Math Strategies – Page 2 – Educational Aspirations

Conceptual

This weekend I started to read a book on how the brain learns mathematics. The first chapter highlights the different ways people develop number sense. One of my takeaways came from a section related to subitizing. Subitizing involves recognizing a number of items in a collection. There are two types of subitizing that are communicated in the text: perceptual and conceptual.

Perceptual Subitizing

Perceptual subitizing involves looking at a number of items and recognizing the number without much pause. Generally, the items are separate from each other and a quick glance will often reveal a correct answer. Perceptual subitizing can remain fairly simple if the digits are close to zero. Larger amount of items often gives way for people to start counting each item. Counting individual items increases the amount of time it takes to find the total.

Group dots together, e.g. 3 groups of 4

Conceptual Subitizing

Conceputal subitizing is a bit different. This type of subitizing relies on the person to find patterns and use those spatial relationships to find a total. Grouping items together (such as 3 groups of 4) would fit into this category. Analyzing the spatial arrangement of the items can lend itself to people using conceptual subitizing.

I’m finding more and more that subitizing plays an important role in the early elementary grades. To a certain extent, I feel like students use subtilizing to quickly identify the number of dots on dominos and dice. Whether students use procedural or conceptual subtilizing depends on the number of dots and the arrangement of the pattern. Students that have a conceptual understanding of subitizing can group items to find sums. Grouping items together with spatial reasoning can lead students to discover additional computation strategies, such as splitting items into equal groups or constructing mental arrays. I see potential in using subtilizing strategies in the classroom.

While researching this topic I came across Steve’s subitizing page. Feel free to browse this amazing resource for more information and classroom resources.

Standards for Mathematical Practices

This year my school district adopted a new K-5 math text. This new text is more aligned to my state’s standards and emphasizes number sense strategies much more than in the past. It’s been a change from what’s been used over the past few years. One of the major shifts involves the use of using multiple strategies and visual models to put together and take apart numbers. Although they aren’t explicitly taught in our newly adopted math text, the Standards for Mathematical Practices (SMP) are highlighted as part of the CCSS.

Just like many educators, I have a child-friendly SMP poster hanging around my classroom. As the months passed I feel like I haven’t been referring to the SMP as much as I should. This is a missed opportunity. The poster has started to fade (literally) and students haven’t been referring to them since the very beginning of the year. I doubt students notice it anymore since it’s basically blending into the wall. One of the benefits of using the SMP is being able to refer to them while teaching. Perseverance, using the right tools and attending to precision happen just about every day.

So after introducing the concept of pan-balances, I decided to have the students revisit the SMP. I felt like the students were having a challenging time persevering. Okay … that’s an understatement. They were struggling and were very willing to tell me about it. I stopped the class and we had a brief discussion on the meaning of being able to persevere in math class. The talk on perseverance lead to discussing the SMP in more detail. I wanted students to internalize their meaning and see how it applies to their math learning. The class had a conversation about the different mathematical practices and how they’re used. The math discussions that followed were amazing. Students started to find examples in their own lives of how the SMP connect to what we’re doing in class. The class finished the lesson on pan-balances with a renewed approach. A few days later I had students complete an activity related to the SMP.

I printed out eight sheets with a standard practice statement on each one. Students were grouped into pairs and asked to draw a picture that represents a particular SMP. The picture also needed to include some type of caption or written statement. Students first put together a rough draft, refined their idea and created a final product. The final product was cut out and glued onto our SMP board. A few examples are below.

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Thursday night was my school’s annual open house. Parents and students come into the school and visit the classrooms during this time. It was great to see my students become tour guides and show their parents the role the SMPs play in their learning and how they approach math.