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Motivating students

Motivational techniques are a great way to get students interested and involved in the classroom. I looked into an article written by the National Board for Professional Teaching standards about their top 5 strategies for motivating students. Their first tip was about the benefits of students having a growth mindset. I have written on this before and I do think that creating a growth mindset with students motivates them and allows them to look outside of their usual thought processes. One thing that they do mention about fostering a growth mindset is to praise students for their efforts and hard work. Students will not keep up their hard work if they do not feel the work they are putting in is appreciated.

The next tip is to have meaningful and respectful relationships with students. This tip is to help teachers inspire and motivate their students. It would be difficult to plan an interesting lesson if you do not know what interests your students. One way this article says teachers can make meaningful connections is by spending a few minutes of class time to allow students to share good news or things that have happened in their lives. This allows teachers to learn more about their students and also shows them that they are cared for by their teachers. These discussions do not have to be highly personal but should reveal some interests of the students. This all starts when teachers are willing to share their personal experiences and stories which will hopefully promote learners to do the same. After creating this relationship with the students, they are able to grow a community of learners within their classrooms. This happens to be tip number three.

The fourth tip that this article lists is to have high expectations and clear goals. There is a certain level that we are expected to teach at and there is also a level we expect our students to be learning at. Students want to know what is going on, what is expected of them, and how they should do things. This article mentions having transparency. They say to be transparent with expectations, but this transparency can also help with creating personal relationships with students. Going back to expectations and goals, how to implement this into the classrooms, they say to have daily learning goals that are posted and visible and discussed on a daily basis. These can also be implemented in an exit ticket by having students answer questions that are based on these learning goals. Another aspect they mention within this article is how these expectations can go past just learning, they can be set for behaviour, academic language, group work, and how individual work is to be done.

The final tip of this article is to be inspirational . I feel as if teachers go into their profession to be leaders and help students find their way. We want to inspire these students to greatness and help them succeed along the way.

Online Math Resources

Online math practice is something that teachers have been working toward for a few years now. Incorporating some of the main websites such as Khan academy, Desmos and IXL allow students to practice within the classroom and also at home if they have the resources. But there are more interactive websites outside of these main three. One website that I learned about in my internship was called prodigy. The website has students going on a quest like activity and in order to advance in the quest they must answer math problems. I went to their website and found an article called “ 7 Reasons Prodigy is Right for Your School.” To me, one of the big positives of using prodigy is that it has a curriculum that is aligned to the content standards. This is great so when students are going over these activities, they are still creating building blocks to go off of other lessons. Another great thing that prodigy does is that it has differentiated and personalized learning. The article states that they have a feature that allows teachers to edit their templates for them to create specific lessons or differentiation and even if teachers do not use this feature, the prodigy program will differentiate following the standards. The final piece that I like about this website is that it uses the data collected from student work and turns them into progress reports that help track the student development and growth.

Going back to the first three, they all do still have their positive aspects and they must be doing a few things right if they are the main three I see teachers using. One that I have been looking into lately is Desmos. One of the common things I have noticed as I was researching about desmos is that most teachers use it for the graphing calculators as they can cost upwards of $200 each and these online ones are free. Although this is a great resource of desmos, they offer many other things through the teacher activities. A blog about Desmos in the Math Classroom discusses the ways that one teacher utilizes desmos in their classroom. They discuss how they use Desmos to easily solve the students conjectures, bring in outside elements such as art, and even how desmos allows them to have a more social classroom. I think my favorite part about this blog post is that the teacher wrote about how desmos activities got the students excited to be a part of class. One of the students had gone on a vacation but still wanted to participate in the class activity, so the teacher sent the student the access code and this student was able to participate even when they were not in the classroom. Having students who are excited to learn and using a platform that promotes that will help create a welcoming learning environment within the classroom.

Growth Mindsets

Within the classroom, teacher’s hear all kinds of statements such as “math is too hard” and “because my parents are bad at math, I will be too.” Although these may be just words the students are saying, they actually affect the mindset of these students. There are two different types of mindsets, One is called a fixed mindset and one is called a growth mindset. Using a website called growth mindset maths, I found their article of growth mindset vs. fixed mindset which is mainly focused on developing a growth mindset, however it does discuss what a fixed mindset is. How this website describes a fixed mindset is that students believe that talent alone creates success, are fearful of making mistakes, and believe that talents and abilities are set in stone, you either have them or you do not. Although a fixed mindset is not a bad thing, the focus of our classrooms should be a growth mindset.

Mr. Elementary Math wrote an article about 5 Simple Ways to Develop a Mathematical Growth Mindset. The first thing discussed is how teachers or students in the math classroom are perceived with a growth mindset. The four points they list are to believe that intelligence can be developed, focus on learning vs getting the “right” answer, do not give up and try new strategies if something does not work, and to reflect and learn from mistakes. These correlate to the Standards for Mathematical Practice as they both value the process over just getting the answer. The first tip this article lists is the use of think alouds to model how to solve problems. Making a habit of showing how you would solve a problem while adding in the principles, perseverance, and effort needed to have a growth mindset. The tips then continue to list things such as asking questions that promote a challenge, allowing for opportunities when students work together, and providing time for students to share how they solved the problems. The final tip is one of my favorites. This tip discusses taking time to reflect even over errors. I love the thought of normalizing errors within the classroom as well as creating a safe environment for this to occur.

A final article I found was by Carnegie Learning that discusses 4 Ways to Help Your Students Develop a Growth Mindset in Math. Their top tip was to give students quality math tasks because students can grasp these high level ideas but they can not develop the skills if they are not given a task challenging enough. They also discuss peer work by doing assessments, feedback, and revisions with their peers. Just like the article before, students working together will help promote the growth mindset and also helps them analyze their own work for errors and correctness. The final tip is also to be very mindful of the messages because our mindsets will help develop the students mindsets and the way that the teachers act in their classrooms will affect their attitudes as well.

Inquiry Based Learning

Inquiry based learning is a new style of learning focusing on the curiosity of students according to edutopia. This article is all about describing what inquiry based learning is and four steps to promote inquiry based learning. When trying to promote inquiry based learning within the classroom, modeling enthusiasm as well as learning something new that generates our own curiosity even if it is a topic that you have been covering for years. The four steps that edutopia discusses to help generate inquiry are

Allow students to develop their own questions that they are eager to answer.
Research the topic using time in class.
Have students present what they’ve learned.
Ask students to reflect on what worked about the process and what did not.

Wabisabi Learning also wrote about the four C’s which dive deeper than just discussing curiosity. This article also discusses communication, creation, and connections. Although the main focus is bringing the curiosity into the classroom to create better engagement from students, connecting the content to the students and making relevant connections will help to inspire different concepts that inspire real learning within the classroom. Although using inquiry based learning relieves some pressure from educators by allowing students some autonomy, communication is necessary from the educators so that students understand what they expect them to gain from the lessons as well as what we as educators consider as essential points.

The final product of this inquiry based learning is where creating comes into play. Using the fourth C of creation, this is where students are put to the test to show what they know. During this stage, students demonstrate their understanding of and appreciation for what they have learned. This Wabisabi website continues to list ten examples that use the 4 C’s to create a cycle of inquiry. One example from this list is titled scavenger hunt. During this activity, students are given a list of locations but rather than listing the title of the place, they are given math problems that tell them how far to go in steps, feet, yards, or any other hints they will need to arrive at their next destination. The curiosity of this lesson comes from distance and location and the connection is to the mathematical concepts used to determine them. Students communicate using those mathematical concepts and utilizing them in finding the distance and using directions to finally create the overall scavenger hunt.

A final article I found is 10 tips for launching an Inquiry Based Classroom.This article has some great adaptations and reminders for teachers. I think one of my favorite tips from this list is to indulge in interesting student questions even if it does not fit the pacing guide. I like this tip because if you have the student engagement, it gives them validation and if you do not have the student’s engagement, they will feel disempowered and that will result in a difficulty to continue an inquiry based classroom. Overall I think that some of these tips can be extended past just inquiry classrooms. Not telling students what they should know, not teaching the standard but rather giving kids information to find the information, and also not giving struggling students the most boring version of the work are all tips that can be used within a normal classroom as well.

Problem solving in the classroom

When bringing a problem into a classroom, each student will have a different path to finding the solution. As an educator, it is our job to teach multiple methods that help promote problem solving within the classrooms and later in their lives. Promoting problem solving skills within the classroom can sometimes be a struggle for educators. The Knowledge Network for Innovations in Learning and Teaching ( KNILT) wrote an article over The Importance of Problem Solving Strategies.This article discusses the importance of problem solving, benefits of problem solving, and other places problem solving is applied. A great reminder this article discusses is that problem solving is not an ability, it is a character trait and a mindset. Creating that mindset and mentality within the classroom will help promote problem solving in the classroom.

The NDT Resource center published an article on Problem Solving Skills. This article gives six tools to be used in problem solving as well as a process to follow when problem solving. The five step process includes:

Identify the problem
Analyze the problem and gather information
Generate potential solutions
Select and test the solution
Analyze/Evaluate the results

These five steps will help keep the students’ efforts focused as well as eliminate the chances of them becoming stalled. Some of the tools that are listed are brainstorming, flowcharting,and root cause analysis. Brainstorming helps students look at different approaches to one situation. Brainstorming is also used to encourage participation from each student and allows them to voice their opinions. Flowcharting can be used to help map out a process and make sure that all parts of a process are accounted for. Root Cause Analysis is also called the five whys which can be used to help students dive deeper into a problem or situation and figure out the deeper meaning behind it. Although these are for problem solving in general, they can be used within the math classroom with slight modifications.

The Root Cause Analysis was one that intrigued me so looking further into it I found this article which describes what it is, the basic process, and lists a few tools as well. As stated above, root cause analysis is used to help students dive deeper into a problem or situation, but it also is used as a tool for continuous improvement. One thing that this article mentions on root cause analysis is that when it is first used, it is reactive, but after gaining experience, it becomes proactive and problems can be anticipated in time.Although there are different variations, I think the five whys method would be suitable for the math classroom. Continually asking students questions such as “why they did this step here” and “why does this cancel” will help students get to the fundamental portions of the math.

Three – Act Tasks

Dan Meyer got his claim to fame from his blog dy/dan and writing about Teaching With Three Act Tasks.Although there are many others who have created these three act problems, I have chosen to focus on Dan Meyer for this entry. As the name gives way to, these tasks have three parts to encompass all of student learning. Laura Wheeler posted this video on youtube that helped me understand three act tasks more thoroughly.

The first task is to start setting up the problem. Students are given a picture or short video that allows them to ask their own questions that could pertain to the image or video. During this time the instructor will ask the students some thought provoking questions to assist them in their question formulations. These questions can be asking students what they notice or what they wonder. After discussions about students’ answers,the instructor can ask questions more specific to the question they have down for the image or video. This is also the time to integrate the math into the lesson. In Laura’s video example, she asks her students to estimate the height of a lamppost and to make three estimations on it. Their first two estimations should be fairly unreasonable. One should be a high estimate and the other one will be a low estimate. These estimations give students a range to make their third estimation within. The third estimation will be their best guess to the actual height of the lampost. On this stage, there is no right or wrong answer per se, but the objective is to have the students think critically and use problem solving skills to make a plan to solve the problem that they created which leads into the second task.

The second task is to actually solve the problem that has been created. In act two, the students will use the conjectures they made in act one along with data that they have to collect to solve the problem. This can give students hands-on experience such as in Laura’s video, where the students went outside and actually measured the height of the lamppost. Making sure the teacher is still engaging with the students is very important here. Teachers can stay engaged by continuing to ask questions. Asking students what information they would need from them or why those chose a specific number for their solution keeps the students engagement levels high.

The third task is to reveal what your answer is to your students. Remembering that this is a teacher facilitated student led discussion, teachers can pose their answers as questions to get student involvement and feedback. In Dan’s blog, he has some great ways to rephrase statements to invoke more student discussion. Some examples are “ help me if you are completely finished”, or asking students who was closest to the answer and giving them a small moment of praise for it. This makes students feel as if their work is appreciated and will promote a hard working environment within the classroom. There is also an option for a sequel with these tasks. The sequels are to challenge students who finish quickly or to allow the teacher time to work with students who may be struggling.

Productive Struggle

Productive struggle is a hard concept for some people to come to terms with. Most students do not like the thought of doing something that is not cut and dry. Students like to have that security and confidence that they know what is going on without a doubt. As educators we want to help our students get to the correct solution as best we can while still cultivating that learning. The struggle for educators comes from wanting to “rescue” their students when they see them struggling. Although we feel as if this may be helpful, some of the students will be robbed of that experience to come to the conclusion on their own and get that satisfaction of persevering through the struggle and come ultimately out smarter after it. The Institute for Excellence in Education wrote an article titled “5 WAYS TO ENCOURAGE PRODUCTIVE STRUGGLE.” This article gives five good things to motivate students through a time of productive struggle and also some ways to promote productive struggle in the classroom.

One of the topics I think is the hardest for teachers to remember to implement that is mentioned in this article is promoting non-routine problems. Routines are always encouraged as they give that structure to a class that students are searching for. It also helps students feel more comfortable and in control of their class time as they know what will be happening, when it will be happening, and how they can contribute to spend that time efficiently. However giving students questions that are outside of the usual routine promotes a sense of unease and is intended to promote a deeper and higher order level of thinking. In order for students to get into this higher order of thinking, they need to be exposed to new questions that cannot be solved from just memorized formulas or things that they see in their everyday drills. Students need problems that have different approaches to solving them which will also help them get into the higher order thinking mindset.

I found another article that I thought would be beneficial especially for new teachers. The Mind Research Institute posted an article “ 8 Teaching Habits that Block Productive Struggle in Math Students” A vast majority of these tips will have to come with patience. Having patience not only with your students but also with yourself. One of their points” Calling on students who know the right answer” really plays into this. Having the patience to allow the entire class an opportunity to figure out the question instead of calling on the first student who raises their hand. Another great point this section brings up is turning the “ I don’t know” moments into quality questioning. When a student says those words it is like hitting a fork in the road. This moment can either become a moment of failure for that student, or it can become a moment of deeper thinking all by the facilitation of the answer. One of the points in this article I had never really thought about was how you construct your bulletin boards can affect the way your students perform. Instead of always showing the top scores, also including examples that show perseverance and progress toward the goal will help students to become motivated

Internet access or lack thereof

Growing up, all of my mathematical homework was done on paper and pencil. We turned our notebooks in with the notes we had taken for class, wrote out vocabulary terms and did every assignment on paper. Even my Smarter Balance testing was done on paper up until I think my junior year. I was in highschool just two years ago and even now classrooms have switched to doing more work with technology rather than paper and pencil.I think it is a good idea to use different methods of delivery for a classroom but there are questions that arise when doing so. One consistent question that comes to my mind when I think of integrating technology into the math classroom is how do we accommodate the percentage of students who cannot access these resources? In what way can I as an educator make these students be up to date with the times even for the short amount of time I see them during my day?

Technology is a great resource that educators should be utilizing, but how useful is it when students do not have access to it outside of class hours? I went and looked at the National Center for Educational Statistics and they state the average percentage of children ages 3-18 who have internet access is 61%. So in a class of thirty students, only eighteen of them have the ability to complete assignments such as IXL or Khan Academy. I see many classes assigning programs like these as either actual assignments or just busy bonus work. How as an educator can we make these great resources available to children who do not have the straightforward access at home? I found an article that discusses 6 Ways to Support Students Without Internet Access. It gives some great suggestions such as getting students involved within the classroom and trying to ensure that when they are paired in groups the more “tech-savvy”students can assist those who may not have the same abilities as them. They also discuss giving parents a list of places that have free wi-fi or computer access but to me personally, this seems like a very touchy subject that may cause more problems than solutions. Would I insult these parents by giving them a list like this even with my good intentions behind it?

I found another article by US news that focuses on high schoolers without internet access. Although the ideas given by US news would cause more work on the district’s side, I think they had some great ideas. One example came from the Boulder Valley School District. Working with providers within the community, this district was able to provide low-income students with free chromebooks for them to do their assignments on. They also discuss how this district is in the process of working with an internet provider to help provide free internet to low-income families in the district. Out of all the articles I have read the main takeaways I have gotten for assisting students without internet access are researching students and families, advocacy for digital literacy and resources within a district, and being accommodating to students to help them succeed.

Resources for Engagement

This past week I was at the SDCTM conference in Huron, South Dakota. This is a convention for STEM educators around the state to come together and share ways that they are progressing in the field with other educators. One of the main themes that I saw throughout the conference was teachers sharing ways to engage students more in the classroom. One way that teachers were doing this was by using materials that students could relate to which links back to what we have been talking about in our classroom. Teachers were discussing how they adapted real life shows like survivor, and turned them into math games. For example, students would have an equation on the board and also a playing card with a certain suit. Each suit was its own team. If someone from the diamond team got the answer wrong, it would not be that person who get eliminated, but rather a student would draw a random card and whomever the card matched, that student would go to “elimination” island and work on other games. The classroom that this was done in averaged about twelve students so it was easy to manage. Having the hands on manipulative learning helped students to be more engaged and active with discussions in class.

Another presenter that I thought was very beneficial was a presentation done by Kevin Smith and Jessica Dawson. They created a website Make Math Fun where they linked each activity they would be covering in their presentation as well as some extra resources for teachers to use. One of my personal favorites was the website Esti-Mysteries. These esti-mysteries would show a picture and students would have to guess how many objects are in that picture. They would write their answers down and after all students had their first answer down, a clue would be revealed. After this reveal, students had the option to either change their answer if it did not fit within the information of the clue, or to leave their answer. After this, three more clues would be revealed with the same process. At the end of it all, students should be able to deduce what the answer is. Before the answer is shown on the screen students are allowed to make one final guess and discuss with a partner how they arrived at that conclusion for an answer. There is a variety of difficulty in with level 100 intended for grades kindergarten through second grade, all the way up to level 400 for students ranging in grades three through twelve. One very convenient part of this is that all of the links are downloadable powerpoints that need no modifications as the transitions are already in place for the clues to automatically reveal themselves.

One final resource that Kevin and Jessica shared was Mashup Math. This site has picture equations for almost any holiday or special theme in classes. This is a great way to incorporate the real-world into the math world while also increasing student engagement as students are more likely to tell you why two fish plus a turtle equals twenty-five versus an algebraic equation that is set up as 2x+y=25.

Algebra Tiles and Solving Equations

In the Algebra for All article “Using Homemade Algebra Tiles to Develop Algebra and Prealgebra Concepts”,they mention that algebra instruction and learning styles are mostly leading into the direction of memorization. When I was in school that was how we learned, we memorized the rules and the facts, copied them onto the tests, and then proceeded to forget the concepts. By using manipulatives such as the algebra tiles, it causes more thinking to occur other than just memorization. Students use problem solving skills to find solutions to the quadratics in other ways. Finding the correct orientation of the tiles and figuring out how to translate that into a math statement uses their problem solving skills as well.

The article “How to Teach Solving Equations” discusses the importance of algebra tiles, and although they may be daunting, the students can understand better when working on solving equations hands on. This article also discusses the struggles students have when solving equations in general. They asked other teachers what students struggle with and most of the struggles were previous skills students should have mastered. Some of the struggles listed were “ combining like terms incorrectly, dividing/multiplying a negative coefficient, not distributing when they should, and completing inverse operations on the same side of the equal sign.” This article then leads into discussion on how to implement algebra tiles in the classroom. Like any new material in the classroom, starting small and building up is the best way to learn. In the case of algebra tiles, having students start with one step equations and build up to two step equations is a good way to implement the scaffolding. As the article states, it is easier for students to visualize and place together two long green tiles, than it would be to place together two similar terms.

Another article I found discusses how to transition students from using algebra tiles to being able to solve equations with written algebraic steps. “How to Effectively Teach Solving Equations.” The author Michelle Sigaran discusses how she uses three steps to transition students from algebra tiles to solving equations. First she uses a concrete method of teaching by using algebra tiles. She also mentions in this section to have students circle terms which is a great way for them to know where the signs belong and what terms may potentially go together. Her second section deals with a symbolic representation of the equation. This is like a halfway point between algebraically solving it and using the visual algebra tiles to solve. In this step, students represent variable terms with the said variable and constant terms with the amount of 1’s it would take to achieve that constant. For example, in the equation x-3=10, students would write the x term and three -1 terms = ten 1 terms. From this point, the students can get the x term by itself and combine all of the 1’s together to get x=13.The third step is called abstract. Here is where the students can look at the equation and see how to solve the equation for the x term. At this point, the students do not need the physical representation of the tiles, or the broken down constants, they can simply solve the problem by +3.