What’s More Important

At the end of a unit, a decision must be made. As the teacher, you have the power to decide which mindset you want to encourage. Fixed mindset says this is the end of learning for Unit 1, show what you know and if you don’t know it too bad so sad. A growth mindset says, I know you may understand some concepts more than others. Learning is a process and you have until the end of this school year to master these standards.

I believe these mindsets are communicated to students through what we allow and disallow during the unit test/common assessments. So what did I allow for my first common assessment for my new students?

Our anchor charts we developed as a collaboration of 4 classes. Most math teachers have store bought posters hung in their classrooms. These posters remain up throughout the year and probably very rarely do students refer to them as a resource. Our anchor charts on the other hand are interactive and we refer back to them constantly throughout the learning process. And just as those store bought posters aren’t removed, our anchors are not removed during our unit tests.

I allowed students to ask me questions. Many I couldn’t answer such as, “do I multiply or divide for this question”. But for questions like, “I don’t understand what this question is asking me to do” were used as a teachable moment to apply the 3-Read Strategy to make sense of word problems. Questions like, “what’s a terminating decimal again” I answered because students were introduced to the term only a day before the test and I had yet to put it on the word wall. Here’s a note on word walls.

I helped kids use functions on the calculator. In 6th grade, students are only allowed to use 4 function calculators. Then in 7th grade, they are given TI-30s to use. And we all know the calculators don’t give correct answers if the user has incorrect thinking. So when they ended up with a SYNTAX ERROR message, I explained they had to use a different button from the subtraction symbol to input a negative number. When they tried entering a mixed number, I explained what buttons to push to get the template for mixed numbers.

I feel it’s important for students to have some success on their first assessment to help with math confidence. So on the 1st assessments , I go around checking over a few answers and encourage students to double check their thinking on those the answered incorrectly. In most cases, students have already applied some form of process of elimination and they end up with the correct answer. In other cases I can see their misconceptions even when the question is multiple choice. What I’ve found with using this method is in general students become a little more confident mathematically because of the overall success and they also become more prone to automatically review their answers before submitting their test.

And what I feel was the most important thing for them was, I asked, “is everyone doing okay?” Those that were pressed on. Those that weren’t looked up at me wide eyed and shook their heads no. Imagine the anxiety they were dealing with prior to my question.

At the end of our common assessment yesterday, I shared the class average with each class. We had a brief talk about how hard they’ve work over our two weeks together and how their hard work paid off. We discussed how our timeline for learning differed from the other math classes and how we will continue to work with the concepts to begin to commit them to memory.

I’m sure you have your own opinion about what was discussed within the post. And before you question what I’ve done, may I pose this question to you. What’s more important to you, politics and their rules of engagement or students and their overall mindset?

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Put My Strategy Up There

I have a habit of not saying anything a kid can say.  So when students present a strategy, even if it is the ultimate strategy I wanted to present, I give the student credit.  Here are a few examples of thoughts students have provided.  We can it their strategy and refer to their suggestions often.

 

 

It has become such a habit, when a student stated her strategy for converting a large number from scientific notation to standard form she yelled, “Put my strategy up there, I want my own strategy!”  And so I did.

Using Ms. Pacman to Introduce Transformations

If you aren’t familiar with Robert Kaplisnky’s Ms. Pacman, you may want to take a moment to read through the lesson. 

Before we began our math discussions about transformations, I had students work in their table groups at their vertical whiteboards to describe Ms. Pacman’s movements in the initial video.  All but one group used terms such as slow or “in different directions” or right angles. When I inquired about their descriptions by asking, “how would you describe her movements other than slow” or 90 degree angles (to which I contributed our previous discussions about angles), only a few could produce directional movements. 

I was at a lost of how students would get  from here to describing transformations which was the goal of the lesson. I was bailed out by this group’s description:

As they looked around at other groups descriptions, they erased what they had and wrote slow and in different directions. I quickly asked them to rerecord their original thinking and proceeded to ask about Ms. Pacman’s movement on each pathway drawn. To which they responded up, down, left or right. 

I called the rest of the class’ attention to this group’s thinking. Other groups imitated the pathway requesting to see the video again to ensure they were accurately drawing the path.  This group described her horizontal movement as east and west and her vertical movement as north and south.  After seeing the thinking of surrounding groups, they added more explanations to their board (pictured above).

This group identified the right angles as places Ms. Pacman turned. 

We came back together as a whole group to discuss our layers of thinking. 

Layer 1: Identifying the movement. During a running of the video, a student (without my prompting) came to the board and traced the path used by Ms. Pacman.  I called on the group who I first identified to label her movements by sliding right, left, up and down. We labeled the path with the initials of the direction she moved. I asked the group who used cardinal directions to share their thinking of the path. I asked the class if we could say right or east, left or west, up or north, down or south. They agreed so I labeled the path using the initials of the cardinal directions. We used this video to determine if we correctly identified her slides. 

Layer 2: identifying turns. I asked group 1 why they circled all of the right angles on their path. They explained the right angles are the places where she changed position. One of the group members asked if that was called a rotation, as she had learned about transformation in her Connections class. Someone else blurted out she was turning. We replayed the original video and students shouted turn each time she rounded a right angle. One student asked if she flipped instead of turned. 

Enter layer 3: We briefly discussed what it would look like if she had flipped instead of turned. One student offered the synonym mirrored. We replayed the video and concluded she flipped or mirrored once at the very beginning. 

Layer 4: Summarizing. We summarized our lesson by putting our conclusions on an anchor chart. 

We discussed the moves or transformations made in order. I began by using the language the students stated in their explanations. Then I attached the formalize math language to each. For example, in recording the example of reflection, I drew a representation of Ms. Pacman flipped or mirrored and stated, “this is what we call a reflection”.  Although dilation was not a part of this lessons, we extended our discussions by briefly connecting Pixels, an Adam Sandler movie where Pacman is enlarged or dilated. This anchor chart was hung in the room as a reference for math language and understanding of the four transformations based on this context.