Just Another Friday Afternoon Exploring the #MTBOS

I always knew that the MTBOS was a great place for math teacher to communicate and collect resources since I was exposed to it about 2 years ago and have been collecting what resources I would like to draw from in my classroom since. However, in digging a little deeper today, I found some pretty neat things (resources and blogposts) I thought were worth sharing.

Resources

Desmos activity on exploring aspects of linear functions through legos and superheroes

Desmos activity to learn geometry vocab by playing a guess who style game

Musical Chairs game from Brooke for expression review, could be use with many concepts

Interesting Blogposts

Justin talks about students becoming inquisitive and their rusty integer skills

The power of literacy in math-how big is it? See it at work with Bridget

Mark discusses feedback to students and its importance

Julie shares some neat first day math problems

Fawn shares her first two days of each of her classes and the syllabus for each

Victor debunks 5 myths about the Standards for Mathematical Practice

John on teaching students quadratic through misconceptions

Becoming a Reflective Teacher

With the beginning of another school year comes an abundance of opportunity for teachers and any kind of educator. Opportunities to learn, to grow, to productively struggle, to learn from mistakes and failure, and to impact the lives of students only begin to name them. But with all this opportunity in our hands, we must be ready to seize them in order to become the best educator we can be. This means that we cannot become complacent with who we are as a teacher currently. We must be constantly critiquing and evaluating ourselves as teachers, our teaching strategies and how effective they are for students, if the needs of our students are being met, and much more. In essence, w must be cognitively aware of what impact each and every moment of our day has on us as an educator and be striving to change as necessary to become better each day. Thus, as I immerse myself into the realm of teaching, I will be trying my best to become a reflective teacher.

I have been challenged to be intentional about picking a few areas where I want to grow as teacher over the semester. Let's dive right in to see the areas I want to seize opportunity in!

Specifying and Reinforcing Productive Student Behavior
One of my biggest fear going into this semester--just like a lot of new and training teachers--is classroom management. That is why I am so glad I have a whole college class on the topic this semester. Having worked as a camp counselor for middle schoolers this past summer, I am super glad that I have been able to try various methods to see what works and does not work. I realize that each class will likely be different and that camp is different than the classroom, but I hope that I can use those experiences to have a healthy classroom environment that promotes and reinforces productive student behavior. Some of the specification of what the classroom norms are is out of my hands, since I am learning from my absolutely amazing cooperative teacher, but I look forward to contributing to further specifying them and reinforcing them with students this semester.

Learning about students' cultural, religious, family, intellectual, and personal experiences and resources for use in instruction
I recognize and can identify the power of a lesson striking home to something familiar in learning the content of a lesson. Thus, I want to be intentional about building genuine relationships with my students and be able to find ways to relate to them and ways to relate the content to their lives. One of the most common frustrations with students in a math class is identifying where the concepts can be realistically applied to their life or what life-skills they have gained through understanding the concepts. Therefore, I want to make it my mission to find creative ways to explain the concepts through relatable experiences for students. I would like for students to view math more like Stanley rather than how SpongeBob does, and it begins by getting to know students better.

"Oh, I see how math is useful now!"

"Math is so useless I don't even want to see it!"

Support Productive Struggle in Learning Mathematics
This one I feel as though is going to be an ongoing pursuit to find the sweet spot between giving a student too much assistance that we have done the thinking for the students and too little assistance that the students begins to flounder. In other words, I want to be able to rescue a students in an appropriate manner, or in one where both the students and I can feel confident that they can continue on and understand what is going on.

Thus, I will be working for students to not feel like a flopping fish

 and more like George Lopez.

Currently, I feel that I go back and forth between too much help and not enough, so I want to be intentional about finding the sweet spot in order for the student to have the most powerful learning opportunity they can have.

I know that there are many more ares to improve--and I hope that I can make strides there too--but I feel as though these are important to develop as I develop as a teacher through teacher assisting this semester. Check back with my weekly updates to see how I am doing in these areas!

Glad to be in the Dawg Pound

What a first week at Grandville Middle School!

I came into this week both excited and nervous at what the next semester would entail as a teacher assistant. However, I have now left this week with only the biggest smile on my face that beams all the overflowing excitement and passion that has come to light because of what has happened in the classroom! I even bought some Grandville apparel because I am already digging this place so much!

To put it in a few words, it just seemed natural. There was something right about being in a middle school classroom and in front of the room. Whether it was introducing myself for what seemed like a hundred times, passing out materials, or assisting students in activities, there was an undeniable sense of home-- and it was only solidified once the content began. It has given me lots of courage that I will overcome the fears I had coming into the semester, and it has be feeling ready to take on this semester (just like this bulldog below) as the weeks only get more intense from here. I will fail at some point, but I feel as though I am in the right place and this semester is going to change me for the better with all I have to learn.

The week was most definitely full, and it may have made me feel like the next bulldog when I left the building each day, but I am eager to fully immerse myself in the teaching world throughout this semester. And I get to do just that this week as I get to teach a lesson!

Here's to the rest of the semester! Go Bulldogs!

Improving Teaching, Not Teachers

Although I feel as though I do not fully know this important distinction by any means, I do feel like I am beginning to get a sense of how teachers and teaching differs. James Stigler and James Hiebert's The Teaching Gap offers some insight into the distinction from its opening chapter. 

Much of the discussion surrounding improvement within the educational system is abut changes to standards and assessment. What is not being targeted is the teaching methods being used by teachers. Stigler and Hiebert argue that "making higher standards a reality for students will require more than just the status quo inside our nation's classroom; curriculum, assessments, and--above all--teaching must improve dramatically" (Stigler & Hiebert, 2). Notice how it said that we do not need to usher in a new wave of teachers, but rather change the teaching occurring in the classroom. With all the constant change in standards, curriculum, and assessments being made constantly in education, we are failing to see the results we desperately want. Time and time again, they come with the promise that students will score significantly higher on the countless tests they are given. However, what has yet to be critically evaluated through these many changes is the execution of these changes, or the teaching going on in the classroom. Thus, "improving the quality of teaching must be front and center in efforts to improve students' learning" (Stigler & Hiebert, 3). 

Learning opportunities for students need to be abundant in classroom and come from a variety of approaches. What is common in a lot of American mathematics classroom is a focus "for the most part on a very narrow band of procedural skills" (Stigler & Hiebert, 10) rather than deep conceptual understanding. This repeated emphasis on being able to execute procedure causes the students to look like this. 

This emphasis allows the students to be passive learned in some regards as well as to execute the procedure mindlessly. Don't we want to students to be actively engaged and actually understand what they are doing? Thus, the learning opportunities need to excite students, rather than bore them. Let's make them feel like Kermit when they enter a math classroom!

Now let me make something clear here. I am not saying that a teacher is wanting to bore students and they do not have the intention for students to succeed in their classes. I do believe that, on the whole, teachers are trying to employ methods that allow students to perform well. What I am trying to say is that I think teachers revert to the methods they were taught in, since teaching is a cultural thing, and these methods are making us become stuck. 

The world has changed since these methods were first used. What skills we desire for students to have when they exit school have changed, However, we have maintained widespread use of traditional methods in classrooms. Thus, "if we wish to make wise decisions, we need to know what is going on in typical classrooms" (Stigler and Hiebert, 8) and positively change and transform "the one ingredient most likely to make a difference in students' learning: the quality of teaching" (Stigler and Hiebert, 2). 

It also is important to note that I'm not saying that there are not teachers out there already being all-stars and adapting their teaching to provide avenues for deep conceptual understanding for there students. They do, in fact, exist. However, "although there are teachers using extraordinary methods in all cultures, the extraordinary is not what defines most students' experiences" (Stigler and Hiebert, 10). For the sake of our students, let's work together to make extraordinary a little more ordinary!

From Presenter to Facilitator

Throughout my teacher preparation courses, I have been challenged to make my teaching style one that promotes active learning rather than passive learning. In other words, I have been encouraged to move away from traditional methods, such as the so-called "drill and kill" method, and move toward progressive models that force students to think actively about the mathematics they are learning while mucking around in it as well as having students not only thinking critically, but also articulating it to their peers and the teacher. Essentially, I have learned that the mathematics classroom should be a place where students are actively being mathematicians.

From the beginning, I have jumped on board with this mentality, and I cannot be more excited about reading about a model that can be implemented in the classroom that promotes students to be mathematicians. In Minds on Mathematics by Wendy Ward Hoffer, she argues that teachers should employ a type of lesson called a "Math Workshop" to have students develop deep understanding of the mathematical concepts being taught. Just from Chapter 1, I have a strong first impression of this method and believe that it can provide avenues for students to explore mathematical concepts like a mathematician rather than be a passive learner who memorizes algorithms and processes and mindlessly executes them on assessments. With the latter, students can fall into saying things like what Michael Scott says.

Since this type of experience is not one that I desire for my current and future students, let's explore what this Math Workshop style of lesson is precisely. As Hoffer states, the purpose of such a lesson is to "put into practice our belief in all students' mathematical abilities by creating and facilitating learning experiences that invite individuals to construct and negotiate deep conceptual understanding, as well as develop fluency with numbers" (Hoffer, 2). 

Woah, now isn't that one jam-packed purpose?! Why don't we unpack that to characterize what a Math Workshop style of lesson by going through the purpose phrase by phrase. 

"put into practice our belief in all students' mathematical abilities..."

A friend of mine once said, "Students don't care what you know until they know that you care." With all the negative stereotypes surrounding mathematics and the seemingly abundant lack of self-efficacy when it comes to mathematics, I think that this style of lesson definitely actively works to combat these by putting a positive light on mathematics and pushing students in a healthy way while simultaneously communicating that understanding the mathematical concepts at hand is, in fact, able to be accomplished. Through the structure of this type of lesson, we can demonstrate that each and every one of our students has the capability to learn the concepts being taught, and, thus, showing our students that we do care. 

"...by creating and facilitating learning experiences..."

Further, it is that structure that allows for this type of lesson to be centered around being engaged in thinking about the mathematics through "minds-on tasks that require deep thinking and evoke understanding" (Hoffer, 6). The goal here is to have learning experiences that demand thinking to be not only internally transparent within the student's mins, but also externally transparent by having a student share their thinking with their peers, where appropriate, and the teacher so that, in combination, come to an understanding of the mathematical concepts. To accomplish that goal, the duty of the teacher is to then have created minds-on tasks that allow for deep understanding to occur and do so in a way where the teacher is a facilitator rather than a presenter by conferring with students instead of presenting the material to the students directly and/or rescuing students when they are struggling with the material. 

"...that invite individuals to construct and negotiate deep conceptual understanding,..." 

It is critical that these minds-on have the students actively being engaged in the learning process, not the teacher; the teacher should not be doing the thinking for the students. Therefore, the workshops have the students looking at a given concept from numerous angles. As a result, rich discourse on the concept can occur and student thinking is put on display. Students are then, in fact, constructing their knowledge and negotiating deep conceptual understanding through communicating their thinking and being exposed to other ways of thinking about the given concept. 

"...as well as develop fluency with numbers."

Moreover, this lesson style will allow students to be fluent with numbers through the amount of dialogue built into a math workshop. The teacher is conferring with students throughout and students are discussing with each other. In both cases, students are making their thinking visible. Thus, student misconceptions are actively being made known and are being actively combated as the lesson unfolds. This only allows for the misconceptions to not be held as long as they would be in a traditional classroom and the hurdles to achieving number fluency are being eliminated quicker.

Now wouldn't it be cool to see students be as determined and confident
as Lolo Jones when going through a lesson because of its structure? 

At the heart of a Math Workshop style of lesson is "students [building] confidence and competence as members of a community of mathematics" (Hoffer, 5). Through its general structure of an opening, minilesson, work time, and reflection, the deep thinking and active discourse that occurs has students building a mathematical community that builds confidence and competence. It does so by having students construct the big ideas in the lesson. Thus, problem sets will become easier to manage. 

As Hoffer states, "once students grasp the concept, practice will be more efficient because the big idea is already solidified" (Hoffer, 15). Rather than trying to come to the big idea through the problem set, any remaining misconceptions can be cleared up through the problem set, since the big ideas have already been established. 

In short, I would characterize a Math Workshop style of lesson as one that efficiently leads a student to a deep conceptual understanding of mathematical concepts while having students engage with them in the same way a mathematician would. As I continue through this book, I am excited to see the nuances of the method and see what other benefits it has to offer students as I dig deep into each aspect of the method and the teacher skills necessary to execute this method. 

About Me: It's Good To Be Back (EDI 331 Introduction Post & EDT 370 About Me Post)

When I found out that blogging and engaging with the Math Twitter Blogosphere (MTBOS) was going to be a part of my ED 331 class this semester at Grand Valley State University, I became super excited! All my previous blog posts come from another course in my secondary mathematics teacher preparation courses. I thoroughly enjoyed blogging in that course and am excited to become more integrated within the MTBOS through this course.

This semester, I am teacher assisting in an 8th grade math classroom at Grandville Middle School, where I will have the opportunity to see a pre-algebra and Algebra 1 in action and then actually teach in it! I am so excited to see where this semester will go and what I will learn about teaching as well as who I am as a teacher. My cooperating teacher works with quite a few students with special needs and co-teaches with a special needs teacher a couple hours of the day, and I could not be more excited to gain experience in this area!

Grandville Middle School is a one-to-one Chromebook school, so I am also very excited that I get to integrate technology--where appropriate--into my lessons. In my secondary math education major courses, both specifically for teachers and not, I have had the opportunity to become familiar with some excellent math education technology resources for use in the classroom. To name a few, I have experience with Geogebra, Desmos, KaHoot, Socrative, and many resources from the MTBOS,and I would like to integrate these in future lesson plans. I even have a folder of resources that I have accumulated from the past couple years! Other past experiences include the use of a SMART board in both high school and college. For one of my classes, we were planning and implementing lessons for a one-to-one iPads school and used some of the features they had in these lessons. I'm cannot wait to lean on these past experiences in developing new lessons that integrate technology!

As for a little bit about me, I am coming off a summer where I was a middle school camp counselor for SpringHill this summer. This summer was so incredible and I had the best time hanging out with middle schoolers, so this makes me so excited for the semester ahead. Some interests of mine include hammocking, high-adventure activities, binge watching a good TV series on Netflix (currently The Office), watching all kinds of movies, going on spontaneous adventures in either a city or in nature, jamming out to music, cheering on my favorite sports teams but refraining from actually playing them, enjoying breakfast food at any time of the day, going to various ministry events and services, and serving others in numerous capacities (RA, tutor, Young Life college leader, etc.), among many others. The video below is an excerpt of me introducing myself as a Young Life college leader at our first club meeting. I really enjoy serving in roles where I have the opportunity to build relationships with others and serve them in some capacity, which is probably one of the many reasons I enjoy teaching!

The year ahead offers so many opportunities for me to learn, and I cannot wait to take advantage of those opportunities. In fact, I'm feeling like as ready as Andy Bernard does below! Ok, so if you were to put the photo in action, I would be just as excited as Andy is about riding this elevator. Stay tuned to hear about what I am learning as I pursue to become the best teacher I can be!

Communicating Mathematical Ideas

If someone were to ask me the which college class I have learned the most from, I would have to say my answer would be MTH 210 Communicating in Mathematics. The course has immensely helped me understand the importance of clarity and the difficulty that comes with trying to communicate your thought process and ideas. As a future teacher, I must recognize that no matter what career path my students choose to pursue, the ability to communicate their thought process and ideas will be a vital skill. Thus, if one of the purposes of education is to prepare students for their life after school, I feel as if it necessary to foster this skill in the classroom.

In my experiences as a Math Center Tutor at GVSU, I have found that the questions I most enjoy helping students with are what many professors are calling a journal entry. Essentially, the student is given a prompt where there is not enough provided information to compute a numerical value and they are asked to find an arbitrary solution and explain the how and the why of it. For example, a journal entry prompt I have seen is something to the effect of "If a > 0, for what values of b will
ax^2 + bx + c have at least one real solution?" What makes these questions great, in my opinion, is that it asks students to apply what they have learned in a conceptual sense and write about it.

Yes, math and writing can be integrated!

Often times, when I am helping a student with this type of problem in the tutoring center, what the student needs help with is not arriving at the solution, but rather communicating their computational work. My advice to them for how to proceed is to write down their thinking process in way that someone in their class who does not understand the concept quite yet could read it and comprehend it. Ron Swanson does a terrific job of depicting the facial expression I receive from students after saying this.

Ok, but...um...how do I do that exactly?

Sometimes the reaction stems from viewing the task as "stupid" or a lot of work, but I have a few students genuinely wonder exactly how they can put what in their mind on paper as they either believe the computational work constitutes a translation of the thinking process or they have difficulties with the translation from mind to paper. In response, I say that sentences in their entry can be formed by saying that "(insert known information) tells me that (insert conclusion)" or "since we want to (insert objective), we know that (insert way to show it)." For example, related to the sample prompt above, a sentence in the journal entry would be "Since we want the polynomial to have at least once real solution, we know that the determinant must be greater than or equal to zero; thus, b^2 - 4ac >= 0." This is definitely a challenge for some students, so in my future classroom, I plan to foster communication skills through a variation of the concept of journal entries: student blogging. For more on this idea, see this previous post of mine. Just like journal entries, student blogging has students explaining the how and the why, thus developing their written communication skills. Below is one of the examples in the linked post.

However, communication of thoughts and ideas is not only written, but also verbal. To help foster verbal communication, not only do I plan to infuse group work into my lesson plans, but I am considering to incorporate what the teacher I am currently observing calls "board problems." What she does is require that once a marking period (quarters at this school), each student goes up to the whiteboard and explains the how and the why of a "challenge" problem in the homework assignment.

A written computational solution is written on the board,
but a verbal explanation is required as well.

Students have the choice of deciding when in the marking period they can present their board problem. The benefit in doing it this way is that it does not harm the student if the board problem was to be preassigned and the concept did not go over well. I realize that giving student's choice is important, however, I am not quite sure that if I use this in my classroom I will let the student decide when they present. I want students to realize they can, in fact, learn from their mistakes, learn more from wrong answers than right answers, and become unafraid to share their work and thought process. Any suggestions on which way to go are definitely appreciated!

The benefits of incorporating journal entries/student blogging and board problems in the classroom goes beyond the development of communication skills. In using these, the teacher has multiple types of formative assessments that allows he/she to get a deeper and more accurate look into the student's understanding of the content, both computationally and, more importantly, conceptually. So with this win-win situation, other than the fact that it might be more work on the teacher's end, I cannot find a reason to not include these in my future classroom.

For more ways to incorporate discourse and writing in a math classroom, take a look at this presentation on the topic from a couple Michigan math teachers.