Recreational Math

When students are in the younger grades, teachers see more of their students actively engaged in their learning and what is being presented in the classroom. As they move through to higher grades, however, more and more students begin to feel and seem disconnected from their teachers and the classroom. A main difference between the elementary and high school classrooms is how content is presented. In elementary school, students learn content through direct instruction at times, but also get to use and practice the skills through games, puzzles, songs, etc. High school classrooms consist of much more lecture and worksheets assigned as homework, a process that repeats itself year after year. If more teachers in the upper grades included some games and puzzles, teachers would likely see more of their students interested and actively engaged in their learning, as they did when the students were in elementary school. 

The article What Is Recreational Math and How Can It Help Students gives an explanation of what recreational math is –  “any game, puzzle or activity that teaches math skills to help participants “win.”” (Fresno Pacific Staff, 2018) – then continues to explain some examples of recreational math and some of the benefits it can have for students. While the article focuses more on implementing recreational math in the younger grades (“with younger students” is how the author describes the age level intended), there is no reason recreational math can not or should not be included in the secondary math classroom as well. As described in the article, recreational math can be from playing games such as Sudoku to solving brain teasers. This comment means that teachers would not even necessarily have to recreate their lessons, but simply incorporate different ways of allowing the students to explore the content being taught. 

This article made me think about how recreational math can be implemented in all aspects of education. Since most assessments tend to reflect the types of problems presented in class, I think recreational math problems (such as brain teasers or puzzles) can be included in student assessments. If students are learning the content through puzzles and games, I don’t see any reason why they can’t be assessed using those same puzzles and games. These kinds of assessment questions could also challenge students’ logic, reasoning, and sense making skills. For example, if students were presented with a picture of a game they play that requires several steps to win (similar to chess, just math version), the question could ask students what their next move would be, why they would make that move, and to show and explain symbolically (i.e. with math) what their move does (whether it be checkers and it subtracts the other person’s number of pieces, adds to your number of kings, etc.). I also think recreational math could be implemented in students’ daily routines. I have always liked the idea of, every month or so, giving students a “free time packet” that includes activities students enjoy that they can work on in down atime during class. These packets could include some recreational math activities and puzzles that students can practice over time. The puzzles could be looking ahead to something the students will be learning soon to see what they already know, or it could be practice of skills they already know to make sure they practice those skills regularly throughout the year. 

I will use the information from this article in my career as a teacher when planning activities for my students. I want my students to think of my classroom as a place where it is safe to explore and question what is presented. I think including recreational math in the classroom will help students develop those skills, as they will be solving problems that they are interested in to practice and develop their skills in certain math concepts. I will challenge my students to try finding other ways to solve the problem, and if they can’t or they keep coming back to the same answer, I will again challenge them to write a math rule that is applied in the activity. Using these strategies in the classroom will keep students engaged, challenge them to develop the math for themselves, and lead to them remembering the content, since they now have ownership over what they discovered. 

The main thinking beyond the overall idea of recreational math that was presented in the article was the benefits recreational math gives students. The benefit I found to be particularly interesting was the benefit of improved scores. The article claimed that some teachers said they have seen improvement across math topics with their students when recreational math was introduced and practiced. I think this point is crucial to the argument for recreational math. Since recreational math helps students develop skills such as problem solving and reasoning, and teachers have seen improvement in all areas of math, recreational math does not need to be in every lesson. Even if teachers can only find time in their schedule to include recreational math once in a while, it is still important that they do so, since developing problem solving and reasoning skills are things that will help students with lessons that are taught without recreational math. 

Another resource that I explored about recreational math was a slide presentation on the topic. This slide made the interesting point that the games students play do not need to include actual math when playing, but may just have rules and/or outcomes that can be explained by math. The example the presentation gave was the game of Mancala. Though playing Mancala does not require any actual math, it is a game of combination theory that can be explained by math. For students in higher grades, a scenario like this could be presented and students (or groups of students) could be challenged to explain how the game works using math (i.e. discovering and explaining the combination game theory behind Mancala) or create the rules, timeline, and game board/card/pieces needed to play a new game that uses the same math as a game that already exists. 

Games and puzzles are things that are commonly seen in elementary school classrooms but, for some reason, disappear as students move to higher grades. Whether this issue is because of students maturing/teachers assuming students will not want to play games, or because teachers feel they do not have time to use games because of their massive curriculum, this is a pattern that need to change in the US. The US has the mindset that it is more important to cover more topics, even if it means going into less detail, rather than helping students gain a true mastery of the skills they are learning. Even though it would require a major culture shift, changing the mindset in the US to focus on depth over breadth will help students at all levels engage in their learning, and gain understanding and mastery of their skills – which would lessen review time needed at the beginning of each school year – and allow teachers to cover more new content with their students each year. 

Sources

Fresno Pacific Staff. (2018, September 26). What Is Recreational Math and How Can It Help Students. Fresno Pacific University. What is Recreational Math and How Can it Help Students? (fresno.edu)

Gupta, M. (2010, June 30). Recreational Mathematics. [PowerPoint Slides]. SlideShare. Recreational Mathematics (slideshare.net)

Using Pre-Assessments in Math

Teachers and students alike can feel overwhelmed with the amount of material that they are expected to get through in a single school year. From long, confusing standards, to complicated procedures that seem to go over students’ heads, teaching and learning math can easily become an overwhelming process. One way to break down this daunting task is to introduce pre-assessments into the math classroom and use them to assess students as they progress through their learning. 

Using pre assessments in the math classroom can be a helpful tool for teachers to assess student learning and students express what they already know and understand in a low risk setting. While many teachers may think it would be beneficial to see what students know about the entire curriculum at the beginning of the school year, as the article Using Digital Pre-Assessments in Math mentions, giving students a comprehensive overview of all topics they will learn becomes intimidating and the data gets outdated as students progress throughout the school year. It is instead easier and a better representation of student knowledge to do smaller assessments right before introducing the new topic, chapter, or unit to be covered. This way, teachers are seeing what students understand right when they are about to learn new content and teachers can better adapt and differentiate their instruction to meet the current needs of their students. A way to make these assessments even more user-friendly for both teachers and students, as mentioned in the article, is to use digital versions of these assessments that can automatically grade student responses so teachers can spend more time planning instruction rather than grading pre-assessments. 

This article made me think about how technology can be used as a helpful tool in classrooms. I personally think it is valuable to keep “old fashioned” styles of learning that involve tactile experiences and materials, but when used strategically, technology can be extremely beneficial for gathering and evaluating student data. Technology, such as Google Forms and other forms that can be implemented for pre-assessments, can be incorporated in classrooms to improve efficiency in seeing where students are and which areas need more focus and attention during instructional time. I also think these technologies can be an easy way to save activities and assignments that can be reused or modified from year to year for new groups of students. 

I will use the information from this article in my future classroom to justify using pre-assessments for all subjects, including math, as well as advocating for one-to-one ratios of students and technology. Through my K-12 career, we had access to devices such as laptops and iPads, but we never reached a one-to-one ratio. The information in this article can help show a practical application and justification for investing in these devices so each student can have access to digital resources and give teachers access to the data that can aid them in differentiating instruction to meet each student’s needs. 

The main thinking beyond the original idea of pre-assessments in math was how digital pre-assessments in particular can be helpful for both effectively assessing students are getting results in a timely and organized manner (i.e. how Google Forms organizes student responses into a spreadsheet). The article also talks about how to use the information gathered from digital pre-assessments can be interpreted and used. One point I found interesting was how teachers can interpret the information for the class as a whole. For example, if a group of your students are all ahead of the game on a particular topic/unit, you could plan an accelerated activity that they could work on in a small group while the rest of the class works on the grade level lesson. 

Another resource I explored about the topic of pre-assessments is a slide presentation explaining and justifying the use of pre-assessments in the classroom. This presentation contributed examples of various uses of pre-assessments in classrooms, questions to ponder when evaluating pre-assessments, and possible examples of pre-assessments. Following the slide with the list of examples, the presentation gave details for each example as well as tips for what to remember when using the assessment. 

Pre-assessments in the classroom may seem like a time-consuming element that is unnecessary, but finding ways to implement them on a regular basis is a way to benefit teachers by gathering relevant information about students as individuals as well as classes as a whole. Pre-assessments are yet another example of classroom elements that seem time consuming to plan and implement at first, but over time they give valuable insights into student understanding as well as examples of student work over time. These pre-assessments can be put into student portfolios and shown to administration and/or parents during conferences as proof of student work and improvement throughout the school year. When choosing which elements and activities to include into the classroom, teachers need to weigh pros and cons, considering the benefits the activities bring to students and teachers and how those benefits match up to the time needed to plan and prepare for those activities. 

Sources

Paul, K. (n.d.). Planning for Preassessment. [PowerPoint Slides]. n.p.       http://www.johnston.k12.ia.us/schools/elp/documents/preassessment08.pdf 
Using Digital Pre-Assessments in Math. (2019, March 2). Alyssa Teaches. Retrieved April 2, 2021 from https://alyssateaches.com/using-digital-pre-assessments-in-math/

Engagement in Distance Learning

Ever since the Coronavirus pandemic hit in spring of 2020, students and teachers have struggled to find ways to create and participate in meaningful learning from a distance. This unprecedented barrier to education created a new struggle that no one had encountered before. Teachers, students, and parents all struggled to maintain a high level of education quality, while working and learning from home, amidst a global pandemic. This presented many challenges, with a main one being students’ reluctance to actively engage in online learning. 

As a student in higher education, on the path to becoming a teacher, I can understand both sides of this struggle. I can see how teachers struggle to create a welcoming environment when they feel they are talking to a group of black screens and are unable to connect with the students behind the names. I can also, though, understand the students’ side of this struggle. Many students struggle putting themselves in the vulnerable position of sharing their thoughts and work in class in face-to-face environments, and a brand new environment where you feel you are learning on your own does not increase the welcoming feeling or the desire to be vulnerable and share thoughts with classmates. As the pandemic has endured, and distance learning has come to feel more normal, these fears and struggles have lessened for some, but there is always room for more engagement and participation. The edutopia article 8 Strategies to Improve Participation in Your Virtual Classroom describes multiple strategies that some teachers have started to include in their virtual classrooms that attempt to get students to share and participate in class discussions in synchronous and asynchronous classroom settings. The article includes a variety of strategies, shared by professionals in multiple areas of education. One general idea I found most interesting was the idea of giving students time to ponder concepts and ideas before being put in the position to share. It is well known in the field that students benefit from time to think about their own responses to questions before being asked to give an answer; hence the ever-popular “think-pair-share” activity. I think including this practice in online learning would not only be beneficial for students, but fairly easy for teachers to incorporate into their instruction. 

This article made me think about how popular in-person classroom activities (i.e. think-pair-share) can be incorporated in virtual classrooms – and possibly even keep their typical names. Having activities and names of them that students are familiar with and have done before can help make the virtual classroom space feel more familiar and welcoming. One specific idea I came up with for math was sending out a “morning work” type problem to students before class. At the end of one day’s class, the teacher could show students the problem for the next day (and send it out in email to students) and have students simply explore and brainstorm how they may go about solving the problem. The next day in class, the teacher could start by putting students in breakout rooms in small groups (3-4 students at most in one group) and have students share their thinking with each other in a format they are comfortable with (i.e. camera on or off, talk out loud or discuss in chat). When this time was over, the teacher could bring the class back together and ask students to share what they came up with, again in a format they are comfortable with. Over time, the teacher could encourage or offer incentives for students to be more vulnerable (i.e. talk out loud more than in chat) to create a space that feels a little bit more like a normal classroom. Using these activities on a regular/everyday basis could help students feel comfort in the support they receive from their teacher and help them become more comfortable sharing their work and thoughts in an uncomfortable setting. 

I will use the information from this article in my teaching to make any virtual or hybrid environment I find myself in more comfortable and familiar for both my students and myself. Though the COVID pandemic will likely be past by the time I am teaching, after this experience, I am likely to come across some situations that will include virtual or hybrid learning at some time in my career. The information from this article can help me find ways to make the uncomfortable setting more familiar and friendly for everyone involved. 

The main thinking beyond the original idea of ways to get students engaged in distance learning was the overall topic of challenges distance learning presented. Some of the challenges mentioned included those such as how it became more difficult to read facial expressions and body language over the computer (even with cameras on) and how technology struggles hindered back-and-forth communication between students and teachers as well as among students. 

Another resource I explored about this topic was a comic by npr that explained one teacher’s struggle with getting students to engage. The teacher explained how she felt isolated and like she was “teaching in an aquarium” when students were not participating or having their cameras on. As the comic went on, however, she showed how showing her own vulnerability to her students helped them warm up to the online classroom, turn their cameras on, and begin engaging more in the classroom. I think this is an important point for teachers to remember in virtual, hybrid, and face-to-face classrooms; seeing their teachers’ be vulnerable helps students feel more comfortable letting their guard down in the classroom. 

Though the COVID pandemic presented teachers and students with numerous challenges, after over a year of distance/hybrid learning, teachers and students have come to see this as the “new normal.” Though they have adapted to some aspects of this unprecedented learning environment, students and teachers still struggle with engaging in the classroom and making Zoom feel like a real classroom. By incorporating some simple strategies into virtual learning, teachers can show their students that the camera on their laptop is nothing to be afraid of and encourage students to open up to their teachers and classmates online. 

Sources

COMIC: How One Math Teacher Broke Through To Her Virtual Students. npr. Retrieved March 24, 2021 from Remote Learning Was Breaking This Math Teacher So She Showed Her Emotional Work. : NPR

Minero, E. (2020, August 21). 8 Strategies to Improve Participation in Your Virtual Classroom. edutopia. 8 Strategies to Improve Participation in Your Virtual Classroom | Edutopia

Escape Rooms in Education

Escape rooms have become a popular trend around the country; people enjoy the challenge of time pressure and puzzles these activities present. These escape rooms give people a fun and engaging way to use life skills that are also used in everyday life. With this trend, more and more teachers have begun creating escape room-style lesson plans. These lessons appear in any and all subject areas as a way to engage students in a fun and entertaining way to practice and strengthen their skills. 

Escape rooms can be a very effective tool for teachers to use in their classrooms. As the article Educational Escape Rooms: Benefits, Examples & More! explains, escape rooms provide an opportunity for students to develop life skills such as teamwork, problem solving and respect. Especially when a time limit is included with these activities, students must focus on working together with their teammates/group members while solving challenging academic problems. By participating in these types of activities regularly, students will learn how they act under pressure, and become aware of new aspects of their personalities they may not have been aware of before these experiences. 

This article made me think about how escape rooms can be used at different times in teaching. From what I have seen/read, it seems escape rooms are most often used as review activities and/or additional practice on topics already taught. I feel escape rooms could also be used at the beginning of teaching certain topics. Having answer options that are chosen based on anticipated student answers will allow teachers to see which misconceptions students have on the topic and adjust their lesson(s) accordingly. 

I will use the information from this article to justify using class time to include escape rooms in my teaching on a fairly regular basis. While these activities are time consuming, both in planning and execution, they have many benefits that justify them being included in a classroom environment. I will use escape room-style lessons to review before chapter and/or state testing, as well as introduce certain new topics to see what misconceptions my students have and cater my lessons to their needs. 

The main thinking beyond the main idea of escape rooms that was presented was how games in general help students engage and actively participate in learning. While escape rooms are more physical and engage students in multiple aspects of learning, other games that have less plan and/or execution time can also help students get excited about school and learning as well as see content in a new way. 

Another resource I pursued about escape rooms was an article by The Atlantic titled The Rise of Educational Escape Rooms. This article talked about many of the same things that the first article did, but something it added that I found particularly interesting was its discussion about how engaging forms of learning can help prevent students from leaving school. It talked about how, in addition to being fun, hands-on engaging learning activities help students retain information and can lead to fewer students dropping out of high school and/or college courses/institutions. This is yet another point in justifications for using games and, in particular, escape rooms in the classroom as another aid in teaching and instruction. 

While escape room-style lessons are time consuming, both in planning and execution, they are great tools for helping students develop and strengthen their academic and social skills. These activities can be used as review and/or additional practice on concepts as well as an introduction to topics to see what students already know about the material and what misconceptions they have. Using these techniques on a fairly regular basis in the classroom can help teachers cater their instruction to their students’ needs while creating a classroom environment that puts the focus on students and takes it off of teachers. Regardless of how long the trend of recreational escape rooms lasts, the trend of escape rooms in classrooms is one that should become regular practice in all classrooms. 

Sources

Educational Escape Rooms: Benefits, Examples & More! (2018, June 7). Dig-It. Retrieved March 19, 2021 from Educational Escape Rooms: Benefits, Examples, & More! – Dig-It! Games (dig-itgames.com)

Stone, Z. (2016, July 28). The Rise of Educational Escape Rooms. The Atlantic. Educational Escape Rooms Engage Students with Innovative Puzzles and Tasks – The Atlantic

Goal Setting for Teachers

Many teachers spend grueling hours writing effective goals for their students in their lessons. They consider how realistic the goals are, a timeline for achieving them, and steps for getting there. These are all things that are important to remember when setting goals. However, many of these teachers are spending all this time on writing goals for their students and neglecting setting goals for themselves as teachers. 

The article How to Create Teacher Goals That Get Results focuses on explaining a goal-setting framework that teachers should be using for all their goal-writing, including the goals they are setting for themselves. The article picks apart the SMART goal-setting strategy, explaining in detail and giving examples for each letter in the acronym. As the article goes through the parts of the acronym, the author uses a consistent example of a goal, highlighting the relevant parts in each section. The article, along with the main focus of the SMART acronym, provided things for teachers to keep in mind when writing goals for themselves that can help teachers feel guided and confident that the goals they are writing are truly SMART.  The article finishes with several examples of SMART goals written by teachers. 

This article made me think about how important it is for teachers to be writing goals not only for their students, but also for themselves. It is common to say/see that teachers put more focus on their students than they put on themselves; this is fine when it comes to creating a classroom environment and choosing posters for the school year, but when teachers have goals only for their students and not for themselves, a great deal of focus and purpose can be lost in lesson planning and teaching. I think it is important that teachers start splitting the time they spend writing goals between writing goals for their class(es) and writing goals for themselves. In addition to adding more purpose and focus to a classroom, I think that being able to show students that teachers have goals for themselves as well as the students, they foster a learning environment that emphasizes that everyone is learning, and everyone can improve. 

I will use the information from this article in my career as a teacher to keep myself accountable for constantly wanting to improve my teaching. By writing SMART goals for myself on a regular basis, I will keep myself in a growth mindset when it comes to my teaching and show that I am never “just fine” where I am, I am always wanting to improve as a teacher, both for my students and for myself. Having goals for myself will also show others, such as principals and superintendents, that I take teaching seriously and do not think “good enough” is good enough; there is always room for improvement and I want to make that improvement. 

The main thinking beyond the original point of writing SMART goals in this article was the section that gave ideas for teachers to keep in mind while writing their goals. It summarized each part of a SMART goal, and gave simple questions teachers can ask themselves when writing goals to see if the goals are SMART or not. I liked that this section condensed the information from the article into a smaller section that can be easy to come back to in the future to check goals and ensure they are following the SMART guidelines. 

Another resource I pursued about the topic of writing goals for teachers was the article Setting SMART Teaching Goals for Next School Year. This article also talks about how to write SMART goals, but the section I found particularly interesting was the section that explained why teachers should be writing goals for themselves at all. I think many teachers think they know their goals for themselves, and that is good enough. However, as this article stated, actually taking the time to write out goals for yourself as a teacher helps you stay focused on your goal as you move toward reaching it; having a hard copy of your goals also gives you something to look back on and see how you have improved as a teacher over time. I also think keeping a running record of all your teacher goals can help a teacher see what areas they are putting lots of focus on and what they may need to focus on more; for example if all of your goals for six months focus on teacher-student and student-student relationships, then you may consider having fewer of those goals and more goals focused on content and learning. 

Teachers spend hours over the course of a school year writing effective goals for their students, and neglecting the importance of writing goals for themselves. By splitting this time up, and including time to write teacher goals, teachers can put emphasis on improving their teaching, which will in turn improve their classroom culture, environment, and overall learning. This is simply one step in a long line of how teachers can be keeping themselves as a priority in a career that seems to center around others. 

Sources

Nisbet, J. (2020, January 6). How to Create Teacher Goals That Get Results. Prodigy. How to Create Teacher Goals That Get Results [Free Template] | Prodigy Education (prodigygame.com) 
Setting SMART Teaching Goals for Next School Year. (2020, June 18). Waterford. Retrieved March 5, 2021 from Setting SMART Teaching Goals for Next School Year | Waterford.org

Realistic Math Education (RME)

Too many math classes that students in the US take involve watching the teacher complete problems, practicing similar problems in class, memorizing meaningless formulas and procedures, and forgetting it all once the test passes. Instead of focusing on making sure students know formulas, math teachers should be putting emphasis on students building the knowledge and math for themselves, through contexts they are familiar with. 

RME focuses on presenting students with problems in contexts they are familiar with and can relate to. These contexts can be in the real world, in a fictional world, or in a math setting students already know. I personally think that contexts should be taken from real or relatable fictional situations more often than they are taken from previous math knowledge in order to keep students thinking critically and interested in how to apply the math to real situations. The article What is RME? talks about how RME allows the teacher to encourage students to find multiple solution paths for the same or similar problems that students come across naturally. The article also mentions how, by staying connected with the context of problems, students are able to make better sense of what they are doing and why. I think this is a critical point missing in many classrooms; students are able to memorize formulas and procedures but lose the ability to see why they are taking certain steps, and eventually lose all interest in knowing why. 

The information in this article made me think about how students could maintain their curiosity throughout more of their schooling. Many teachers think high school students do not care about school or learning. This is true in many US high schoolers, because they have gone through multiple years of memorizing facts and copying procedures being the way to succeed in school. This process caused the students to lose their curiosity and desire to learn and question what they are learning. I think implementing RME throughout students’ schooling will help students maintain their curiosity and lead to high school classes being more exciting and seeing more conversation and discussion. 

I will use the information from this article to justify and advocate for my school exploring more effective ways to teach math. Another article mentioned the curriculum Mathematics in Context (MiC) which is a curriculum that is centered around teaching math in real context and getting students to connect concepts to solve mathematical problems. The information from these articles can help me justify exploring this curriculum to be implemented in my school, or implementing bits and pieces of the curriculum in my own classroom. Having this curriculum as a resource can help me create a classroom that does not center around memorization and copying procedures, but focuses on problem solving and seeing “the bigger picture.” 

Another resource I pursued about the topic of RME was article title. This article, in addition to mentioning the MiC curriculum, noted on how it would be useful to find ways to incorporate RME across wider age ranges. The MiC curriculum is for grades 5 – 8 only, so all other grades do not have a strong curriculum centered around RME. This leaves a place for future research and curriculum development that  I could pursue in my career as an educator. I can also simply use the knowledge that there is not a strong curriculum for other grades on RME to refer back to MiC and find ways to incorporate RME style problems into my classroom. Whether it is the central focus of a classroom, curriculum, or school or not, RME is a topic and theory that should be implemented into more US classrooms. Without it, students’ curiosity and questioning skills will suffer. 

Sources

Realistic Mathematics Education (RME). (n.d.). Mathematics Education Innovation. Retrieved February 25, 2021 from https://mei.org.uk/rme 

What is RME? (n.d.). Realistic Maths Education. Retrieved February 25, 2021 from https://rme.org.uk/about-rme/what-is-rme/

Lesson Study: Impactful Learning for Students and Teachers

Creating engaging and effective lessons can be challenging for teachers. Teachers struggle to decide which practices will be most effective for their students; and how each year’s students change and differ. The practice of lesson study can help teachers see which practices are effective for certain lessons and learn how to create engaging and exciting lessons for their students. 

The article Personalized Professional Development gives a general guide of the process of lesson study and how it can be educational for teachers. One thing, in particular, I found interesting and important was how the author talked about the research, and research lesson should be centered around already determined goals for the lesson. The teachers in the study chose two of the mathematical practice standards to focus on in their lesson and centered their research around those goals. I think using this practice in all lesson planning will help teachers create more focused and productive lessons for their students. I also liked how the article described how the learning was assessed through observation; the teachers watched their lesson recording and looked for things such as student engagement, behavior, and interest level to determine what was working and what was not. 

The article made me think about how aspects of lesson study can be implemented on a regular basis for teachers, as teams, and as individuals. The author described how the team they worked with was not in the same place, so they recorded them teaching the research lesson rather than having the teammates in the room while the lesson was taught. I think recording lessons is something that every teacher should practice occasionally. Even if it is not for a project, observation, or study, having a video record of their teaching can help teachers look back and notice things they are not seeing while they are teaching. This can help the teacher make adjustments to their teaching, lesson organization, and/or classroom management strategies to create a better learning environment. These videos could also be saved and shared during potential future interviews for the teacher as an example of their teaching. 

I will use the information from the article in my teaching to be consistently evaluating and working to improve my teaching. As the author noted, lesson studies can be time-consuming, but bits and pieces of lesson study can be implemented regularly to help teachers improve their teaching constantly. The information from the article can also serve as a reminder that no lesson is perfect, and that exploring research about teaching will only help teachers become more well-rounded and diverse in their teaching practices and skills. Finally, I can use the information from the article in my (hopeful) future career as a principal to implement lesson study as a form of professional development. 

The main thinking beyond the idea of lesson study, in general, was the author’s reflection on how their lesson study impacted them; it humbled them and helped them remember that plans aren’t final and “even the best plans can be revised” (Paul, 2019). The author also encouraged readers to embark on lesson study, as it can help strengthen teachers’ relationships with each other as well as their students as well as serve as an opportunity for teacher and student learning. 

Another resource I pursued about lesson study was the article Lesson Study: Practical Professional Development. One thing this article mentioned that I found important was the idea that teachers in lesson study need to learn how to be effective observers. As teachers, it can be easy to notice things such as student reaction to manipulatives and the amount of talking that occurred during the lesson, but in lesson study, it is important to look deeper into the lesson to analyze if and how the lesson contributes to student learning and understanding. 

Sources

Delisio, E. (2008). Lesson Study: Practical Professional Development. Education World. https://www.educationworld.com/a_admin/admin/admin382.shtml 

Paul, A. (2019, May 13). Personalized Professional Development. edutopia. https://www.edutopia.org/article/personalized-professional-development

Fostering Growth Mindsets in Students

Many students in higher grades, especially in math, believe that their status is set; they are either smart/good at something or they are not. Research has shown that implementing a growth mindset in a school is important to help students feel and believe that they can grow and get better; even if they think they are already good at something, they can get even better (there’s always room for improvement). This research has begun to get teachers and administrators on board with the concept of growth mindset but one key group is missing from this bandwagon; the students. Students need certain things in the classroom and school environment in order to develop a genuine growth mindset. 

The article 4 Ways to Help Your Students Develop a Growth Mindset in Math gives ideas for how teachers can adjust their classroom culture and environment to foster a place where students believe they can (and are expected to) grow and get better. One idea I particularly liked in the article was utilizing peer- and self-assessment. Students should feel comfortable making mistakes, learning from others’ mistakes, and allowing others to learn from their mistakes. As many posters in classrooms say, “mistakes are proof that you are trying.” This idea made me think about how I can use group work as well as peer- and self-assessment to foster a growth mindset in my students. I can have students split into groups (groups could be consistent or change each time) and each member of the group passes their work to another member, who evaluates the work for new ideas, possible misconceptions, and places for improvement. Once students have had the chance to review someone else’s work they can look at their own work again and apply new strategies they saw or correct mistakes they may have made. 

I will use this information as guidance as I set up my future classroom. I will use the tips from the article to guide how I decorate my classroom (posters, sayings, etc.) as well as ways I can guide my students to having and maintaining a growth mindset. I will also use the information to demonstrate to my students my own growth mindset. I will be willing to take risks in my classroom and show students mistakes I make. This information will help me create a classroom where it is understood that we are all learning and we are all going to make mistakes. 

The main thinking beyond the original idea was a quote towards the beginning of the article, “without a growth mindset, it becomes easy for students (and adults!) to fall into a pattern of avoiding risks and feeling defeated.” This quote made me think about how adults in students’ lives can, even unintentionally, work against a growth mindset. If a student’s parents believe that they (the parents) have a fixed ability with math, then they are going to be more reluctant to help students explore the math they are learning. If/when they are helping their students with math, they may be saying things such as “what did your teacher tell you to do?” and “follow the steps in the book.” Parents may think that these tips are helping their students learn math, but they are truly crushing their student’s curiosity and encouraging them to copy the steps in the book. It is the teacher’s job, then, to explain to parents how how they help their students at home impacts their learning and give parents tips on how to encourage their students to persevere in math, take risks, and not be afraid to make mistakes. 

Another resource I looked at for growth mindset was the article Teachers Nurture Growth Mindsets in Math. One idea explained in this article was how the way teachers approach math impacts the amount of growth mindsets their students have. One specific idea the article presented was the idea of open problems; problems that have multiple ways to solve them, even if there ultimately is one correct answer. This contributes to the concept of teachers fostering a growth mindset and students taking risks, knowing it will likely often lead to mistakes. Fostering a growth mindset in the classroom, school, and home environment is one of the most important things teachers can do to keep their students curious and growing, both in school and in life. 

Sources

Blad, E. (2015, September 8). Teachers Nurture Growth Mindsets in Math. Education Week. Teachers Nurture Growth Mindsets in Math (edweek.org)

Carnegie Learning. (n.d.). 4 Ways to Help Your Students Develop a Growth Mindset in Math. Carnegie Learning. 4 Ways to Help Your Students Develop a Growth Mindset in Math (carnegielearning.com)

Coherence in Math

When students are in elementary school, they seem to be curious about connections between concepts and can see those connections fairly easily through exploration. As students move through the middle and upper grades, many subjects become more about memorizing facts than understanding the topic as a whole. Math is no exception. Throughout middle school and high school, students lose the interest in finding the connections between concepts and begin to care more about getting the right answer than understanding what they are doing and why it works. By implementing coherence as an important part of math education at all levels, students will come to a deeper understanding of basic concepts and will learn more advanced math easier.

The article Understanding Math Coherence, talks about how the Common Core standards put an emphasis on coherence and connecting each math concept to one students have already learned. This is something many middle school and high school math teachers do not do enough of; they teach each lesson in the book, in the order the book gives them, and do not take the time to help students see how the new concepts may simply be an extension of something they already know. This would likely lead to more students finding an interest in math and taking advanced math courses. The article mentioned that one way to implement coherence throughout students’ schooling is for teachers of different grades to work together on what they teach, and how lower level teachers can foreshadow to upper levels and upper levels can revert back to things learned earlier. This would help students connect, not only Algebra I to Algebra II, but connect algebra to geometry to calculus. Putting each of these concepts together would lead to students who can not only do the math, but explain what they are doing and why it works.

This article made me think about how coherence is the job of the teachers; even if they are assigned a set of standards and a textbook to teach, they can work with other teachers in their school and district to find an order of the lessons that leads to coherence, as well as put more emphasis on finding connections in math than memorizing procedures and formulas. I also considered how teachers struggle with implementing coherence because they were taught through memorization and formulas, so they do not feel like they are prepared to change how math is taught and still be successful. That coupled with the, as the article put it, “laundry list” of standards they are expected to cover leads to many teachers giving up on changing education and reverting back to teaching how they were taught. The main thinking beyond the original idea of coherence was how, as schools and districts adopt Common Core curricula, they need to be thinking about the order topics are taught and a path of lessons that will lead to coherence; even if that means teaching in a different way or order than the teachers were taught. 

I will use the information from this article to apply to how I teach math. I will put the emphasis on student coherence and away from lecture style teaching. I will ask students how/where they have seen something similar before and hold classroom discussions about how new topics/concepts connect to ones students have already learned. An extension on the idea that came to mind while I was reading, was the idea of putting words/phrases on the board that lead to what concepts connect to the new ones to spur students’ thinking. I can put keywords from previous lessons on the board and have students brainstorm how the new material may connect to that. 

Another resource I pursued about this idea was an article that talks about the coherence map and how it can help teachers connect concepts for students. This map could also help teachers see connections they may not have been taught when they were students, thus making them better equipped to teach the connections. The article mentioned how teachers could use the map to identify students’ gaps in knowledge and help students make the connections between concepts that they missed, either in concepts from their current grade level, or previous ones. This article and the coherence map can be great tools for teachers to help them create classroom environments that stimulate coherence and understanding.

Sources

Student Achievement Partners. Creating a Coherent Math Curriculum. (2015, October 29). Achieve the Core. Retrieved February 4, 2021, from Creating a Coherent Math Curriculum – Achieve the Core Aligned Materials
Understanding mathematical coherence. (2018, May 18). Bright Education. Retrieved February 4, 2021, from Understanding mathematical coherence (funeducation.com)