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The first thing that is part of making a good math lesson is the planning that happens prior to the lesson. You need to make sure the lesson is something your students are ready for. You need to make sure the lesson is engaging and will be easy for the students to understand.
The second thing that is part of making a good math lesson is allowing collaboration between the students. This will help the students learn to work together. Sometimes thing are also easier for the students to understand in kid language. You could use this when you notice some students just aren’t getting it no matter how many times you explain it. Spelt them into groups and let kid language go to work.
The third thing that is part of making a good math lesson is giving students a choice. There are always multiple ways to solve a math problem. By showing the students multiple ways gives them a better chance of understanding the math concepts while also giving them the ability to pick and choose the best way for them to complete the problem.

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Three essential aspects of a good math lesson are flexible grouping, thorough planning, and fostering a safe, mathematical environment and community.

While reading, I found myself agreeing heavily with the section on flexible grouping in chapter four. I think it is very important to provide the opportunity for collaboration in the classroom, especially in mathematics. Flexible grouping allows students to work together to problem solve, defend their reasoning, educate one another, etc. I loved how the book specified flexible grouping is not ability grouping. Flexible grouping encourages student-to-student learning and teaching.

The planning that goes into a lesson is as important, if not more than, the lesson itself. It may seem self-explanatory, but I found this part of the readings to be a point of reflection for myself. It is so, so important for the teacher to be well-educated and prepared, not only to teach the lesson (with multiple strategies created for different types of learners) but to also answer any questions students may have. I found the part about knowing your students to be interesting. You are able to anticipate and plan for questions and speed bumps better if you know your students well.

Creating a welcoming and safe classroom community in mathematics is something I strive to accomplish in my future classroom because I never felt I had one myself. I hope to create an environment students feel comfortable trying and failing. When a strong community is created, students not only learn more through trial and error, they are able to help one another.

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1. Differentiated instruction.
This is essential to a good math lesson because most math problems can scaffolded to an easier level or more challenging level for more advanced learners. It is the teacher's job to deliver instruction that is challenging yet attainable for all students. By differentiating instruction, the teacher learns to plan, teach, and understand where students of all learning levels come from during the lesson.

2. Positive attitude/ safe learning environment.
This is essential because students look up to us as their educators. If I am negative about math, and express that freely to my students, they will begin to reciprocate the same attitude, further damaging their learning and retention of math in future practices. If we also foster a safe learning environment, students learn that it is okay to make mistakes, especially in math. This will help students build a better relationship with the subject.

3. Communication
This is essential in every lesson, not just math. Communication is essential to make sure students understand what they are being asked to do in a math lesson. Without communication we have confusion. It is up to the teacher to clearly state what is being asked in each math lesson, and if it is not clear to students, it is essential that students can communicate their confusion, and the teacher can respond appropriately.

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One aspect of a good math lesson is that it has clear before, during, and after sections. These sections contribute to a good math lesson because they help deepen student learning by helping them understand the context of the lesson, the lesson itself, then helps them engage in a collaborative conversation with their peers about what was taught.

A second aspect of a good math lesson is that it has flexible grouping. By having flexible grouping, students can collaborate in pairs and groups when appropriate to do so. This allows students to get the experience of working collaboratively as many people do at work. Flexible grouping also incorporates grouping without it being done by ability. Ability grouping can limit students’ access to learn math.

A third aspect of a good math lesson is that there are different routines incorporated into lessons. Different routines can help student understanding and allow them more practice with concepts. These routines, such as number talk, have students practice problems and come up with different strategies and then collaboratively talk about different strategies they used. These promote problem solving, figuring out with method/strategy is the easiest for them, as well as collaboration while talking to others.

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One thing that makes a good math lesson is making sure the problem is understood. We do this before the lesson begins and because we need to ensure that students understand the task at hand before they begin working on it.

The second thing that makes a good math lesson is promoting a mathematical community of learners. This includes encouraging students to share ideas, respect each others strategies, and encouraging them to take risks. By doing these things, we allow students to complete their work with the help of peers and also see how students got to the answer using different strategies.

The third thing that makes a good math lesson is posing purposeful questions. When we ask students questions like, "How can this help you in the real world?" or "How did you get to that answer?", the response is open-ended. Any student can respond in any way and it gives other students the opportunity to hear the problem from their peers' perspective.

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One thing that makes a good math lesson is allowing collaboration. Students enjoy when they can work in groups because it "improves confidence, engagement, and understanding." Working in groups allows students to bounce ideas off of one another and use each other for help. It can also help students to work in groups because they may have a different method or explanation a teacher has not shown.

Another thing that makes a good math lesson is having a good plan. Planning of lessons is important. You should show students where they are and what the end goal is and have set steps of what is going to get them there as well as adapt away from your plan as needed. For example, if you thought you would do one day of division review before starting long division and it is obvious your students are not ready, you may need to do 2-3 days of review before teaching new content.

A third thing that makes a good math lesson is adapting content for different learners. This can include the use of calculators, one on ones, or partner support. This could also include helping students by having things such as word problems in native language.

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Through this weeks reading there are many things that can make up a good math lesson, but three of the most important things that I️ believe make up a good math lesson is the promotion of a mathematical community of learners, allowing students to be curious, and promoting productive struggle to occur.

First, the promotion of a mathematical community of learners is very important because when students are comfortable in the classroom while learning math, the piece of competence then comes at an easier rate then if students do not feel confident in their math classroom.  Through the JCPS framework, it mentions that assignments need to matter and relate to real life, and through doing this students will be more inclined to do the work that they are being given. Creating the environment that students trust what you are teaching and feel trusted with exploring different methods of solving will foster an environment that they will feel and know that they are growing.

This leads to allowing students to be curious. Part of during and after the lesson, there should be time that students can explore the ideas that they have about the topic to generate the connections and discussions that are important to have during the time that mathematics are being taught. If students are being told and then given 20 problems to do, they are not given time to explore their curiosity, which is not fair to students who are naturally curious. This creates excitement and fosters and environment that allows mistakes and learns from mistakes as they are exploring what they are wanting to know.

Lastly, as students are working, it is important for the teacher to promote students to engage in productive struggle. This would mean that students are trying and then are exploring their curiosity as they work through the tasks that they are given. It was mentioned in the text book that one of the best ways to grow as a learner is to not repeat what you know or to do things that feel impossible, but to have a challenge that really makes you think and you know that a mistake is okay, you will only learn from it. In order to promote this in the classroom, students need time to work while their effort is being encourages, and then the feedback that is given should focus on perseverance.

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The first component of a good math lesson that I believe in is flexible grouping. I have always preferred working through math lessons while being able to utilize my peers as a resource. I think in larger classrooms where the teacher has to float around, having peers is helpful. However, I also like that the textbook talks about setting roles in groups, how a teacher can influence these roles, and how individuals still need to show thinking and work.
I also thinks a good math lesson should clearly be able to build or demonstrate a progression of skills. The book talks about students seeing skills and concepts has a big interconnected web, rather than small individual skills. I feel like there have been many times that I have not understood how things connect or how to take strategies from one lesson into the next. I think providing connections for students allows them to pull from a larger knowledge base and helps thinking.
Lastly, the math community is so important. While reading about the three phase lesson process and all of the math routines which encourage so much sharing and talking to the whole class all I could think about was how I never did that in any of my math classes, because myself and others did not want to share and we were not really given the opportunities. I think creating a good classroom community where peers support each other and mistakes are ok is really helpful to planning and teaching a meaningful lesson for students.

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1. One thing that is very important to any math lesson are the things that becoming before the problem solving begins. Like the book discussed we need to focus on the 3 phases of the lesson and the beginning phase is very important. I believe that not only getting your students engaged before you begin but also giving them that time that is specifically for them to develop that background knowledge and determine what the problem is going to ask them. Having set time built in to your plan for this is so beneficial to not only make sure all students are ready but also help students build their confidence before being forced to complete a problem they don't understand.
2. Another thing that I find very important to a good math lesson is the environment in which you teach math and the attitude surrounding math in your classroom. From personal experiences and also throughout our reading it showed how important where and how you talk about and teach the lesson can have an impact on what your students gain from that lesson. If the students have a bad experience related to math during the lesson, they will not hold on to what they learned but instead how they felt.
3. Another crucial part to a positive good math lesson is focusing on differentiating for your students. No matter what group of kids you are working with they are all going to have different abilities, interests and attitudes towards math. In order to keep them motivated and foster positive math experiences you must meet your students where they are at.

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One aspect of a good math lesson is learning to activate, as the book said, their prior knowledge. It mentions how we are to remind students of what their personal experiences is and how it relates to the math concepts of the day. It helps them to be able to create a connection with the math and helps them recall what they need to solve the problems.
Another aspect is allowing students to let go. This gives them the opportunity to figure out how their personal experience is apart of their learning. It also gives them the opportunity to connect with different learning styles that are feeding off of each other and how they are problem solving together. This is also an opportunity for students to collaborate rather than having a teacher only answering their questions.
One last aspect is that all lessons will have a language-focused base. Rather than throwing a bunch of math vocabulary, we will ease into it. With using simple questions to figure out what they are doing, it allowed them to be able to understand it rather than it just being told to them with no working. This allows the students to fully understand what a concept is rather than just knowing what a quantity or other math vocabulary.

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Week 2 Reflection - Jacqueline Boulanger

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Week 2 Reflection - Jacqueline Boulanger

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There are many aspects to a good math lesson. First, a good math lesson is formed because the teacher has carefully and intentionally planned. During our chapters this week, we learned about The Planning Process. This is an 8 step process that outlines how to plan a unit or lesson. This process is essential to form a good math lesson because the teacher thinks through each part of the lesson, from how relevant the lesson is to the students, what the learning goals need to be, to deciding what activities and exercises need to be done to meet the learning goals. This process is critical to math instruction and using it will result in productive learning for students.

Secondly, it is essential for good math lessons to occur in a comfortable and safe environment. Creating a safe and open classroom environment helps students to feel more confident in the room they are in and the people they are around. Establishing good community norms will be beneficial for not only math lessons, but lessons and community building on an everyday basis.

Lastly, a good math lesson has a sense of equitable instruction. This includes providing clarity when needed, considering alternative formative/summative assessments, and providing extra practice for students who need it. It is also important to incorporate choice. This can be done through setting up different math stations or forming groups within the classroom for students to pick from. This will help students to build their math identity and agency, which will help them to build their math proficiency.

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1. One contribution that I think makes a good math lesson is careful planning. It is important to plan with the students in mind so that the lesson can reach their individual needs. Part of careful planning is first determining the learning goals. This connects to what we have been learning in EDTP 355 on assessment and planning in that planning should be done in a backward design process, starting with the learning targets. We must then consider our students' individual needs and select a worthwhile task. When careful planning is used, our students are more likely to succeed.

2.  Another important aspect of a good math lesson is phrasing. Chapter 4 and 6 discuss many different phrases to avoid and phrases to use. The way we form questions and encouragement for our students matters. It will either build or break down their mathematical agency. For example, instead of saying, "it's easy" or "let me help you," phrase it in a way that students feel encouraged to keep trying. Some better phrases are, "I wonder what would happen if you tried..." or "Please tell me how you figured that out."

3. A third aspect that I think is essential to a good math lesson is building a strong classroom community. When a classroom has a strong sense of community, students are more likely to share their strategies and encourage each other to succeed. This includes "encouraging students to take risks, share ideas, and respect each other's strategies even when they disagree" (61). This can be done by facilitating learning centers where students can collaborate. It is also important to "incorporate children's questions, interests, and lives" (105). This way students can connect what they are learning to their own experiences.

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One thing that makes a good math lesson is establishing clear directions. The textbook talks about students needing to know how they will work and what products they are to prepare. I like the idea to do a think,  write, pair, share. This gives students the opportunity to really think abut what they are being asked to do and if their is any confusion they have a chance to talk to their classmates about what is expected. I think talking to classmates helps because they can sometimes explain it better in a way kids can understand.

Another thing that makes a good math lesson is incorporating choice. The textbook talks about how choice increases student motivation and helps students become more self-directed learners. I know in reading when students choose their books and in writing when students choose what to write about, they are more engaged and willing to do their work so I think this is also just as important in math.

One last thing that makes a good math lesson is providing appropriate support. The main key to this is to keep them engaged in the task without giving away to solve it. It is important in math to not just give the answers because then they will never really know. The textbook gives a variety of questions you can ask to provide this support like, "What have you tried so far?" or "Does this remind you of another task we have done recently?" This support is essential for math lessons because it is the only way they will truly learn.

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One thing I believe is essential to a good math lesson is that the student feel comfortable in their learning community, meaning the math community is acceptable to all learners and their contributions in class. I think this is important because it shows students that their answer is acceptable no matter how right, wrong or small it may seem. This way students still contribute to show that they are trying to learn.
Another thing that I believe is essential to a good math lesson is listening actively without evaluation and asking follow up questions. This way the students can explain their thinking so the teacher is able to understand how they go the answer they did and helps them to think more about the question if they are stuck.
Another thing that I believe is essential to a good math lesson is making sure expectations are clear for students. This way the students are not confused going into the lesson and they know what is expected of them. I think that this is important because if the students know what they are doing going into an activity they are more likely to participate.

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One thing that I believe is essential to a good math lesson is establishing norms and building a safe space for students to share their ideas. Many math routines involve listening to others and sharing ideas, so it is crucial that students feel comfortable and safe to share their ideas and make mistakes. Math can be anxiety provoking for many people, so you want students to know that in your class everyone supports each other and their learning.

Another thing that is essential to a good math lesson is a well-planned lesson. This includes using the standards to determine goals, considering student’s needs, strengths and designing effective assessments.

The last thing that is essential to a good math lesson is differentiating instruction. We want to be able to support and challenge all students to learn math. I like how the book refers to it as a low floor and a high ceiling so that everyone can engage in the task and extends to challenge anyone. One way to do this is by giving student choice in their learning. Giving choice increases student motivation.

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1. Use of manipulatives:
Incorporating manipulatives during a math lesson support explicit strategy instruction. Allowing students to play and use manipulatives during the lesson allows them to view the math concept more concretely rather than abstract because they are able to  feel and use the manipulatives in a way that make sense to them.
2. Establishing clear expectation:
In order for the lesson to run smoothly, students need to master the expectation. When the routine is practiced, students are able to use the time wisely and it can create an environment that everyone feels safe during instruction time. Setting an expectation for students allows them to thrive in a routine where they understand their role and how they should work.
3. provide clarity:
In chapter 6 on page 117, it describes ways to provide clarity during math. Clarity is something that will make students succeed during instruction because they are being informed through visuals, conversations, and collaboration. These are three ways that support students' development in math and it will ensure that students understand the content that they are learning. Providing examples and non-examples through a visual representation is another way to clarify to students to support their understanding.

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There are three major components that make a good math lesson. The before, during, and after all have an impact on how the lesson will go.
I believe making sure the class understands the math problem first is the most important step to follow before they start the problem. If students do not understand the task at hand, they will most likely never start it. This was something I struggled with in class a lot. If I already did not understand the problem, it made me feel defeated and not want to even try. Ensuring students understand the problem does not mean giving them the answers. It is better to approach this by analyzing the problem with the students and giving them examples to how they use various strategies to approach doing the work. This correlates with the framework because one of the things teachers are supposed to do is model thinking.
During a good math lesson, students should feel supported while the teacher is letting go. In the textbook, letting go and providing support were under separate categories. I believe there should be a good mix of both. Teachers should make students feel supported as they embrace productive struggle. There should be a shift to use their classmates as a resource to explain an area another student may be struggling in. With that being said, when a student is stuck they should feel safe enough to go to the teacher for help.
After the lesson, it is good to listen actively without evolution. This works to build a community in the classroom and makes students feel comfortable while sharing their answers. With this approach, students are more willing to share their ideas rather than focus solely on if the answer is correct. While students share their ideas, it is better to suggest comments of interest and extension because it shows more value to their thoughts. This will continue to build student's confidence.

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1) Establishing clear expectations is crucial for a math lesson. In our textbook, VDW discusses the 'think-write-pair-share' approach (page 58). I think using this approach can allow students to ease themselves into the lesson and get a grasp for what is expected of them. This also gives students the chance to collaborate on the content before tackling it on their own.
2) Implementing open questions instead of closed would be helpful as well. For example: The answer is 9, what could the equation be? Instead of asking: What is 4+9? This is an easy way to transition into a number talk and can be used as a introduction into a number talk activity.
3) Integrating assessment into instruction is crucial to a good math lesson. If the only way you assess your students is through tests, you will not be able to gauge their progress. Assessing your students throughout the lesson by simply asking questions can help you determine if students need more explanation on the content.

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1. Intentional design in three phases (before, during, after). Designing math lessons with the before, during, and after sections in mind ensures that each lesson is well-structured and includes time blocks for important pieces of the lesson.
2. Number talks. Number talks are important because they get students thinking, allow for all students to participate, and contribute to a safe and inclusive learning environment, among other things.
3. Differentiation. Differentiating lesson plans is important because with 20-30 students in a classroom, there will never be a full class of students who all think and learn the same way and at the same level. Therefore, teachers need to prepare for flexibility and create lessons that will include all types of learners. Students with special needs, multilingual learners, and everyone in between may need different things in order to be successful. One way to ensure differentiation is offering choice.

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One aspect of a good math lesson is that it connects to students' prior knowledge and experiences. Both chapter 4 and the JCPS instructional framework explain that teachers should activate prior knowledge during lessons so students can form connections using things they already understand. During a lesson, teachers can help students by asking questions such as “Does this remind you of something you have done before?”.  I think this gives students confidence, and their prior knowledge gives them a good foundation to tackle new problems.

Another thing that contributes to a good math lesson is when students have opportunities to collaborate with others. Chapter four of the book explains that flexible grouping and collaborating during a lesson helps students improve their confidence, engagement, and understanding. This also applies to the after lesson phase- the environment should be set up in a way for students to share their ideas and have meaningful discussions with their peers, whether they agree or disagree.

Clarity is also very important in a math lesson, especially for students who may need additional support. Clarity includes emphasis on the most important points, supporting organizing written work (providing charts, tools, templates) , providing examples and non-examples, using correct math language, etc. When a lesson is planned with clarity in mind it prioritizes equitable teaching and helps students learn in a way that is clear and not overwhelming.

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What makes a good math lesson? Tell me three things you believe to be essential to a good math lesson based on what you read this week.