An assumption that is often made about me is that I have always loved math and that I was always good at math. People are surprised when I share that math was the toughest subject for me in school and the one where I made my lowest grades. I remember working example after example trying figure out a pattern to the correct answers. I was trying to learn or understand the math, rather I was just trying to find a way to get the right responses. I only attended tutoring & office hours for math classes in both high school and college. I got high B’s and A’s in my math classes, but I didn’t actually understand the math. I had the opportunity to take Algebra 1 in middle school, but I deffered until high school because I was afraid of math and I knew there was no point in taking a Calculus AP test my senior year because I would not score well. In complete contrast, I have always loved reading. I am an avid reader and one of my favorite things to do growing up was going to the library every week to pick up a new stack of books. I was able to interpret and analyze texts and I always found my literature classes easy. I scored well on AP tests that required writing and won multiple writing awards. When I became a third-grade teacher, I found it easy to guide my students to enjoy reading. I had numerous comprehension strategies in my toolbox ready to teach my students.
My math teacher-toolbox was very limited. I made it my goal to help my students feel confident about their mathematics abilities. I made math as engaging as possible and worked with them to become problem solvers. In order to do this, I had to face my fear and learn the math. I had to understand how math works, why math works, and the connections between different math concepts. I made a conscious effort to question “strategies” that were shared with me. What is the math being taught? What is the purpose of this shortcut? What does this part of the shortcut mean? What is the purpose of this strategy? Is this a real strategy or trick? These questions led me conclude that the “butterfly method” for comparing fractions is a trick that does not support the understanding of fractions. It was the same thing as me working out textbook problems until I found a pattern that helped me get the correct answer regardless of me not understanding the math. In my experience, many elementary educators have a fear of math. It is that fear that should prompt us learn more about the math we don’t completely understand and teach students real mathematics rather than “strategies” or “methods” that have little to no math sense.
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The numbers should be ignored and they should be visualizing what is taking place in the problem. Are we at the grocery store? Is the problem about a sports game? Thinking about the context will activate students' background knowledge and help them recall Tier1 & Tier 2 vocabulary they have already internalized.
During the second read, students read the problem in order to understand what the question is asking or what the prompt is asking them to do. Rereading the problem provides students the opportunity to process and think about the purpose of the task or problem. Sometimes when a task or problem is too lengthy it is common to miss the goal of the task. During the third read, students read the problem to determine the important information. Students should take the time to reason quantitatively. What does the number ___ mean? What is the value of the number ____? What quantity is represented by the number _____? The part of the gradual release model is the "You Do" during which students practice and apply what they have learned. The assumption is that students have a solid understanding and that they are able to practice correctly. What I have noticed is that not all students are practicing correctly, there are usually misconceptions that need to be addressed, and students are using ineffective strategies because they want to get the answer correct. When teachers see that students are making errors it leads to modeling again for students, providing numerous scaffolds, or guiding students step by step until they are able to complete each task or problem correctly. Because this time is not effective it leads to what appears to be students not transferring or applying what they have learned. I believe that having the last part of the lessons be the "I Do" or teacher does is an effective way to address misconceptions and help synthesize student learning. There will be enough anecdotal data to provide examples for the teacher to anchor this part of the lesson.
While the gradual release model might make sense in language arts instruction, it would be more effective to flip the model to You Do, We Do, I Do during mathematics instruction to support multilingual learners and all mathematics language learners. It is important to guide students to take ownership of their own learning and provide supports & scaffolds when they are needed for students to make sense of the mathematics. During the "We Do" part of the lesson, the teacher solves a problems or completes an example and then the students have the opportunity to complete additional problems following the steps explained by the teacher. For our multilingual learners, this portion of the lesson can be too reliant on teacher talk. Many times in an effort to help students "get it" (math or academic language), a teachers explain or show their thinking rather than having the students do the work. Instead of "We Do" , let's restructure the time as "Students Do". Tasks or activities can be designed to provide multiple entry points & use comprehensible input in order to get students to "do the math". If language support is needed then differentiated based on language proficiency can be provided. Students can have the opportunity to use a variety of tools/manipulatives rather than just one tool. Students can work with a partner or in cooperative group. This shift in instruction will lead to students completing less problems/tasks, but the quality of the mathematical thinking will increase.
(Part 3 of this post continues next month) There are many instructional strategies and moves from language arts instruction that are applicable to mathematics instruction. In experience & observation, the Gradual Release Model or "I Do, We Do, You Do" approach is not effective in the mathematics classroom. Starting with "I Do", means that the teacher models or thinks aloud through a problem or task without giving students the opportunity do the math first. All of our students are capable mathematicians and they bring with them experiences that can help or hinder their understanding. By going directly to teacher modeling first we teachers miss the opportunity learn about the previous knowledge, level of conceptual understanding, & possible misconceptions. Do students need guidance at the start of a lesson? Yes. Will students need supports & prompts to know what to do at the start of concept unit? Yes. Am I encouraging teachers to have students frustrated & practice incorrectly? No! Is it important for students to use what they know from in previous grade levels & at home in order to make connections to other math concepts & previous learning? Yes! Our students do not begin each school year, concept unit, or lesson as blank slate. We cannot assume that they know nothing & that during the "I Do", we are going to teach them everything they need to know. This leads to teaching too much at a time & not allowing for processing time or repeating what they already know & not going deep enough. (Part 2 of this post continues next month) In my opinion not being able to add, subtract, multiply, & divide fluently is equivalent to not being able to read fluently. Yet, it seems that there is a greater urgency for students for students to be able to read than for students to be able to do math. It is interesting that common message shared is reading is an essential and long life skill. Yet, understanding addition, subtraction, multiplication, division, measurement, money, fractions, etc. are also essential life long skills with real-world applications. Math fluency and deep understanding of math concepts will only happen in our school systems when there is a balance between the priority given to all content areas. I don't agree that math is a universal language. Math is it's own language that multilingual students have to learn and mobilize. Math has specific vocabulary, phrases, and different ways to communicate. In order to learn the language of math, students need consistent math instruction that is taught at a high level. If we cut down math instructional time & move quickly to shortcuts/algorithms, this will cause gaps in students mathematics understanding. If a Kindergarten student does not have a deep understanding of composing/decomposing 10 then they will have difficulty with Addition/Subtraction facts in Grade 1. This will then lead to students having difficulty with Addition/Subtraction regrouping in Grade 2. By the time students get to Grade 3 & Grade 4, multiplication & division will be a major challenge. It is not uncommon that when students reach the end of elementary school or begin middle school when the ALARM is rung because these students do not know their facts, they are counting on their fingers, they get confused with steps in standard algorithms. Instead of waiting until waiting until a student is 10-11 years old to help them develop math skills & dispositions that will encourage them to join higher level math courses, let's provide solid high level math instruction starting on their first day of Kindergarten. For our multilingual learners, gaps in teaching need to be avoided as much as possible as they navigate adding English to their language repertoire and/or developing multiple languages. All students are capable mathematicians! They can maintain the belief if balanced instruction is provided and the message is shared that mathematics is also very important. The pandemic continues and a new school year has begun. My district has started the year in person with as many safety protocols as possible in place. Something that I have noticed is we are having more "teacher talk" that usual and classrooms are more silent. In my opinion this is one of the impacts of emergency remote learning. Teachers were thrown into virtual teaching and instruction via Zoom led to students needing to be muted due to background noises as home. In order to manage classroom behavior virtually, students had to wait to be called on & unmute - many were used to various ways of responding rather than being called on one by one. It was difficult to to have students think-pair-share effectively. Yes, teachers found ways to make their lessons interactive such as, using the chat feature & using tools such as Padlet & Jamboard. But, students had less opportunities to have their actual voice heard during instruction.
It is important for teachers to intentionally bring back some of effective strategies that they had in place pre-pandemic. While socially distancing, students should be given the opportunity to share their thinking with a partner. Students can also participate in choral counting & choral responses without the delay on audio. If a district or school has students attending in person instruction, then it's time to acknowledge that some virtual teaching practices might not be the most effective. Let's maximize student voice to help them take ownership of their learning and provide teachers with real-time data as to their current mathematical understanding. It's not about adding more work to a teachers already full plate, but rather tweaking how time is spent during instruction. |
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