Magic School AI

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The world of AI tools is vast and ever-evolving. Amongst the sea of options, one particular tool has caught my attention: Magic School. With a focus on teachers and schools, it offers a unique approach that sets it apart from the rest. Its comprehensive range of categories opens up exciting possibilities for integrating AI into different educational contexts. The best part? It comes in both a free and paid version, tailored to suit varying needs. Allow me to share an image of its advantages from their official website. Get ready to dive into a world of innovative possibilities!

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On the home page, you will find 66 different categories. Some examples of these categories include Math Spiral Review, Standards Unpacker, Sentence Starters, Text Leveler, and IEP Generator, among many others. As I was curious, I decided to take a closer look at the Standards Unpacker category. What caught my attention was the fact that it addresses the specific skills that students need to succeed, provides clear Learning Targets, and summarizes the standard. However, I found the Instruction and Assessment Plan section to be somewhat vague. Nevertheless, one interesting aspect is that you can go back to the tool and use that initial plan as a starting point to create a more detailed and thorough plan.

Standard: 5.NBT.A.1

Break Down Standard:

Skills: Recognizing place value in multi-digit numbers
Knowledge: Understanding how the value of a digit changes as it moves to the left or right in a number
Concepts: Place value, base-ten number system, positional notation

Define Expectations:
In this standard, 5th-grade students are expected to understand the concept of place value in multi-digit numbers. They should recognize that each digit in a number has a specific value determined by its position. Additionally, they should understand that the value of a digit in one place is 10 times greater than its value in the place to its right, and 1/10 of what it represents in the place to its left.

Formulate Learning Targets:
By the end of this standard, students should be able to:

-Identify the place value of digits in multi-digit numbers.
-Determine the value of a digit based on its position within a number.
-Describe the relationship between the value of a digit and its position.

Instruction and Assessment Strategies:
Use manipulatives, such as base-ten blocks, to help students visualize and understand the concept of place value.
Provide opportunities for students to explore and compare the values of digits in different positions within a number.
Use number lines and number charts to reinforce the concept and relationship of place value.
Engage students in problem-solving activities that require them to apply their understanding of place value.
Assess students' understanding through quizzes, worksheets, and real-life problem-solving tasks that involve place value.

Summarize:
In this standard, 5th-grade students are expected to develop a deep understanding of place value in multi-digit numbers. They should be able to recognize the value of each digit based on its position within the number and understand the relationship of each digit to its neighboring digits. Instructional strategies such as hands-on manipulatives, visual aids, and problem-solving activities can help students master this concept. Assessment strategies should include both formal and informal methods to gauge students' understanding and application of place value.

From my brief exploration, I believe that this tool has the potential to greatly assist teachers in working more efficiently. It eliminates the need for teachers to come up with learning objectives, develop grading criteria, and design lesson plans. Although AI should not replace all of a teacher’s work, it can certainly assist them in the more demanding tasks. Teachers will still have the ability to review and customize the generated outputs to suit their specific requirements. Overall, I am optimistic about the potential of this tool.

Winter Break Activities

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Winter Break is just around the corner, bringing with it a well-deserved break from schoolwork. The question of whether to assign homework during breaks has always sparked debate. In my district, we are lucky enough to enjoy a generous three-week break. This extended period of downtime can be a blessing for students. To make the most of this time, I developed an exciting Winter Break Activity board and a Kindness Calendar, taking the opportunity to engage students in meaningful and enjoyable activities. It is important to note that these are optional.

  • Activity Board

As you explore the Activity Board, you’ll discover a variety of captivating activities that students can freely choose from. Completing just three out of the nine options is all it takes to participate! It’s important to note that these activities are not meant to be completed within a short 15-minute period. They are designed to be flexible, allowing students to engage either with or without the use of technology. Additionally, I’m thrilled to share that during the break, I received proposals from some students who were keen on pursuing alternative activities, and I happily accepted their ideas! When we reconvene after the break, I make sure to allocate dedicated time for students to showcase and present their remarkable projects.

The Kindness Calendar is a favorite among parents! I have received numerous expressions of gratitude from parents and guardians for this calendar. They particularly value the reminders to “clean your room” and “get along with your siblings ALL day.” Parents also appreciate the underlying concept of promoting kindness, gratitude, and appreciation. This calendar is really a gift for parents.

And did I mention that this is available in English and Spanish? Well, it is!

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Mastering Mathematical Language Routine 8: Discussion Supports

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Looking back at the series of Mathematical Language Routines (MLRs) we have explored, we can see that their collective aim is to foster robust mathematical discussions and enhance language proficiency among students. These routines serve diverse purposes, such as refining ideas through structured conversation (Stronger and Clearer Each Time), stabilizing oral language as a reference (Collect and Display), refining written arguments through critique (Critique, Correct, and Clarify), promoting collaborative problem-solving through information sharing (Information Gap), empowering students to craft mathematical questions (Co-Craft Questions and Problems), facilitating comprehension and negotiation of math texts (Three Reads), and encouraging comparison and connection between various mathematical approaches and representations (Compare and Connect). Together, these MLRs not only elevate student participation and conversation but also cultivate meta-awareness of language, fostering a deeper understanding of mathematical concepts.

We conclude this series with Mathematical Language Routine 8: Discussion Supports. The goal is to foster inclusive discussions in math by combining multi-modal strategies that aid in understanding complex language, ideas, and classroom communication. These strategies encourage student participation, conversation, and awareness of language nuances. With continued modeling, the aim is for students to adopt these techniques independently, prompting deeper engagement among peers in discussions.

Having rich mathematical discussions can be challenging, especially when there are barriers that hinder effective communication. Recently, I encountered a situation where I was assisting a student with a math problem. The task was to determine the combination of rolls of coins needed to reach a specific amount. The problem provided information about the rolls of nickels and dimes, including the quantity each roll contained. However, during our discussion, it became evident that the student misunderstood the task. They believed they needed to determine the number of dimes or nickels in each roll, rather than finding the overall combination. To clarify this confusion, I decided to show them an image of a roll of coins and briefly discussed its concept, which helped them grasp the correct approach. This incident highlighted the importance of uncovering and addressing any gaps in background knowledge. It also underscored the significance of reflecting on the relevance of certain questions.

Having sentence frames is not only helpful to me but also to the students. The above image is one that I created based on Illuminate Math‘s suggestions. These sentence frames can guide the class towards deeper thinking and understanding. As mentioned before, the main objective of this routine is to encourage students to take the lead in these discussions. Additionally, it is important to note that this particular routine can be integrated into any of the other Mathematical Learning Routines (MLRs).

This concludes our multi-part series on the 8 Mathematical Routines. I highly encourage you to start implementing these routines in your day-to-day math class. To further support you on this journey, I have gathered a variety of helpful resources, which you can access here. If you have any additional resources to share, please don’t hesitate to reach out. I will gladly add them to the collection and give you proper credit.

Mastering Mathematical Language Routine 7: Compare and Connect

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In the previous Mathematical Language Routine (MLR) discussions, we explored a variety of essential skills. MLR 1 focused on enhancing our understanding by revisiting and reinforcing key concepts, making our knowledge “Stronger and Clearer Each Time.” We then moved on to MLR 2, where we delved into the crucial skill of “Collecting and Displaying” data effectively. Building on this foundation, MLR 3 emphasized the importance of “Critiquing, Correcting, and Clarifying” our models and methodologies for optimal results. In MLR 4, we explored the “Information Gap” and how to use this strategy to be thoughtful of the information needed to solve problems. Continuing this journey, MLR 5 introduced the skill of “Co-Crafting Questions and Problems” collaboratively to foster innovative approaches and insights. Finally, in MLR 6, we explored the technique of “Three Reads,” emphasizing the significance of multiple reads in order to enhance student understanding. Let’s now embark on our next MLR discussion, MLR 7 Compare and Connect.

MLR 7: “Compare and Connect,” has the purpose of fostering students’ meta-awareness in their exploration of different mathematical approaches, representations, concepts, examples, and language. Through this MLR, students are encouraged to reflect on and verbally respond to these comparisons. This involves analyzing why certain mathematical actions or statements are done in a particular way, identifying and explaining connections between various mathematical representations or methods, and pondering how one idea relates to others in terms of both concepts and language. To support this learning process, teachers should model their thinking aloud when addressing these questions. This routine allows students to engage in rich mathematical conversations. We will explore two ways in which to accomplish this.

Which one doesn't belong

Getting students to engage in discussions about math, make connections, and consider different perspectives can be quite challenging. I often encounter students who simply say, “It was in my brain” or “My brain told me the answer.” However, by modeling and encouraging metacognitive awareness, students can begin to make connections on their own. One effective routine that focuses on linguistic skills is called ‘Which One Doesn’t Belong‘. This activity can be done in groups, in pairs, or as a whole class. Students are presented with four images, equations, numbers, graphs, or geometric shapes, and they are asked to identify a commonality among three of them and explain their reasoning. The interesting twist is that any combination of three out of the four options can be correct. For example, in the orange example, one could argue that the three triangles go together and the hexagon is the odd one out. Alternatively, one could justify grouping all the white-filled shapes while excluding the shaded shape. This activity is both enjoyable for students and provides the opportunity to hear and consider different viewpoints.

Another interesting activity that aligns well with this MLR is the Math EduProtocol Sous Chef from The EduProtocols Field Guide Math Edition (Chapter 9, page 56). In this activity, students are grouped together to solve a problem using different approaches and then present their work to the class. For instance, if students were given the task of solving 4 x 6 in third grade, one student might use equal groups, another could opt for repeated addition, a third student may create an array, while the last student represents the equation with the area model. Through this activity, students can establish connections with previously learned concepts and broaden their understanding. There are numerous ways to implement Sous Chef, but the central focus remains on fostering connections among ideas and encouraging students to share their thought processes orally.

In conclusion, incorporating this MLR into your math class will greatly benefit your students. It will help them enhance their meta-awareness, make connections between different concepts, and foster a deeper understanding of the subject. While we have explored two approaches to this MLR, there are numerous other equally powerful techniques available. In our next discussion, we will delve into MLR 8: Discussion Supports, which focuses on stimulating rich and meaningful conversations in the classroom.

Mastering Mathematical Language Routine 6: Three Reads

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In our recent posts, we have explored various Mathematical Language Routines (MLRs) that aim to foster language development in the math classroom. We have covered MLR 1: “Stronger and Clearer Each Time,” MLR 2: “Collect and Display,” MLR 3: “Critique, Correct, Clarify,” MLR 4: “Information Gap,” and MLR 5: “Co-Craft Questions and Problems.” Each of these MLRs has offered valuable insights into different aspects of language acquisition in mathematics, be it written and oral expression, oral language proficiency, or the comprehension of tasks and word problems.

MLR 6: Three Reads

Building upon these discussions, let’s now delve into our next MLR, MLR 6: “Three Reads.” This routine plays a crucial role in enhancing reading comprehension and developing meta-awareness of mathematical language. By engaging in this exercise, students get the opportunity to practice navigating the intricacies of math-related questions, which often pose challenges for them. Through multiple readings, they can better understand the unique ways in which math concepts are presented and effectively plan their strategies for problem-solving. MLR 6: “Three Reads” serves as an important tool for supporting students’ grasp of mathematical language and equips them with the skills needed to tackle word problems with confidence.

The Three Reads protocol is a powerful tool designed to enhance students’ understanding of mathematical word problems. Its main purpose is to break down complex problems into manageable steps that students can comprehend, analyze, and solve successfully. This protocol is particularly beneficial for multilanguage learners and students with academic disabilities who often struggle with comprehending mathematical texts.

The Three Reads protocol begins by encouraging students to focus on the meaning of the problem. Instead of rushing to perform calculations, students are prompted to truly understand the context and situation described in the word problem. This initial step allows students to connect with the story or situation presented and reflect on its implications.

After gaining a solid understanding of the problem’s context, students move on to the second read. Here, they concentrate on identifying the units and quantities involved in the problem. By focusing on these key components, students can make sense of the mathematical concepts and relationships embedded within the word problem.

Finally, during the third read, students shift their attention to the specific tasks or questions asked in the problem. By this stage, students have already engaged deeply with the problem’s meaning and mathematical content. They are now able to formulate a plan of action and approach the problem in a strategic manner.

The Three Reads protocol supports not only reading comprehension but also sense-making and meaningful conversations around mathematical texts. By emphasizing understanding and meaning before diving into calculations, students are given the opportunity to reflect on different presentation styles, negotiate interpretations, and explore multiple solution strategies.

Let’s explore an example that demonstrates how to implement the protocol of co-crafting questions with students. In this example, Mateo’s M&Ms, the quantities are initially hidden to allow students to focus on comprehending the story. Once they grasp the concept that Mateo has a bag of M&Ms with different colors, the quantities are revealed. At this point, students can create a T chart to organize the quantities and their corresponding units. Although the units are the same in this particular example, it’s important to note that it may not always be the case in every word problem. Utilizing the T chart helps students effectively organize the information. Moving on, the final phase of this example involves students creating their own questions, reminiscent of MLR 5. By allowing students to differentiate and choose their own questions, they are encouraged to tackle more challenging problems rather than opting for the easy way out. This approach also fosters open-ended questions that lead to a variety of possible solutions. It’s a wonderful way to introduce this routine. Additionally, another teacher in my district, Nicole Garcia, and I have developed a recording sheet to assist students in organizing their thoughts and work. It’s worth noting that it’s also practical to address problems that already come with pre-established questions. In these cases, steps 1 and 2 of the protocol remain the same. However, in step 3, students formulate a plan to answer the provided question. Once again, reading the story multiple times allows students the necessary time to grasp and organize the given information.

Example of a 3 Reads

In summary, the Three Reads protocol encourages students to engage actively with mathematical questions, reflect on presentation styles, and negotiate meaning. By following this routine, students can develop a deeper comprehension of word problems, improve their mathematical reasoning skills, and ultimately enhance their overall problem-solving abilities.

Mastering Mathematical Language Routine 5: Co-Craft Questions and Problems

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In this ongoing blog series on Mathematical Language Routines (MLRs), we have covered four essential routines so far. Let’s recap their key ideas: MLR 1: “Stronger and Clearer Each Time,” MLR 2: “Collect and Display,” MLR 3: “Critique, Correct, Clarify,” and MLR 4: “Information Gap.” These routines are designed to enhance oral and written communication skills in mathematics. Now, let’s turn our attention to MLR 5: “Co-Craft Questions and Problems,” which offers a unique approach. It encourages students to actively participate in the question and problem-solving process, enabling them to explore mathematical contexts before seeking answers.

In MLR 5, students are given the opportunity to dive deeper into problem-solving by creating, analyzing, and enhancing mathematical questions, problems, and situations. The purpose of this routine is to provide students with a space where they can generate, analyze, and improve their understanding of mathematical concepts, specifically word problems. Through engaging in conversations, students refine their ability to formulate, select, and refine questions, allowing them to develop stronger critical thinking skills. This routine fosters students’ ability to use conversation skills effectively in the process of formulating, selecting, and refining their mathematical questions and problems. By actively participating in these conversations, students take ownership of their learning and become more proficient problem solvers. Curiosity Creator, found in The EduProtocols Field Guide Math Edition, Chapter 18, is one way to practice this routine.

Another excellent routine that can be seamlessly integrated into MLR 5 is the 3-Act Math Task, originally developed by Dan Meyer. This ingenious task involves providing students with minimal information, serving as a catalyst to foster curiosity and encourage them to generate questions that they can later answer with additional information provided in subsequent acts.


The first act, known as Act 1, is designed to stimulate students’ observation skills and curiosity. During this phase, students are encouraged to ponder upon what they notice and wonder about the given scenario. They also formulate questions that they will eventually solve. Act 1 is an opportune moment for students to engage in conversations regarding their observations, estimations ( too high, too low, or actual), a specific focus question, and the type of information they need to answer their own question.


In Act 2, students are provided with the necessary information to solve the problem or question they crafted in Act 1. Armed with this newfound knowledge, they embark upon the solving process.
Finally, Act 3 allows students to review the actual answer and assess whether their initial predictions were correct.

This routine is highly engaging for students across all levels, offering a perfect balance between accessibility and challenge. It also offers a wide range of ready-made, standards-aligned tasks suitable for students from Kindergarten through high school. By incorporating the 3-Act Math Task routine into the classroom, instructors can empower students to actively participate in problem-solving, develop critical thinking skills, and cultivate a deep understanding of the importance of co-constructing problems and questions.

Mastering Mathematical Language Routine 4: Information Gap

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Recap of the previous MLR discussions: We have reached the halfway point in the series of Mathematical Language Routines (MLRs). So far, we have explored MLR 1: “Stronger and Clearer Each Time,” where the focus was on enhancing understanding and communication skills through the use of the “Convince Me That” technique. This was followed by MLR 2: “Collect and Display,” which aimed at expanding students’ academic vocabulary. MLR 3: “Critique, Correct, Clarify” was centered around improving both oral and written skills, utilizing the EduProtocol Nacho Problem. Now, let’s introduce MLR 4: “Information Gap,” a personal favorite, which promotes collaborative work and helps students identify critical information necessary for solving word problems. This routine plays a vital role in fostering meaningful interactions and communication in the realm of mathematics.

One of the biggest issues in math classrooms is the challenge of word problems, also known as story problems. These problems require students to go through multiple steps, including reading comprehension, deciphering the question, creating a plan, and solving the problem. However, students often struggle with knowing how to use the given information and which details are relevant to the solution.

To address this problem, Information Gap tasks have been developed to help students navigate this challenge. In these tasks, students are divided into two groups: one group has the data card, while the other group has the problem card.

The group with the problem card reads the problem silently and asks the group with the data card for the information necessary to solve the problem. It’s important that neither group shows their cards to the other. Before sharing the information, the group with the data card asks the problem group why they need that specific information. This process encourages the problem group to justify their reasoning and ensures that they have thoroughly thought out the solution process.

This collaborative process continues until all the required information is obtained. Once both groups have shared their cards, they can work together to solve the problem. The goal of this approach is to create a need for students to communicate and collaborate, as this type of task cannot be accomplished alone.

When starting this process, it is beneficial to demonstrate it to the class. Initially, I present the problem card to the entire class while holding the data card myself. I then instruct students to work in pairs and determine what information they need. They are encouraged to formulate questions to obtain the necessary information and provide a rationale for why they need it. I repeat this process several times until the entire class understands their roles. Gradually, I reduce the group size over time until they are working in pairs to complete this task. This routine helps students to slow down and approach their thinking more deliberately.

In summary, Information Gap tasks are designed to promote collaboration and problem-solving skills among students. By requiring them to share different pieces of information both orally and visually, these tasks facilitate effective communication and enhance their ability to work together towards a solution.

In the upcoming post, we will delve into MLR 5: Co-craft questions, where we explore how 8 P*Arts meets Word Problems, 3-Act Math Task, and Emoji Word Probz perfectly align with this approach. Join us in the next installment of the series to discover exciting examples and techniques that will surely ignite your interest and leave you eager to come back for more. Stay tuned!

Mastering Mathematical Language Routine 3: Critique, Correct, and Clarify

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Welcome to the fourth installment of our series, where we delve into the fascinating realm of Mathematical Language Routines (MLRs). In our previous discussions on MLR 1: Stronger and Clearer Each Time and MLR 2: Collect and Display, we explored the crucial role they play in cultivating critical thinking skills and fostering a deep understanding of mathematical concepts. Let’s continue our journey toward mathematical success by exploring the next MLR in line.

MLR 3: Critique, Correct, and Clarify is a routine designed to enhance mathematical writing and discussions. The primary purpose of MLR 3 is to foster a culture of critique and improvement in mathematical conversations. By engaging in this routine, students are encouraged to actively evaluate, correct, and articulate mathematical concepts with clarity. Through collaborative groups or partner talks, students can refine their thinking as they work together. To introduce this routine, teachers can model it by providing a predetermined piece of writing for critique, ensuring that it includes common errors and vague language to encourage more precise language. This approach empowers students to identify and rectify mistakes while enhancing their ability to clarify their ideas effectively.

Beginning this routine can be tricky, especially since it involves critiquing and correcting another person’s work. However, there are strategies that can help create a safe space where students feel comfortable critiquing and correcting each other’s mathematical reasoning.

At the middle school and high school levels, it is a bit easier as students change classes, and using an example from another class can happen – with names removed.

For elementary-level students, making up a problem/solution that they can use to critique is advisable. It’s important to ensure that the problem/solution contains common errors related to the content being studied.

Once this routine is established, it will become easier for students to seek out peer feedback. Teachers play a crucial role in creating a safe environment where students feel encouraged to seek out one another for critiquing. By implementing these strategies, teachers can foster a supportive and collaborative atmosphere for students to improve their mathematical reasoning skills together.

One Math EduProtocol that works well with this MLR is Nacho Problem. This EduProtocol was developed by Ligia Ayala-Rodriguez with the intention of addressing common errors exhibited by students. The main concept behind Nacho Problem is to task students with identifying and explaining the errors they encounter. Let’s take a look at an example to better understand how it works:

Second-Grade Nacho Problem Example

Ms. Daines needs to drive to San Jose which is 109 miles away. Along the way she stopped in Salinas which is 48 miles away. When she began driving from Salinas, how far away was Ms. Daines from San Jose? The work was provided but no explanation was given. This allowed for students to critique and analyze the provided work, find the error, and clarify their reasoning.

In this example, which was taken from an introductory lesson using Nacho Problem, the wording is kept basic and straightforward. However, as students progress with this EduProtocol, their written expression and complexity will naturally grow.

The beauty of Nacho Problem lies in its simplicity and effectiveness. By encouraging students to find errors and explain their reasoning, it promotes a deeper understanding of mathematical concepts. So, if you’re looking for an educational approach that fosters critical thinking and problem-solving skills, Nacho Problem is definitely worth considering, but not your only option. Sometimes, always, never is another good approach to this MLR.

Incorporating MLR 3 into your math class can greatly enhance your students’ understanding and written communication skills, which are vital for their success. This instructional approach can be implemented as early as kindergarten, allowing students to develop the valuable ability to analyze others’ work critically. This fosters a deeper comprehension of mathematical concepts and empowers them to ask more precise and insightful questions. In our next discussion, we will explore MLR 4: Information Gap, where students are encouraged to engage in critical thinking by identifying the necessary information to solve word problems.

Mastering Mathematical Language Routine 2: Collect and Display

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In the previous post, we delved into the significance of the Mathematical Language Routine 1 (MLR 1) “Stronger and Clearer Each Time.” MLR 1 focuses on nurturing a deeper understanding of mathematics by encouraging students to thoughtfully articulate their thinking process, either individually or in groups. Through explanation and attentive listening, students refine their writing skills and strive to explain concepts at a more profound level, akin to mathematicians.

Mathematical Language Routine 2: Collect and Display

Now, let’s turn our attention to MLR 2, known as “Collect and Display.” The primary objective of MLR 2 is to capture the oral language utilized by students during discussions, creating a valuable reference for later use. This capturing process encompasses various forms, including words, diagrams, and images. By collecting and displaying this language-rich content, MLR 2 aids students in establishing connections between different mathematical concepts, as well as facilitating the integration of academic language into their understanding and expression. Additionally, MLR 2 provides immediate feedback, an essential element in student learning, and offers a structured framework for self-reflection and language usage. Join along as we explore MLR 2 further in this post.

The focus of this routine is to collect students’ thoughts using verbal, pictorial, and diagrammatic representations. Although visuals play a role, they are not the main focus. The purpose is to explain the importance of using visual aids to collect and showcase student ideas in mathematics.

This routine aims to stabilize the ever-changing language used by students so that their own output can serve as a reference in developing their mathematical language. The teacher actively listens and records the language employed by students during discussions, whether it’s in pairs, small groups, or the entire class. This includes capturing written words, diagrams, and pictures.

The collected output can be organized, restated, or connected to other language in a display that all students can refer to, build upon, and make connections with during future discussions or writing activities. Throughout the unit, teachers can use the displayed language as a model, update and revise the display as student language evolves, and create connections between student language and new disciplinary language.

This routine provides valuable feedback to students, enhancing their understanding while simultaneously fostering their awareness of language.

When it comes to collecting data during student discussions in math class, there are effective strategies to encourage students to represent their mathematical thinking visually. One popular approach is incorporating Number Talks, a practice already utilized by many teachers. During Number Talks, teachers can record their methods and thoughts, which not only helps them make connections but also allows for discussions about the most efficient approaches. However, it’s important to note that sometimes students may overcomplicate their solutions to showcase the flexibility of their thinking. To address this, scribing these methods can help students realize the value of efficiency. Apart from Number Talks, there are other strategies to encourage visual representation of mathematical thinking. Teachers can introduce visual organizers like graphic organizers or mind maps, which help students organize and illustrate their ideas. Additionally, utilizing tools such as virtual or physical whiteboards or digital sketching apps can enable students to visually capture their thought processes. Activities like creating diagrams or pictures also enhance the collection of student ideas in a visual format, providing teachers with valuable insights into student understanding and promoting deeper mathematical thinking.

The method of collecting student data can vary depending on the teacher’s preference. Some teachers may opt for traditional methods like chart paper, prominently displayed in the classroom. Others may choose digital tools like Padlet. Regardless of the chosen method, the collected data will be easily accessible to students whenever they need it. It is encouraged for students to utilize these records when expressing their thoughts, whether orally or in writing. As a teacher, it is important to highlight this resource for students and demonstrate how to effectively utilize it.

In conclusion, we have explored the significance of MLR 2: “Collect and Display” in fostering effective language students use to communicate their mathematical thinking. This routine has proven to be a valuable tool for students, as it allows them to actively engage with mathematical concepts and communicate their ideas effectively. By collecting and displaying their thinking, students can enhance their understanding and learn from their peers. Moving forward, we will delve into MLR 3: “Critique, Correct, and Clarify” in our next blog post. Stay tuned as we continue to explore the power of Mathematical Language Routines in promoting mathematical discourse and deepening conceptual understanding.

Mastering Mathematical Language Routine 1: Stronger and Clearer Each Time

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Mathematical Language Routines (MLRs) play a crucial role in enhancing students’ comprehension and communication skills in mathematics. Developed to meet the diverse language needs of learners, these frameworks have become an invaluable tool in promoting a deeper understanding of mathematical concepts. In this series, we will explore each MLR in detail, starting with MLR 1: “Stronger and Clearer Each Time.”

Mathematical Language Routine 1: Stronger and Clearer Each Time

MLR 1: “Stronger and Clearer Each Time” focuses on refining students’ ideas and communication through various activities. By incorporating writing, listening, explaining, and integrating new language, students are encouraged to continually improve their understanding of mathematical concepts. This routine, often conducted in pairs, provides students with the opportunity to collaborate and build upon each other’s ideas, fostering a culture of shared learning and growth.

Throughout this series, we will delve into the different structures and strategies that can be employed within MLR 1, unveiling how this routine nurtures students’ confidence and fluency in mathematics. Join us as we explore the remarkable impact of MLR 1 and its profound influence on students’ language development and mathematical achievements.

The purpose of this routine is to foster the refinement of students’ verbal and written output through structured conversation and revision. By engaging in this process, students can enhance both their thinking and their expression of it.

In this routine, students initially work individually or in groups, gradually progressing towards partner work. This approach allows students to acclimate to the task and build their confidence. For those who may be less familiar with writing, explaining, and refining their thoughts, supportive strategies can be implemented to ensure their success.

Once the structures are in place, it is crucial for students to recognize the ultimate goal, which is either a deep understanding of the concept or the ability to articulate it like an expert. The listener’s role becomes significant as they ask clarifying questions, enabling a comprehensive understanding of the speaker’s thoughts. Simultaneously, the speaker benefits from this exchange, refining their thinking more clearly.

To encourage thorough responses, it is valuable to have students switch partners multiple times during the routine. By engaging in back-and-forth conversation, with equal emphasis on speaking and listening, students not only refine their thoughts but also strengthen their language and reasoning skills. The iterative nature of this process reinforces the importance of pressing for details and encourages the continual refinement of ideas.

Convince Me That, by Daniel Kaufmann, is a highly effective protocol that teachers can implement in their math lessons to foster deeper understanding and engagement among students. To successfully introduce and implement this routine, educators can follow these step-by-step guidelines:

  1. Introduce the Problem: Begin by presenting a math problem along with its solution to the students. For instance, students can be asked to explain why 3 x 4 equals 12.
  2. Form Partners or Small Groups: Divide the students into pairs or small groups to facilitate collaborative learning. This structure encourages peer interaction and promotes the sharing of ideas.
  3. Restrict Algorithmic Thinking: Emphasize that students should focus on concrete or pictorial methods rather than relying on algorithms. This restriction encourages students to think deeply about the problem and explore alternative approaches.
  4. Initiate Individual Thinking: Give students time to think individually about the problem and develop their own explanations for the solution. This step helps to build independence and promotes critical thinking skills.
  5. Structured Pairing: After individual thinking, partners or group members should share their explanations with each other. This process enables students to refine their understanding through constructive discussions and peer feedback.
  6. Revise Written Responses: Encourage students to revise and improve their written explanations based on the feedback received during the structured pairing phase. This step promotes self-reflection and reinforces learning.

To facilitate the refinement process and prompt students effectively, here are some examples suitable for Math Learning Routine (MLR) 1:

  • “Convince your partner why the sum of any two even numbers is always even.”
  • “Explain to your group why dividing by zero is undefined and cannot result in a finite number.”
  • “Justify why the product of any number and zero is always zero.”

These prompts stimulate students to think critically, apply their knowledge, and refine their explanations. By implementing the Convince Me That routine with these strategies and prompts, educators can foster deeper conversations, encourage active learning, and enable students to demonstrate a more profound understanding of mathematical concepts.

For a more detailed explanation and implementation guidelines, you can refer to Chapter 19 of The EduProtocols Field Guide Math Edition. This invaluable resource offers comprehensive insights and practical tips for effectively utilizing the Convince Me That routine in math classrooms.

In conclusion, the implementation of MLR 1 has proven to be highly beneficial for students. It provides them with a structured platform to refine their thinking, improve their communication skills, and deepen their understanding of the subject matter. By engaging in the collaborative and iterative process of MLR 1, students are empowered to develop clearer and more coherent responses.

We invite you to stay engaged with our series and continue exploring the world of Mathematical Language Routines. The second routine in our series, MLR2: “Collect and Display”, has a specific purpose. It aims to capture students’ oral words and phrases and transform them into a stable, collective reference. The main goal is to preserve the language that students use and use it as a reference point for developing their mathematical language.