Ways to Motivate Students

When I tell people that I’m going to be a math teacher, the general reaction is something along the lines of: “Gross. I hate math.” Math is arguably the most disliked subject in high school. People may dislike writing papers, but they can write about things they like. People might dislike science, but they at least might enjoy doing experiments and such. Students don’t see the reason to like math if we don’t properly motivate them. I found an article recently called 21 Simple Ideas to Improve Student Motivation that has some good ideas, in my opinion.

One general idea that I like is giving students some control. This could be through letting them in on decisions like what type of assignments they do or it could be giving them responsibilities or positions in the classroom. Another idea I like is to create variation in most things. One point the author made was to change up the scenery. This could be how the classroom set up or leaving the classroom to go outside or just to another room. Another variation that could be done is in what type of lessons are done. Switching between lecture, group work, projects, etc. can be very beneficial, because students will show up eager to find out what kind of activity is being done for the day. A third idea I like is to just try to make things fun. Rewarding students both verbally and with physical objects is fun for the students. Being exciting as a teacher and making jokes is something I really believe should be done more. Students also love a little competition in class too. I think that these are some things that I will include in my own classroom so my students will be as motivated as possible.

Yummy Math That Doesn’t Involve Eating Pie on Pi Day

If you were hoping for excuses to eat food while teaching math, this probably isn’t you blog post to read. Instead, I am writing about Yummy Math, which is a website that provides interesting lessons for students of all ages. While not the most visually appealing website, it is very useful for a math teacher looking for resources. . The lessons they have are about things that are useful or realistic (unlike the problems about buying 60 pumpkins or eating 20 candy bars). They are also aligned to standards. They have tags on every problem with the standards they are aligned to. There is also the option to search for lessons based on the standards you want to address. The lessons go from 2nd grade mathematics to high school. A one- year membership only costs twenty-two dollars and gets you access to all the materials that they have on the site.

As someone who will be student teaching next year, I’m always on the hunt for valuable resources to help me teach. I think that one of the best ways to do this is to find websites like Yummy Math. It can be a challenge if one wants lessons that are geared towards standards, challenging, and interesting to students, but we have to put in the work as teachers. It’d be great if we could come up with really fun yet challenging tasks for our students on a daily basis, but the truth is that there just isn’t always time in the day, especially if you have to teach five or six different classes each day. This is why great resources are important, and I’m happy to say I’ve found another one.

If In Search of Practice Problems…

I volunteer at the local middle school in a resource room for an hour every Tuesday and Thursday, and the last time I went, the teacher suggested that I help students prepare for the standardized testing they’ll be doing in a week. Coming up with a way to help them broadly study eighth grade mathematics without knowing what they know stressed me out a bit, but then the teacher asked if I’d ever used IXL. She showed me it, and I’d have to say, it’s an impressive tool for review. It basically gives problems for each concept you could teach in math, language arts, science, social studies, or Spanish. For example, the teacher who runs the resource room said I should work on real life examples of area and perimeter. There’s a section called “area and perimeter: word problems” that I could use. It gives problems that are exactly as described.

The way I used it was by just going through the problems up on the board, but it’s really set up for students to use on their own. It presents a problem that the students have to answer. If they get it right, it adds to their “SmartScore.” If they get it wrong, it takes away from their score and gives them an explanation for how to solve the problem. It also keeps track of how long they’ve been working. After students are done, a teacher can look and see what each student’s areas of need are, which can help the teacher differentiate for their students. IXL can present information in graphs to show “your students’ growth, trouble spots, and even their readiness for standardized testing.” IXL is built around content standards, so it’s great for preparing for standardized testing. I think that it can potentially be a great resource, especially because of this reason, but it can be easy to go overboard with it.

While it’s great to have so many problems available, they are pretty simple problems. They should be used for repetition, not teaching. I could see some of my own high school teachers delivering a quick lesson and then just letting us loose on IXL for the remainder of class, which doesn’t help the students much. The problems don’t encourage much deep thinking; they’re better for practice. This is fine, I’d just had for teachers to become too in love with it and use it constantly. To conclude, I think that IXL can be great for practice and review, and it can help teachers learn more about their class more quickly, but shouldn’t be overused.

IXL Home Page

Silent Discussions

Some major goals of mathematics are to have a deep understanding of the content and to be able to make connections to other concepts. I decided to look around the NCTM website for articles about such things, and I found one called “Visible Thinking in High School Mathematics.” This article is about two main methods: Chalk Talk and Claim-Support-Question. I’m going to focus on Chalk Today, because it really caught my interest.

The main idea is to have a variety of posters around the room with questions on them, generally sounding something like “What do you know about (concept).” Forever however many posters there are, say five, that many different colors of markers are distributed among the students. Students with all the same color markers are sent to a poster, and are told to write what they know about the concept. This is a totally silent activity, which is why the author called it “Silent Discussion.”Students then rotate around the room and either respond to what other students wrote or write their own new idea.

Chalk Talk gives students the opportunity to look at other students’ ideas and get their questions answered at least partially by other students. For a question such as “What is a quadrilateral,” a student may have thought of a square, but with Chalk Talk, they can get the opportunity to see a non-square rectangle, rhombus, parallelogram, or any other quadrilateral, possibly with a picture and description. It gets them thinking outside the box. If they aren’t sure about something, they can ask, and the next group at the poster won’t even know who wrote it, and they can get an answer for their question. That’s ideal.

The posters really end up looking like a mess, but the teachers can somewhat gather what the class knows and doesn’t know, as well as where the class should go next. Even if questions get answered, it still shows that students might not quite feel comfortable with a concept. On the other hand, a question asking about a possible future direction from their new knowledge can make for a great transition into the next topic. Also, students enjoy getting out of their seats, and this is a productive way to do that. It is a great idea overall, in my opinion.

Visible Thinking in High School Mathematics

Not Only Should We Use Real-Life Examples, but We Should Choose Real-Life Examples That Target Interests

In order to motivate students and deepen their understanding of math concepts, we as teachers/future teachers should use real-life examples. If the only problems we ever use in our classes are basic problems consisting of numbers and variables, students will get bored very quickly. Many textbooks include problems that could occur in real life, but these problems are rarely ones that students would do on any given day. They may include buying 40 shirts or 60 pumpkins. I distinctly remember doing a problem where we figured out the length of a guy wire when given the length of a telephone pole and how far away from the pole the guy wire touches the ground. I can’t remember the last time I figured that out in real life. One of my professors preaches that the real-life problems we do actually need to be things we would do in real life. I wholeheartedly agree, but I’d like to take it a step further and suggest that we do problems that students would want to do in real life, even if they haven’t thought of it.

The first step is keeping up with students. Right now lots of people, especially boys, are obsessed with Fortnite. Many more enjoy sports. People obviously love social media. Teachers need to take the time to get to know their students’ interests so they can create lesson plans around these interests. Next is identifying numbers within these interests. This could be numbers of calories, numbers of followers, completion percentages in football, etc. Then problems that challenge the students need to be made. It needs to be at the correct level of difficulty while also deepening understanding and encouraging discovery. Finally, the teacher needs to find a way to smoothly fit these problems into the curriculum. They should not be random problems using concepts from weeks or months earlier.

A great website that has such problems is Mathalicious. It has 135 challenging problems for all types of math concepts that help students find out interesting facts. One problem that caught my eye was about basketball. It involves finding out whether fouling an opponent on a game winning shot is a good idea or not. It has students find the probability of each team winning and losing in either scenario in a real life situation. It really interested me, because I like sports. There are also other problems about social media, food, tv shows, games, fact about the world, and much more. It’s a great resource for finding problems that interest students.

My Internship Week

This past week (12th through the 16th), I completed my secondary education internship. In case you don’t know I have a double major in secondary mathematics education (7-12) and special education (K-12). This internship was for the secondary math education major. I was at North Sioux City Middle School from 7:25-3:05 every day for a week. I learned many lessons during my time in the classroom, but a few I’d like to focus on are: Having a backup plan, making sure everyone understands, and that there are many resources out there.

The first lesson I learned is to always have a backup plan. This is especially true when it comes to technology, since it seems to fail so often. Three out of the four days I was in the classroom, something came up that forced my mentor teacher to change her plans. One day (Wednesday) it was the walkout that took place. Another time it was just that many students had a school activity going on that she wasn’t told about. The third time, the computer program she wanted to use wasn’t working properly. Every time, she seamlessly switched to another lesson. I’m not even sure the students noticed that she had changed her plan. That’s because she always had a backup plan. On Thursday of my internship week, I taught a lesson that required the students to use Desmos on laptops. Logging in to the laptops took at least five minutes, and since I had not planned for this set-back, all I could do was stand up front and ask whether they were logged in. After my lesson, when my mentor teacher and I were talking, we discussed how important space-fillers and backup plans are when it comes to technology. That’s another takeaway, along with just having a backup plan in general.

My second major takeaway is to make sure everyone understands. One thing that I witnessed, and this doesn’t really hurt anyone except the teacher, was that my mentor teacher would plan for the fastest students. I did the same thing when I did my lesson plan. When I was trying to figure out how long it was going to take, I was thinking about how long it took the few fastest students to do a similar task. In reality, learning takes time. Checking whether everyone understands takes more time than I would have thought. A teacher needs to go around and make sure that everyone knows what’s going on, so everyone benefits from the lesson.

My third takeaway is that teachers use a lot of different resources. There’s definitely many teachers that don’t, but there are so many teachers sharing what works for them. Why wouldn’t a teacher want to find lessons that work. On a daily basis, my mentor teacher was trying to find more lessons that work, and she ended up finding more interactive, life-like lessons for things she was going to teach in a less fun way. One collaborative sort of website I found was opened.com. In this website, one can search for a standard in a grade or class and find lesson plans for that standard that other teachers have shared. There seems to be a limited number of people that have shared their lessons, but it seems like a great idea. Searching the internet for lessons that can get students more interested in mathematics in worth the time.

Other notes:

It was really interesting to finally see things we’ve learned in class implemented by real teachers. For example, if someone had headphones in or their phone out, my mentor teacher would go up and whisper to them to put it away, rather than yell or pull it out of their hand or anything like that, which is something we learned in class.

It was a new experience to see the break room at the school I was at. If there’s a reason to not become a teacher, I heard it there. They complained about pay, parents, behavior, etc. It makes sense, though. Teaching is a tough profession and at some point, we all need to vent. On the other hand, it was awesome that my mentor teacher and a few other teachers told me they wouldn’t trade their job for any other one. That was a really cool moment.

Middle school is an odd age to me. In some ways, they don’t even seem close to adults. They don’t take care of their hygiene, they behave like middle-schoolers, and they love games and throwing things. On the other hand, some have the same interests as me. There’s also always a group that thinks they’re too cool for me. I’m not saying I don’t like it, it’s just an interesting age.

Those are my takeaways from my internship. I definitely learned a lot, so it was a very valuable experience. It’s great to get out of the college classroom and get some time doing what I want to do the rest of my life.

10 Strategies to Highlight Strategies

Angela Watson’s Article

So often, students just want to find the answer to problems so they can get done with the assignment and do something else. I’m guilty of this myself. When I took Calculus 1-3, for online assignment, I’d look at an example problem, find where the numbers in the problem came from, switch in my answer, and move on. However, a few weeks after the test, I could not remember how to do the problem. How can we expect students to do well on standardized tests when they get homework done by taking shortcuts while gaining no real understanding of the mathematics? In our 7-12 Math Methods class, we’ve been talking about having students explain their strategies and recognize that there are multiple available strategies for many problems. We need to employ strategies to help students understand…well…strategies.

To learn how to help see students understand all strategies more effectively, I read an article by Angela Watson titled “10 Classroom Strategies to Get Students Talking (and Writing) About Math Strategies.” As the title suggests, there are ten different strategies that Ms. Watson suggests to get students to talk and write about their strategies and also just to ensure that they know.

1. Start a lesson by talking about possible strategies, rather than with an easier problem. This strategy involves having a more difficult problem that you want them to solve, and instead of requesting an answer, the teacher has them think about how they might solve it, then get together with a partner and discuss, and finally share potential solution strategies and use them to solve the problem.
2. Along with number 1, another strategy to use is to have students do problems without finding the answer. This has students recognize the importance of the process. The teacher can also have students discuss their strategies, and if there are multiple strategies to solve the problem, this method can help students realize it. I agree with this idea, because it will help students remember what they did to solve a problem rather than the answer to a problem they’ll never do again.
3. Ask students about what they did throughout the process and about their work, not just how they arrive at an answer. Ms. Watson came up with 100 questions to ask to students to start conversations about their mathematics. These include questions asking about real-life examples, where certain values came from, how one could estimate answers to similar problems, and, obviously, many more. I might have to use some of her questions in my classroom.
4. Discuss different strategies for solving problems and why people chose the strategies they did. According to Ms. Watson and probably many other teachers, students get annoyed when doing math because they can’t figure out the one single solution strategy. Showing that there is more than one strategy for solving the problem can make students more eager to do math, because they can do it in their own way. I believe in this strategy for teaching mathematics, because we do it in our methods class, and I’ve learned about connections between different types of mathematics that I never knew existed.
5. Use math journals. In math journals, students can do their work for problems, as well as state what they were thinking at every step. They could write about what went right, where they got confused, and reasoning for it all. With math journals, we as teachers can figure out where they’re at mathematically while they have to explain their reasoning and understand it more. I might be open to using math journals, although it seems like it might take a lot of time if I were to actually read all of them.
6. Have a smaller set of questions you can use all the time. These may be similar to the 100 questions mentioned earlier, but there are much fewer of them, and they should be used often enough that students start to think of them on their own. Some of the questions I might use are: How did you get your answer? How do you know it’s correct? What are some other strategies for solving this problem?
7. Use effective techniques for getting students thinking. There are many ways to do this. Asking the right questions is one way. Another is to walk around and encourage or help students. Selecting the right order to address solutions in for discussions is another one. Getting to know all the ways could make me a very effective teacher.
8. Play math games. I think that Ms. Watson might have had longer classes than the 50 minutes ones I had when I was in high school, because she suggested breaking up a class period with a 10-15 minute math game, but I think that would probably take some valuable time if done on a daily or nearly daily basis. I think I would use this strategy once a week or so to check understanding and provide an incentive for the students to learn the information.
9. Use a program that allows you to see their work as they’re doing it. I think the main takeaway from this is that there are apps and such for which teachers can have students record their screen as well as anything they say while they’re working on homework, so they can see the whole process. This gives a good idea of where students are at with the concept.
10. Have students create posters that contain all the strategies they’ve seen. They can start making these posters at the beginning of their learning about a concept. As time goes along, they can add the teacher’s strategies, other students’ strategies, and their own strategies.

Teaching Through Problem Solving

In our 7-12 Math Methods class, we’re talking about problem solving, so I decided to read an article about using problem solving techniques to teach. The article was “Teaching Through Problem Solving” by Cos D. Fi and Katherine M. Wagner. The article gives five steps for using a problem to teach. The first step is to give the entire problem to them. This means that the problem shouldn’t be broken up to make it easier for the students. This encourages productive struggle for the students, meaning they have to persist and figure it out on their own, which will help them in the long run. The next step is to let students discuss the problems and make predictions about the problem. Students should share their work and listen to other people share their work to build understanding. The third step in this is to “focus on the big idea of the mathematics.” This means that students should make connections to other ideas and explain how to use prior knowledge to solve it. They could also make predictions about where the mathematics is going. The fourth step is to show student work. This should include mistakes and successes. Showing where students made mistakes can increase understanding. It can also make students more open to sharing their ideas and get them feeling more comfortable around their peers. One method I’ve seen is after a test, a teacher will take pictures of problems on people’s tests and project them and talk about where mistakes were made. Step five is giving students time to reflect on what they learned. There could be assignments with this where either students do a journal article or something similar to discuss what they learned or they can do additional problems that show understanding.

I think that one general theme with every step was that students had to struggle a bit and share what they were thinking and doing while they were completing the problem. This makes the problems a teacher does much more valuable and understandable for the students. In our class, we would call these problems higher-level demand tasks, because they force students to dig deeper into the mathematics and learn why they’re learning the information and explain their reasoning. I can use these methods for teaching in my classroom by keeping these steps in mind every day. I doubt that I’ll use problems to teach every concept, but I will probably teach through problems for some concepts, and these advised steps can help me teach more effectively.

Teaching Through Problem Solving

Using Learner-Generated Examples to Increase Understanding

Learner-Generated Example (LGE): Examples of concepts that are created by students

In the majority of mathematics classrooms, teachers use what is called lower-order thinking to teach their students. Some verbs that are in Bloom’s Taxonomy, which shows what’s higher- or lower-order thinking, that are a part of lower-order thinking are words like calculate, solve, apply, complete, produce, and manipulate. These are all words that teachers use after teaching a lesson and giving students a large amount of problems and tell them to do finish them. This approach is fine. Practice does help. However, if we want our students to have a deeper understanding through the use of higher-order thinking, we should use activities that use verbs like create, compose, invent, and formulate. One way to promote this higher-order thinking is by having students create their own examples and interpretations of concepts, called Learner-Generated Examples (LGE).

I learned about Learner-Generated Examples from an article in NCTM’s Mathematics Teacher titled “Learning about Functions Through Learner-Generated Examples” by Martha O. Dinkelman Laurie O. Cavey. The article describes how they used a multiple-step process of formal formative assessment using LGE. They started by teaching about functions. After this step, they had students list everything they knew about functions. They worked up to having students give an example of a function in four different formats. They later came back to this method after seeing what they needed to teach and teaching it to the students. This is a great use of LGE, because students may not be able to put into words what they know about functions, but having them give examples of functions shows what their preference is. The teachers learned that while students could have written out the equation, drawn graphs, or written what the function did in words, students usually just wrote a series of numbers for x-values and y-values. This showed that most students thought of functions and x- and y-values, which meant that the teachers had to work on helping them understand all the forms of functions.

In our 7-12 Math Methods class and our Curriculum and Instruction for Middle/Secondary School class we’ve learned about the value of having multiple correct answers. If there’s different correct answers, that means that there’s multiple ways to come up with those answers, which provides an opportunity for students to struggle and collaborate. There is certainly multiple correct answers when students have to come up with their own examples. For an example of an example, if students have to give examples of how a difference in slope in a linear equation changes the appearance of the line on a graph, there’s an infinite number of potential answers. They also have to identify what number in an equation symbolizes the slope and make the connection between the equation and the graph.

Another useful part of LGE is that it can be used for many different concepts. Students can create their own graphs. They can create their own equations. They can create tables or dimensions of objects or shapes. They can also use technology to create these examples. Students could draw a random line and try to figure out the equation of it. This is a great way to use Desmos. Students can experiment with entering equations and seeing what shapes they can create.

The way that I would use this in my classroom is as a formative assessment to check and see what students have learned and what I need to work on. I like the idea that the article had about asking students to provide multiple examples for a single function. This can show what they’ve learned and what they need to work on. It can help me as a teacher to figure out what my weaknesses are in a lesson. Most importantly, I think it deepens students understanding of a concept by having them create an example that fits the main idea.

Link to NCTM article:

Learning About Functions Through Learner-Generated Examples

Using Student Input for Planning a Course

In our 7-12 Math Methods class, we’ve discussed how relating lessons to students’ lives is very important for keeping them interested. When we discussed reasoning and sense-making in mathematics, we decided that one of the main purposes of teaching mathematics is to prepare students to use mathematics on a daily basis. More recently, we’ve learned about coherence in a mathematics classroom, that is “artfully piecing together segments, creating tensions and dilemmas, building toward a conclusion; also can be seen as links/connections to/between parts of the lesson or from one day to the next or from one lesson to the next or to the real-world” according to the TIMSS study. One part I’d like to highlight is the last part of that quote. It should relate to real life. Mark F. Russo, in an article written for NCTM’s Mathematics Teacher titled “Customizing and Math Course with Your Students”, writes about taking it a big step further and actually giving students a substantial say in what they learn. In this post, I will write about my takeaways from the article, as well as what I agree and disagree with and how I will use the information in my classroom.

Russo’s idea was to allow students to have input on what units they were going to cover throughout the year at the beginning of the year and to allow them to give input throughout the semester for how he taught and what kid of homework he gave. One thing you should know is that he was teaching a discrete mathematics class, which was basically an alternative to college algebra or calculus that still prepared students for college. One idea he had for gathering ideas was to put students in small groups and have them talk to each other about what they’d like to learn. He listened in and used their conversations to decide what he should teach. After determining a couple topics of interest, he made the class so that there were three units on topics that he felt were part of discrete mathematics that should be taught and two units on topics that were very similar to what the students had chosen. Once the class had begun, he allowed the students to fill out regular surveys where they could state how they wanted the class to be different in terms of teaching approach and types of homework. He found that the students didn’t necessarily like the units he picked, even with the changes he requested, but they were really genuinely interested in the topics they had chosen. He barely had to do any work, because the students were very enthusiastic and willing to learn on their own. If students did not like the topics that the rest of the class had chosen, he had them write about another subject they would’ve liked to cover and how they would teach it. This way, they still got to learn about the subject they liked.

I do think it’s nice to address subjects that students like, and it seems that it could work in a class like his where it’s the final math class of their high school career. However, in most math classes, it’s not an option to totally remove whole units and replace them with something the students are interested in. It doesn’t seem practical to do this in, for example, an algebra classroom. They most likely wouldn’t know information that would be on standardized tests and wouldn’t have the information they’d need to succeed in algebra 2. So I think it could work in some situations but most likely wouldn’t work in most situations.

Some aspects I do like are the consistent feedback throughout the semester and letting the students have some say. The feedback is nice, because I know that throughout my academic career, myself and other students will constantly discuss assignments we don’t like or how the teacher teaches things, but the teacher would never know until the end of the semester, when we did evaluations. Letting the students give feedback on a weekly or even monthly basis allows for the proper adjustments. I also think that letting the students give information that they’d like to learn about can be helpful. It can help us learn about our students and their interests, as well as what they know and find important. In my classroom, I’ll allow students to provide feedback on a consistent basis and make sure I know what their interests are. I like the idea of students working in small groups as well. I think that this can help build their confidence and make them more willing to express themselves and answer questions in the future.

To wrap things up, the article “Customizing a Math Course with Your Students” was about a class in which the teacher, Mark F. Russo, let his students decide what two-fifths of their class would be covering. He had some intriguing ideas and some that I do not wholly agree with, but overall, I think I gained some information and methods that I can use in my own classroom.

Link to article: http://www.nctm.org/Publications/Mathematics-Teacher/2015/Vol109/Issue5/Customizing-a-Math-Course-with-Your-Students/