It has been about a month since school let out and I’ve been enjoying the summer so far. I’ve been reading, working on the lawn, painting and took a vacation. During the last month I decided to focus my time on things not related to school work. This balance of time tends to give me a better perspective when I do come back to working on items related to school. Now I’m starting to see school supplies (already!) in stores and am looking back at how the school year went last year. Every year I attempt to gather information about my students and how they perceived the school year as a whole. I give a survey and use that information moving forward for the next year. I decided to wait a bit over the summer to look over the results.
Back in June I gave a survey to all of my students in 3-5th grade. The survey was related to instruction models and preferences. This year I intentionally varied my models throughout the year and didn’t stick with one particular tool for activities. I started off the survey with a brief question about their favorite math topic this year.
Before giving the survey I went into detail about each topic. The purple is measurement and I’m not sure why it didn’t show up with my advanced table Gform add-on. The next question was related to why they felt this was their favorite topic. Here are a few responses:
Next time I’m going to put a minimum character limit to extract more information.
The next section, which was the largest, was related to instruction models/activities. Students rated them (1-5) 1 being the least effective for learning and 5 being the most. A brief explanation of the items is in each caption.
I had 59 students take the survey, but I have 65 + students in 3-5th grade. Some of them were out for other activities during the time the survey took place. Something to consider … some of these activities were used more frequently so students had a larger sample size. Overall though, it seems students enjoyed most of the tools/activities for learning about mathematics. I think it should be mentioned that there’s a difference between a tool and strategy and I might be blending the lines a bit in this post.
The tools in the box were used independently or with a partner. They also required some type of technology (iPad, Chromebook), while the other four didn’t. I think having a blend between the tools/strategies is helpful and students aren’t dependent on using one medium to show their learning. I’m looking forward to diving more into this data as the summer progresses.
During the last week of school one of my classes explored dilatations. It was a rather short lesson since there were only a couple days of school left. After some review, I pulled out a project from last year and thought might be applicable since it addressed the same standard for that particular day. I looked it over and made a few changes so this year it would run smoother. Here’s what changed:
I had the students create an exact 4cm by 6cm grid using rulers. This was different than my initial project. I made sure to check each grid before students moved on to the next step. I’m not a fan of having a simple mistake or unclear directions derail an entire project (which it did for some last year) – so I decided to check each students initial grid.
I also created a random piece to the amount of dilation this time around. This picture is from last year’s post.Last year students already knew the grid to use and basically used a “paint by number” approach to fill in each square. Although that was fun, it didn’t really hit the objectives as much as I’d like. I had students roll a die to determine the dilation this time. This gave four different options for students.
I put together a criteria for success component where students could check-off items when completed. I set up the different dimension papers on one of the tables so students could easily grab them depending on their dilation. I also added a short debrief piece near the end of the project where students discussed how they increased the size of the image.
These changes helped improve this particular project and I believe it created a better learning experience for the students. There are times where I completely scrap a project and other times I make tweaks in order to make it better. I opted for the second option this time around.
* Next year I’m planning on updating the project to include dilations that involve reducing the size of an image.
My fourth grade students finished up a project involving area last week. Students were asked to find the area of different playing areas for certain sports. They first calculated the areas of the playing field by multiplying fractions and then found the product.
The next step involved creating a visual model on anchor chart paper. Students worked in groups to put together their athletic park involving the field areas. They were given the area of the park and then had to place the fields where they wanted according to the team’s decision. Students also added additional facilities for their athletic field and then presented their projects to the class.
While presenting, students in the audience were required to either 1) ask a question or 2) provide a constructive comment. Most of the questions that were asked related to why certain fields were placed in specific areas on the field. One question stood out more than the others … does the distance make sense?
Students were looking at the length of the fields and observing whether it was reasonable or not compared to the total length. The class then had a conversation about the terms reasonableness and proportions. The discussion involved how a double-number line and a grid could’ve helped visualize how the distances match.
I’m hoping to revisit this idea during the next few weeks as the school year finishes up.
This year I’ve been using number sense routines* with my 3rd-5th grade classes. The routines have specifically been put into place to help students strengthen their place value and estimation skills. The routines last around 5-10 minutes and generally occur during the first part of class The routines is the first thing on the board as students enter. Students use a template, complete the routine independently and we discuss the results and process as a class.
Two of the more productive routines this year have been Estimation180 (3rd grade) and Who am I (4th). Both ask students to use hints or models and then use those visualizations to solve problems. Students document their thinking on an individual page and then we discuss it as a class through a debrief session. While working with students this year I noticed that not all students participated to the extend that I’d like. The conversations were decent and students were engaged, but the reflection piece wasn’t as thorough. So this year I’ve decided to add an individual reflection component for these specific tasks. The reasoning actually came from a book that I read back in April that emphasized how sentence stems can be used to help students reflect on their mathematical thinking.
I put these sentence stems into practice and added them to a reflection sheet. I added extra space after the “because” to help encourage students to write more about their own thinking process.
Students complete each one of these around 2-3 times a month. Students complete the reflection sheet, discuss the writing with partners and eventually put them in their folders. The sheets are revisited throughout the year to see the growth over time.
* The images from this post are from a math routines presentation on 5/3. Feel free to check out the entire presentation here.
There’s around one month of school left and it feels like the home stretch. The next month is full of changes. The weather changes from chilly temps to sunny days (at least in the Chicago burbs), class lists and sections are starting to take form, driving to/from school with the windows down is the norm, and planning for that final month is in full swing. The majority of my math classes just finished a unit assessment and there’s one unit remaining. So often I find that students perceive the end of a math unit to “close out” the learning on a particular skill set. I observe that this idea often gets pushed out as grade deadlines approach.
As my classes start a new unit I’m pausing to reflect on how my practice has changed. Last year I read How to Make it Stick and I intentionally planned to use more retrieval practices. This year I’ve incorporated more review opportunities through online formative quizzes and by trying to make implicit connections to past learning. I’ve often asked students how today’s objective connects to this week’s learning.
While digging through my resource materials early this year I found optional mid-year and cumulative assessments. Generally, I find that there’s not enough time to complete all of the assignments/tasks in the resource so these particular tests aren’t used frequently. This year I decided to use them to help with spaced retrieval practice. Instead of using a mid-year and cumulative assessment directly following a unit I decided to space out these assignments and take off the grading emphasis. These types of assignments take multiple days to complete and I often have students work with partners to reflect on their progress. So far I’ve seen positive progress as students this year are referring back to past skills more quickly and bridging the connections on a frequent basis. I’m looking forward to using a similar strategy next year.
One of my classes is in the middle of a unit on geometry and measurement. They’ve identified shapes before, such as rectangles, squares, triangles and hexagons. Earlier in the year they found the area and volume of shapes involving rectangles, squares and triangles. The current unit investigates how polygons (specifically triangles and quadrilaterals) are similar and the study of shapes progress as students create hierarchies.
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
In order to dig deeper into the above standards the students starts the classification process. This was fairly new for most of the students. I explained what classification meant and gave a few examples related to the characteristics of triangles and quadrilaterals. Students were given a sheet of quadrilaterals to cut out and classify. The next question I was asked was related to how each shape should be categorized. The class reviewed different vocabulary words associated with polygons and then I left the students create their own categories.
After discussing equal side lengths and parallel sides two of my students created the classifications related to those terms.
Almost every student had a different way to organize their shapes. Students went to different tables and observed how their peers classified the shapes and then the class discussed similarities. Next week students will classify the shapes with a hierarchy chart. I’m looking forward to seeing what they create.
This post has been marinating for a while and I’ve been waiting to write it up. State testing is just around the corner and I feel like this is a good time to press send.
One huge emphasis that I see in schools is related to the idea of student growth. This is communicated in schools, during teacher pd meetings, when talking about Hattie’s next best effect-size list and can even be part of teacher evaluation criteria. I see this when school districts use MAP, state testing, or a similar type of tool that measures growth over time.
Schools, teachers, and parents want students to grow. In schools the focus of growth primarily related to academic content. How is that measured? Well that depends on the teacher/district/organization. Some teachers go the route of using a pre vs. post-test. Others give multiple formative checkpoints and then use them along with student reflection components to show growth on the summative. Case in point – there are multiple methods to show student learning and growth.
Here’s my not so small gripe. In an effort to show growth some educators may feel rushed to “get through” as much content as possible. I hear this a lot more in math classes than other content areas at the elementary level. Math has a subjective linear vibe that I think some teachers hold onto. This idea is often reinforced through the structure of some of the adaptive standardized tests that communicate math growth to teachers and school administrators. This can be a bit troublesome if these types of tests are used for evaluation purposes as it brings along additional pressure.
I find students make meaningful math connections when they’re given time to process and apply information. I believe rushing through concepts or stretching to just expose students to higher-level concepts that aren’t part of the lesson isn’t as beneficial as it seems. Moving off the pacing guide or lesson to stretch to other concepts might not be the best idea. When I first started teaching I remember having a teacher talk about exposure all the time. The teacher would say, “If they’re just exposed… then they’ll complete those problems correct and that’ll push them to the next concept.” This teacher was truly amazing (and made some great coffee in the mornings), but I questioned this then and still do now. If we’re exposing students to math concepts so they’ll score well on an adaptive test then that’s another issue altogether.
If a lesson is looked through a linear math lens a teacher might feel as though they should introduce fraction multiplication if students are doing really well with multiplying whole numbers. Is that the right move? Should a teacher stray from the lesson plan to possibly reach a few kids that seem like they’re ready? I’m not saying yes or no because it depends on the station and students, but I’m more in the no camp. Stretching math concepts in a lesson/task for exposure sake doesn’t last.
Last summer I was able to reading Making It Stick and came away with some applicable ideas related to changing my study guides and how retrieval practice benefits those wanting to learn. I find that there’s sometimes pressure to stretch to another concept for exposure sake. Instead of stretching concepts, there should be opportunities for students to enrich their understanding through connections. This looks different and is more challenging in my opinion than just pressing the accelerate button temporarily. I believe that taking time for students to process, reflect and engage in meaningful math tasks will last more than a glimpse optimistic exposure that may soon be forgotten.