘Lesson plays’ are a useful tool, especially to ensure that you have something that you can refer back to in case some questions develop. Creating them also makes the instructor consider the exact problems that might occur within a lesson, preparing them for discussion and questioning at the right times. 

Teacher: Today we will be talking about linear and non-linear relations. To begin, please take out the sheet titled “stack them.” I will be passing around drinking cups to help visualize the relationship between linear and non-linear relations. Can I have a volunteer draw the fourth frame on the smart board.

Emily: (draws correct frame on the board)

Teacher: So why did you draw the frame with ten cups?

Kyle: I just added another row to the bottom.

Teacher: Well, that is correct, however, do you notice anything about the pattern of first differences?

Ryan: I guess the total number of cups is going up by the same as the cups on the bottom row.

Teacher: So what exactly is happening to the first differences?

John: So the first differences are going up by one every time then.

Teacher: Thank you Bobby. Considering what we now know about the first differences, how many cups will be in the next frame?

Bevan: Fifteen!

Teacher: Thank you Bevan. We are now going to fill out the remainder of the chart. Can someone tell me how many cups will be added in the sixth and seventh frame?

Sarah: twenty-one and twenty-eight.

Ryan: No it’s twenty-one and twenty-seven.

Sarah: Mrs.! He’s wrong. Shouldn't it be twenty-one and twenty-eight?

Ryan: No are you crazy, it’s twenty-one and twenty-seven.

Teacher: Ok, let’s not yell at each other. Ryan, why do you think the answer should be twenty-seven instead of twenty-eight.

Ryan: because you added six to fifteen to get twenty-one so I added another six again.

Teacher: Ok, Sarah, why do you think the answer is twenty-eight?

Sarah: Well, the pattern of the first differences is increasing by one more cup each. So I added seven to twenty-one to give us twenty-eight.

Teacher: Sarah, that is correct. Did everyone hear Sarah explain how we found that or does anyone have any questions about how we reached those answers?

Now we are going to graph the data. Can anyone tell me what values should be on the x-axis?

Carol: Number of cups added.

Teacher: Close, but let’s think about this. What characteristics usually belong along the x-axis?

Rob: Something that changes over time?

Teacher: Yes usually the independent variable, or the one that is in control of the other is placed on the x axis. So Carol, is your answer going to change?

Carol: Yes. So it should be the frame number along the x-axis. And that means the y-axis is the number of cups added or total.

Teacher: Can I have a volunteer come to the smartboard and plot the graph?

Ben: plots the graph (starting point is in the incorrect position- everything is shifted up)

Teacher: Close! Does anyone notice anything wrong with the points that have been plotted on the board?

Kyle: I think it started too high?

Teacher: Would you like to come fix it?

Kyle: Sure, so am I just moving the points down one value each?

Teacher: Would anyone else like to answer Kyle’s question? Do you think he is right or wrong?

Sarah: Yes, Kyle you just need to move it down one value each frame.

Kyle: Alright!

Technology in the Classroom

Welcome back to my blog! Over the last few weeks I have discussed the importance of differentiating instruction, consolidation and diagnostics assessments in the classroom. Throughout these posts I mentioned the used of technological tools and various online resources. I have specifically named Kahoot or Socrative as a tool that I feel are beneficial to use in the classroom, but technology provides us teachers with a much wider variety than that. While school boards and individual schools are constantly updating their personal device policies, teachers must ensure that they are utilizing these devices to their students’ full advantage. These devices not only provide opportunity for assessment within a classroom, they also provide a wide variety of tools that explore new strategies as well as provide assistance with a topic that they may be struggling with.

            During math class this week we were lucky to get to spend time exploring an online math tool called Desmos. We began by simply exploring the graphing calculator. This is an online tool that allows students to visualize the changes that are being made to a graph, without having to complete the calculations in finding the coordinates. It can also be used in various graphing situations to provide students with interception points, inequalities and patters of functions. Once we had explored this calculator our instructor began an online activity called Polygraph. This activity paired students

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together and allowed them to participate in a game-like activity. This game required one student to ask questions, while the other provided the proper response based on a graph that they had selected. The goal of the game is to get your partner to choose the specified graph while asking as few questions as possible. In my opinion, the most beneficial aspects of this game include the opportunity for students to describe these graphs using their own words, and visually comparing the differences between graphs. Students will also help one another improve as they may realize differences between graphs while answering questions provided to them by their classmates.

           

            These types of student interaction will also improve the overall attitude within the math classrooms. While participating in activities such as this students may enter a timeless state, where they lose track of how much time they have spent practicing. I know while I was playing I was very motivated to beat my best score of 4 questions and quickly became caught up in the game. This type of motivation will encourage students to practice their mathematical processes, without knowing they are doing so. Technology will allow teachers to expand the activities that they can implement in the classroom as well as improve activities that currently exist.

           

            In general, I am excited to spend more time exploring the technological resources that are available to all students and teachers. Earlier today I participated in a Smart Board workshop and I am curious to explore how these mathematical resources could be used in partner with the Smart technologies.

Mr. Moore 

Differentiating Diagnostic Assessments

A diagnostic assessment is defined by growing success as an assessment that “takes place before instruction begins so teachers can determine students’ readiness to learn new knowledge and skills, as well as obtain new information about their interests and learning preferences” (growing success, 31). Building off of my previous post that discussed the importance of differentiating instruction and consolidation I feel that it is critical to differentiate diagnostic assessments as well.

http://cnie-rcie.ca/wp-content/uploads/2015/08/2014_
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These assessments must not only be differentiated in a sense that they will include all students learning styles, but they must also be different from the other types of assessments. Formal testing often discourages students since some have become closed minded about the questions that they are asked. In saying this, it is critical to differentiate the diagnostic assessments that we will be using in our classrooms in order to ensure that we get the best idea of where to begin our instruction.

     Earlier this week, our class explored the Gap closing documents and spent some time working on the diagnostic assessment that is within it. We were asked to complete the diagnostic assessment and then explore why we thought each question was there. When presented with the assessment I was hesitant to ‘explore’ since it looked more like a test than an exploration of knowledge. As a result of this I began to think about what a student would feel like when presented with this assessment. It looks and writes as a standard test and would most likely result in an imbalance of results. As I read through and completed some of the questions I did realize that there was some differentiated questions that involved pictures, numbers and words, but there were no opportunities for students to express their knowledge outside of the written answers.

     As such I feel it is critical to utilize the same tools that I discussed last week in relation to consolidation in order to present students with a successful diagnostic assessment. We must allow students to express their current knowledge in more ways than through a written test. Tools such a Kahoot and Socrative that were discussed in last weeks post will also assist in this differentiation. Kahoot not only allows teachers to understand what students have learned, but can also allow teachers to explore new diagnostic assessments. The same classroom activities that would engage students in their consolidation will also engage students in diagnostic environments. Allowing students to engage in the diagnostic activities will not only ensure that that have been given the opportunity to demonstrate their knowledge, but it will also ensure that they do not feel as though they are being ‘tested’. Presenting a formal test may result in students beginning the test with a negative mindset, which ultimately leads to lower test scores. This would not be a fair assessment and would then provide an unreasonable starting place for the classroom teacher. As such, it is critical for educators to ensure we maximize the opportunity for students to show us what they know before we begin instructing. Diagnostic assessments are beneficial as long as every students is given the opportunity to thrive and stay engaged.

Mr. Moore 

Differentiated Instruction and Consolidation

Differentiated Instruction (DI) can be simply understood as providing your students with a variety. It is critical to ensure that all of our students are provided with an equal opportunity to learn and in order to accomplish this we must differentiate our instructional techniques. Edugains describes DI as “effective instruction that is adaptive to students’ readiness, and learning preferences”. The website also suggests that attending to these preferences we increase the chance of students connecting the new knowledge to prior knowledge and ensures that the students stay engaged in their learning.

https://aae.boisestate.edu/know-your-learning-style/

A student’s learning preferences will usually include their learning styles. In my opinion a learning style is a situational preference that depends on the subject matter at hand and the end result of the task. I learn strategies and tactics in games though participation, while I understand scientific and mathematical problems when I hear their explanations. As we differentiate how we teach students we will be allowing a wider variety of students to succeed. I feel as though the mathematics classroom is both a beneficial environment for DI, but can also present a variety of challenges. These challenges include the traditional math setting that was very teacher centered as well as the students who have become accustom to this type of teaching. While there should still be some aspects of teacher-centered education it is critical to ensure that students are giving time to explore all of the learning styles. Utilizing models, manipulatives, videos and games can be a very effective way of adapting to the needs of your students.

In addition to ensuring that you instruction is differentiated I feel as though it is just as important to differentiate your assessments or consolidation pieces. As students are kinesthetic learners , visual learners or verbal learners, some students may only be able to express their knowledge using the same mediums. In saying this it is not fair to give an assessment to the entire class and expect them to succeed. As teachers, we must provide a variety of tools and options for students to show us what they have learned.

http://www.theflippedclassroom.es/dandole-una-vuelta-a-kahoot/

One tool that I am excited to explore is an online tool called Kahoot. In our second class of the semester we played a Kahoot quiz based on our introductions, and I was impressed by the learning and enjoyment that took place. We were learning about one another and I gained more knowledge during the ten minutes it took to complete the quiz, compared to the time I spent reading blogs online. The scoreboard and other game-like features encouraged me to explore it more. After looking into it I feel as though it is an appropriate tool to use in any classroom. You can make your own quizzes and ensure that students are engaged in their learning. The website also provides the students with the opportunity to hear the questions and see them on the screen as opposed to simply reading them off their tests. The game like environment also encouraged students to collaborate with one another in order to help their peers reach the top of the leaderboard.

Mr. Moore

Reference: http://www.edugains.ca/resourcesDI/Brochures/DIBrochureOct08.pdf