Math Instruction and Book Studies

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Over the past year I’ve had opportunities to read books related to math instruction. I volunatarily chose to read these books.  They weren’t part of a college class or assigned by my school. Some of the books I found via Twitter while others were recommended by colleagues in my PLN. Two books in particular have impacted my teaching practice this school year. Both books were used in a math book study conducted through Google Hangouts. Anthony helped lead and encouraged others to join these particular studies.  The discussions that happen during these books studies are valuable.  Through this post I’m going to highlight two books in that’ve helped influence my planning this school year. I believe that the planning has helped produce better instruction and learning experiences for my students.

Teaching Student-Centered Mathematics

I’ll admit that I’m not completely finished with this book. I’m going to recommend it anyways. What I’ve covered so far has been directly applicable to what I’m teaching. The book was recommended to me by a multitude of math coaches and teachers. Their positive experiences helped egg-on my purchase once I heard that this book was going to be used for a book study. So I took a leap, purchased and have been slowly reading it over the past two months. Nuggets of greatness exist inside this book related to instructional design and how to promote student math understanding. The first few chapters emphasize the reasons to differentiate, assess, and how to work with parents. Part II is where I’m finding the most value. The authors’ take apart different math strands and explicitly show a variety of strategies to introduce or engage students in the learning process. A heavy emphasis on using visual models and building a concrete understanding of mathematics is demonstrated throughout the book. I appreciate the examples of the visual models and practical examples. Some of them were brand new to me. As I progress through the book I’m finding useful strategies to have students think more critically about math tasks.  This is taking more time in class but I feel like it’s worthwhile. I’ve used the chapter on fractions more prevalently than others.

How the Brain Learns Mathematics

This was another book that was used for a book study. I skimmed through the first few chapters and found I needed to delve in deeper to get substance. I had to re-read many parts because of the content related to brain science.  Most of the information related to neurons and retention fascinated me.  These were highlight-worthy for me. I thought much of this should have been introduced during my undergraduate studies. The information about how science relates to math instruction helped me see the connections between how students process numbers and what’s developmentally appropriate for students. There were quite a few affirmation opportunities as well as times where I questioned what I’m doing. I love a book that makes me ask better questions.  One of the take-aways that I found helpful was related to how I organize my lessons and that timing plays a pivotal role in retention. All the time involved in math instruction is precious. With that being said, the “prime” time minutes (first 10-15) and (last 10) are very important in how students remember their math experiences. After reading this I started to analyze how I structure my 60 minutes with students. I became more aware of the use of the first and last minutes of class. Another piece that I came away with dealt with the time needed for students to process information. Students need time to process, reflect and create connections about the math concepts that they’re experiencing. I don’t necessarily think that happens as much as I’d like.

Looking forward, I’m hoping to carve out some time to read a couple new books on my shelf. As I’m writing this I have Number Talks waiting for me.   At some point I’m going to crack these open and look for ways to improve my own practice.

Minecraft and Math Strategies

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A few weeks ago my students started using MinecraftEdu during math class.  You can read about our first experiences here.  I used a similar activity with my fourth grade students this Friday.  Students were expected to build a house in MinecraftEdu.  Students followed these instructions.  During the process students will be practicing measurement skills related to fourth grade  math standards.

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Additional components were added to the project.  Instead of working in teams, students built their own houses.  I also added blanks for students to show their number models and other information.  What I found more interesting this time around was the strategies that students seemed to use.  Students started with the first direction:

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Students tried a number of different strategies.  Some students started laying out blocks in a square pattern and decided to multiply that measurement by four.  Other students created a rectangle and then eliminated blocks to match the measurement.  I would say that the majority of students had to use trial and error to create a perimeter that matched the criteria.

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Some students decided to create dimensions that met the area criteria first and then addressed the perimeter.  Almost all the students had to break blocks and change what they originally made.

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Students then started to create the height of the house.  About half of the students started by creating pillars.  The pillars stopped at a height that students determined.  Students then filled in the pillars, added in windows, created a door and double-checked their measurements.  Students then started to work on designing the inside of their houses.

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Next week students will revisit this project and continue to work on the interior.  At some point roads or paths will be created to connect this community.  Additional math skills will be added as the class continues to create this virtual math world.  I can see angles, volume

Representing Fractions

During the past few weeks my students have been studying fractions. I feel like the class is making a decent amount of progress.  The class has moved from identifying fraction parts to adding the pieces to find sums. Pattern blocks have been especially helpful with adding fractions. I feel like students are becoming more confident with the computation and we haven’t used the word common denominator yet.  I don’t want students to by relying too much on just the algorithm.  Throughout this process I’m noticing that students are struggling with fraction word problems. Students are having trouble identifying what the fractions represent in the problems.

Yesterday we had a class meeting to discuss this topic. This fit in well with a book that I’ve been reading.  Chapter 8 emphasizes how to teach fraction concepts and computation.  The chapter begins with misconceptions and the different meanings associated with fractions. The class reviewed all the different ways that they view fractions. We documented the class ideas on an anchor chart.

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Do you notice any trends? The class looked at the list and had no complaints. This is how they visualize fractions. When asked how they use fractions they came back to this list and didn’t have anything to add.  Keep in mind that this is from a group of third graders.  The next step in the class conversation was to discuss different ways that fractions are represented in problems.

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I started with part-to-whole representations. Most kids were familiar with this type of model. After all, students have been using this model for the past week and most of last year. I then moved onto how fractions can be used to measure objects.  Students nodded their heads in agreement and asked questions as I went through the other representations. Connections were made through this process.  Students created examples of each representation in their math journals.

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Students are planning to revisit the word problems that I discussed earlier in this post.  They’ll be reading the question and match the context to the representation.  I’m looking forward to having students use this strategy moving forward.

Visualizing Fractions

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My third grade students started a new unit on fractions this week.  They’ve explored fractions before, but more along the lines of identifying different types of fractions and adding/subtracting with common denominators.  This new unit involves students finding fractions of sets and a heavy dose of fraction computation.  Students need to have a deep understanding of fractions to be able to add them and show a visual model.  So on Friday  the class practiced skills associated with finding fractions of sets.  Students were given this prompt:

Draw four different ways to show 3/4 in the box below.

The student models fell into a few different categories.

  • A number line
  • Pie, rectangles, squares
  • Dots or arrays
  • Angles

 

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The class reviewed the results and we had a discussion about the different ways to represent fractions.  Next week the class will be combining these models to add and subtract mixed numbers.

Coordinate Grids – Part Two

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Last week my students started to plot points on coordinate grids.  They were identifying different quadrants and becoming more confident with drawing shapes on the plane. While reflecting on last week’s activities I noticed a Tweet that was sent our replying to one of my blog posts.

I’m a rookie when it comes to Desmos.  Most of the stories I hear involve middle or high school students. I needed to find something that worked with my elementary kids.  So I started to research and did a little bit of exploring to see how this could be used with my third grade class.  I ended up looking up some of the templates but had a bit of trouble finding an extremely basic rookie-like coordinate plane activity for my students.  I decided to go the route of creating a template and having  students manipulate created points for a project.  Click here for the template.

I quickly found that students had no idea how to use Desmos.  I gave the students 5-10 minutes to orient themselves.  Students were asked to move the points to certain coordinates  on the grid.  As they moved the points students started noticing that the tables on the left side of the screen changed.  Students started connecting how the tables changed and this helped reinforce concepts learned last week.  After this introduction time, students were given a rubric that contained the following:

  • Move the points on the grid to create two angles
  • The angles need be located in two different quadrants
  • The angles need to be acute and obtuse with arcs located in each one
  • Indicate the measurement of each angle

Students were then given 15-20 minutes to create their projects.

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Students created their angles by moving the points around the grid.  Students then shared their projects with the class.

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Students took a screenshot and then added the degree measurements to the angles.  The class reviewed the projects and students explained how they plotted the points.  This project seemed to help students make the connection between points and the x and y-coordinates.  It also reinforced skills related to angle classification and measurements.  I’m looking forward to expanding on this project next week.

Exploring Coordinate Grids

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My third graders started to explore coordinate grids this week. For many, this was the first time that they’ve used them. Some of the students have played Battleship or some other game that involves a grids.  Playing off that background knowledge, I used a road map to show how people can find certain locations by using a coordinate grid. This made sense to some of the students but a few still were unsure of what axis was used first to determine where to plot a point.  This was a reoccurring theme throughout the lesson.

During this process I remembered a strategy that another colleague suggested a few years ago. She borrowed the idea from another teacher and it seemed to work well in her classroom. A colleague of mine used (3,2) as an example of the “go into the building” – first number (right 3) and then “go up or down the elevator” (up 2) method. I decided to use that strategy and a few more students started to grasp the process.  The next activity in the paragraphs below seemed to solidify a better understanding for the rest of the class.

Earlier in the day I created a very short Nearpod lesson involving mostly pictures of coordinate grids. I handed out a iPad to each student. Students logged in and given a picture of a grid and asked to draw and label points.

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I then revealed the pictures to the class on the whiteboard. The names of the students were hidden so that we could analyze each response without throwing judgement lightning bolts towards a specific individual. As the class went through each picture they started to notice trends.

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  • Some were switching up the x and y-axis numbers
  • Some were not creating a point
  • Some were not creating a letter for the point
  • Some were confused by the negative sign in front of the numbers

Students observed these issues from the first question and grid. After a decent discussion on the above trends, the class moved towards the second grid and question. I gave the students that same amount of time and the results seemed to initially improve.

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Students started to become better at finding their own mistakes before submitting their creations. I used the same strategy as earlier and displayed the results to the class. There were a few that had some of the same misconceptions, but not as many. In fact, many students vocalized the class improvement since the last question. One of the evident misconceptions revolved around students having trouble plotting negative numbers on the coordinate grid. The class discussed this and completed the third question and grid. The student responses from this question were much better than the prior two. Students were starting to develop some true confidence in being able to correctly plot points on a coordinate grid. I kept a list of the trends that students noticed and will bring it out later in the unit as we’ll be revisiting coordinate grids next week.

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After our Nearpod lesson (which was about 15-20 minutes) students played a Kahoot on identifying points on a coordinate grid. I felt like this was helpful as students identified the points and were able to gauge their own understanding compared to the goal.

Minecraft and Math

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Earlier in the school year a group of three teachers at my school wrote a grant expressing the need to incorporate Minecraft in the classroom. The idea actually started last summer when a colleague and I attended a professional development event in Downers Grove. During one of the sessions I met two teachers from nearby school districts that used MinecraftEdu in a school club. What they had to say caught my interest and two other teachers and I decided to start a school club in 2016. We wrote the grant and it was accepted. Last week the licenses were purchased and I’ve explored the potential of using the program in the classroom setting.

Before the school year started I knew very little about how to use Minecraft. I decided to purchase a copy and explore the Minecraft world over the summer. I quickly learned the controls and watched a number of YouTube videos to become a better rookie. I’m still a rookie. I found the MinecraftEdu community online and started posting questions to the forums. Moderators answered my questions and I started feeling more comfortable using the program on my own. The forum has been especially valuable in giving me ideas to use in the classroom.

I downloaded a few world templates and started brainstorming. I then bounced a few ideas off of colleagues and decided to start using the program for a math scavenger hunt. The goal was to have students get used to using the program in an education setting while reviewing fraction math concepts in the process.  Most students already understood the controls and the game but weren’t used to using it for a different purpose.  I wanted to start simple and I thought a scavenger hunt would be an easy way to start incorporating the program in my math class.


Math scavenger hunt – third grade

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Students entered into the fraction world that I created.  Once they entered into the world I froze all of them. I explained the goal of the world and answered questions. The goal was to explore the world and find the signs that were posted. Students were using the MinecraftEdu version where they weren’t able to build or keep inventory of items. Trap doors, caverns and bridges were all part of this simple world. Each sign had a particular math problem on it and students were expected to solve the problem. I then passed out a sheet that went with the scavenger hunt. The sheet had spaces for students’ number models and solutions.

I then unfroze the students and they were off to the races. Students split up and started exploring the area. They soon found that working in teams seemed to be more efficient in finding the signs. All students were finished with the scavenger hunt in 30 minutes. Afterwards the class reviewed the answers.


House building – fifth grade

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I created a completely flat Minecraft world for this activity. Students were grouped into teams and given a task related to concepts that we’ve been discussing. The fifth grade class has explored area and perimeter and will eventually be investigating volume in January. Each group was asked to create a building that met a certain criteria. It was stated that each Minecraft “block” was exactly 2 feet on each side. Those measurements were used to meet the criteria.

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Students worked together and started building their houses. A few groups had to restart as they found out that the perimeter and area didn’t meet the criteria. After around 30 minutes students are about 50% complete with their houses.  I’m assuming that another 30-40 minutes and the students will be finished with their projects.  At some point after break the class will be presenting their buildings to the class.


In January my school will be offering a Minecraft club to around 25 elementary students. We’re planning on building our actual school from scratch using some type of scale model. The students are already excited to be using this program in school and I’m looking forward to what students create and the process involved in that creation.