Technology in Education

In an article by Tim Hickey called “Technology for Learning, not for Technology’s Sake: Toolbelt Theory and the SAMR Model” posted on, the author covers two types of incorporating different styles of technology into math education. As stated in the title, these two ways are called the Toolbelt Theory and the SAMR Model. Each of these is its own unique way to involve technology in the mathematics classroom.

I’ll start with the Toolbelt Theory. The Toolbelt Theory implies that teachers should be giving students different ‘tools’ to add to their toolbelt. Once they are shown how to use a different type of technology they then have added another ‘tool’ to their lifespan toolbelt, or types of technology they will be able to use for the rest of their life. By looking past the standard paper and pencil approach, we are able to provide students with lifelong learning tools.

The second method, the SAMR Model, is an acronym standing for Substitution, Augmentation, Modification, and Redefinition. By using these for terms, you can incorporate technology into a lesson in many different ways. Substituting technology can help teach the same lesson but in a more engaging way. Augmentation will help teachers analyze class data. Modifications will require students to step out of their comfort zone and use technology as an assignment. And redefining a task allows teachers to be more creative in lesson planning.

I believe both of these methods can have a good impact in the classroom. I will certainly do my best to teach students how to use different types of programs and gadgets to add to their toolbelt. One way to achieve this is to use the SAMR Model or one similar in my classroom.

The next article is titled “Using Technology as a Learning Tool, Not Just the Cool New Thing” is written by Ben McNeely. In this article, he talks about technology and some of its problems along with its positives. The problems with technology are funding, the urge to cheat using the technology, and teaching people how to use it. The positives are the interaction that technology can spark, the skills that students can learn from it, and using it to connect with other generations.

Narrowing Participation Gaps

One thing that we touched upon this week in class was found in the chapters we read from ‘Strength in Numbers’ that participation in your classroom can be tricky. It can be difficult to make students who seemingly do not care answers questions and volunteer. This creates a “participation gap” where the students who participate, participate a lot and the students who do not participate, never participate. It is no surprise then that this correlates almost one-to-one with achievement as students who participate are the students who gain a deeper understanding material and know it (that is why they are volunteering answers).

The ‘Strength in Numbers’ story about the teacher who drew out participation from all of her students really intrigued me to find out more about how to get your students to participate. Especially when you have students that are all very different in terms of personality, race, backgrounds etc..

I found this article called, “Narrowing Participation Gaps” by Victoria Hand, Karmen Kirtley, and Michael Matassa that does just that. The url is:

The article discusses three specific ways to encourage and increase participation by all students which, in turn, will narrow the gap. First,

  1. Organize Mathematical “Contributions”
  • Participation is not only talking or answering questions
  • More than one way to get math answers
  • Prompt students unclear answers with directing questions

The first bullet point makes the point that teachers too often ask a question and evaluate the student’s knowledge based off of who answers and how they answer the question. It is important to remember that math is all about process and teachers need to evaluate how the students got to their answers. There are other ways of participating in class other than speaking as well. An important quote that goes along with this explanation is, “This orientation also prioritizes correct uses of academic language over students’ sense making”.

The third bullet point is one that was not said, but I observed from the example in the article. These directing questions can be uber-focused on the words that students use such as “length” and “width” as it may have a different meaning to the student than it does to the teacher. Thus, these clarifying questions help the teacher know what the student is saying and it helps the student understand what he/she is saying. This can also help narrow the participation gap when students aren’t afraid that they will be “wrong”, but rather they will get guided to the right answer. It is important not to simply give the answers to the students as they are learning absolutely nothing there. Confusion is the best way to learn.

2. Expand “Smart-ness”

  • Expand perception of who is “good” at math
  • Complex Instruction in groups
  • Assigning roles
  • Reward different ways of thinking

Group work, in general, causes more participation, as each member is responsible for their own work. This is very true for what roles are assigned and each student has a responsibility. In my opinion, group work sometimes creates less participation as the “smart student” does the work. Assigning roles changes this and allows students to see the way others think and it will expand what they deem as smart as well.

3. Engage Instead of Motivate

  • Takes away the blame on students
  • Change the classroom as opposed to the student
  • Don’t label students

While I agree it is important not to label students, I do not necessarily agree with “engage instead of motivate”. Yes, there is a time and place where you do the work along with the students, but giving motivating problems is good as well. I believe there must be a balance of both to really get the students to participate. The article talked about how teachers should allow foreign language speaking students to solve the problems in their first language and then to explain it in english and I think this is a great method. Bottom- line I believe you still have to motivate your students and it is not all about doing the work with your students because then they will start to bank on you for the answer and that will only hurt their learning.

Increasing Student Participation

Student discussion and input can greatly impact learning in a positive way. The issue is that there are always students who are more vocal and have higher status. A few student will throw their hand up every time a question is asked to the class. Meanwhile, there are students who are constantly concerned that their question or answer is wrong. A major question we have to answer is: How do we get all our students to provide their input?

The article I read, “Increasing Student Participation” from The Teaching Center, which is part of the University of Washington in St. Louis. The article gave several ideas, but the ones I found noteworthy, along with some of my own ideas, are the following:

  • Set up ideal physical setup for discussion
  • Set expectations
  • Establish environment of caring and respect
  • Have class schedule set up for time for discussion
  • Respond positively to student ideas

Set Up Ideal Physical Set-Up

According to the article, there are many things that a teacher can do for the class to prepare them to participate in discussions. One thing is just the way the classroom is set up. The article suggests creating a U shape with the desks, which helps, since the students are facing each other and not just the teacher.

Set Expectations

Also, set expectations for how much each student should participate. If the intent is to have every student contribute, let them know that every one of them has to contribute. One option is to have participation be part of the grade, but if we do our job as educators, getting students to contribute to a discussion should not have to be something that we have to force them to do, but eventually something that they will do on their own with our support.

Establish Environment of Caring and Respect

One idea that the article did not address but I’d like to is establishing an environment of respect and caring. If we as teachers make it clear that every student’s input is valued, no matter their status in the class, then students will respect what other students are saying and not degrade them for it. As a result, students will not be afraid to speak their minds as much as they would otherwise.

Have Class Schedule Set Up for Time for Discussion

One way to promote discussion in a classroom is by allowing plenty of time for it in the proper way. If a teacher only asks for questions and students’ thoughts at the end of a lecture, they may not remember what they thought throughout the lecture. On the other hand, if a teacher stops after every fifteen minutes of a lesson and asks a question to the students and asks for their questions and comments, the students may better remember what they just learned. Also, asking a question and taking responses immediately is not always the most effective way for students to formulate ideas and give a response. Giving students 10-15 seconds to think allows everyone to come up with an idea before anyone else responds. Mixing up discussion methods can make it so every student can give a response. Moving from partner groups to small groups to large groups to a whole class discussion can make it so every student feels comfortable sharing at some level.

Respond Positively to Student Ideas

For students that lack confidence, pointing out their good ideas is very important. Even if their answer is not totally correct, pointing out what is correct or paraphrasing so it is correct can give them a confidence boost and think of their response as valuable. As stated in the last section, having students submit responses online or in some other private way and responding positively to that will give them the confidence to participate more in partner groups, where positive feedback will give them the confidence to participate in small groups, and so on.

The article “Increasing Student Participation” gave some intriguing ideas for how to get more students involved in discussions. I think that this is a very important subject to bring up, because all through my education, there were always people who would contribute every day and people that wouldn’t contribute at all. Sharing ideas can be a great learning experience for everyone. Hopefully we can use these ideas to have all our students contribute in meaningful ways.

Equity in Education: The Relationship Between Race, Class, and Gender in Mathematics for Diverse Learners

Equity in Education

Reading about a particular case study for class caught my interest. It was the case study in which a particular school was placing the majority of non-white students in below grade level courses, while just over one-tenth of white students were placed in these same classes. I was curious to learn what could possibly make such a disparity occur. I found the article “Equity in Education: The Relationship Between Race, Class, and Gender in Mathematics for Diverse Learners,” which was written Debra Rohn from the University of North Carolina at Charlotte for The Urban Education Collaborative. The article addresses how race, class, and gender affect learning outcomes and gives some theories on how to fix it.

The first topic discussed is “race and mathematics.” There is huge differences in average test scores between African Americans and Whites and Hispanic Americans and Whites, to put it plainly. This could be the result of direct discrimination, such as placing students of other cultures in classes below grade level just because the teachers do not expect them to do well based on their race. The article seems to suggest, though, that the more likely scenario is the expectations put on minorities by society as a whole. They are likely not expected to do well, and they realize this. The article suggests that many of them probably give up on their math abilities, since mathematics is widely viewed as a “White subject” in America. The article makes the claim that even when African Americans succeed in mathematics, some would describe themselves as “acting White.” Now, at first, this may seem to be more about equality than equity, but the solution that I gathered from the article is to give extra psychological help, of sorts, to children that are minorities. In an equitable classroom environment, students would be taught that a student’s race does not take them out of the running for a career in mathematics. One major issue is that the students are believing that they cannot pursue success in mathematics simply because of their race, and in an equitable classroom, they would be taught to think otherwise.

The second topic of discussion is “class and mathematics.” This has less to do with the idea that someone is behind someone else and more to do with the idea that students from lower socioeconomic status are set behind. When a child is raised by a single mother who may not have even graduated from high school, that mother is probably going to work long hours, which leads to her not being able to be with her children as much as parents from higher socioeconomic status. This leads to less development for the children of the lower socioeconomic status family, since they had less chance to communicate and do learning activities such as reading. This does put them behind from the beginning. A solution to this is for teachers to quickly realize this, and, rather than put them on a lower track for the whole education career, give them added supports and multiple modalities to work with.

The third topic was “gender and mathematics,” which focused on how many people think that men are naturally better at mathematics. There have been studies that show that this is not the case. As with race, the differences in test scores most likely comes from them thinking that they are less able to do mathematics, so they give up on being as successful as they could be. Also similarly to race, the solution is to eliminate these ideas in our classrooms, so that everyone gets a clean slate and can pursue whatever career choice they would like.

My view of this is that the solutions to all of these are to either reinforce positive thinking so that everyone believes that they can learn mathematics or help those that are behind so they can catch up to everyone else. Of course, one shouldn’t assume that a person that is African American or a woman isn’t at a disadvantage, because they could be someone who has a difficult past. Even if a classroom was all white males, we as teachers should know what past they come from, so we can potentially help them come out of it with hope of a better future. I can use this information to help my students overcome racism and sexism to pursue their dreams. I can use this information to help students who come from difficult beginnings get to a place where they can learn more information easily. The point is, teachers should learn as much about their students as possible, and cater to that. That is the point of equity. That is how it can be used with race, class, and gender.

Addressing the Equity Principle in the Classroom

I discovered the article “Addressing the Equity Principle in the Classroom” in Vol. 101, No. 8 of The Mathematics Teacher.

The article describes a research project performed by the University of Wisconsin-Madison involving the math teachers of a chosen school district that participated in defining equity in the classroom. The following four responses emerged from the project:

  1. Equity is about instruction.
  2. Equity is about creating a specific classroom environment.
  3. Equity is about equal opportunity.
  4. Equity is about appropriate curriculum.

This study also asked teachers to identify one student that was performing below proficiency level or a student whom they had little personal connection. The teachers were given questions to facilitate getting to know the student and reflect on how getting to know students on a personal level correlated with achievement. Teachers reported in multiple cases that just getting to know these students better that achievement began to rise for each individual student.

In one of the reflections, the teacher realizes the stress one student has with English being a second language and working to provide for his family outside of school. Another teacher shared how a student simply talks to her about her interest outside of the classroom and have found commonalities in those interests, creating a positive environment in the classroom. This student has displayed a higher level of achievement since these interactions. This appears to have been accomplished without a distinct change in instruction, simply from more positive interaction and relationship building with the individual student.

After reading about this study, I determined that the methods math teachers use in the classroom that promote relationships and interaction among peers and teachers alike are very important to providing equity of access to mathematics. Teaching is a form of communication. By creating more mediums through which we can communicate concepts in which students and teachers can understand, we will have more pathways to communicate understanding.

So how? How do we build relationships that promote mathematical understanding? Even though this appears to be less specific than mathematical instruction, building relationships is very important to general learning. One of the things I will be doing in my classroom involves developing values of our community (classroom) through the students’ eyes, giving them ownership of what the environment should be. I want to break students into small groups, mixing them up periodically in the first period of time that they spend in the classroom. I want students to discuss what standards we want to live by in OUR classroom. There will be a couple that I will have at the beginning such as Follow the Code (school handbook), Look at the Person You are Speaking To. Everything else will be the product of the students. However, finding a way so every student is heard and validated is very important. This sets the tone for students to have ownership of the culture as well as places myself as a teacher as serving the students’ needs that they identified themselves. Once we establish these things, we can move into mathematical instruction with a foundation built on the needs of the students.

The one thing I think is missing from this study is how the students interacted with each other in these math classrooms. There are far more relationships in the classroom than just teacher-student. I believe the dynamics of peer relationships, especially in secondary education, can impact equity in a math classroom. Facilitating positive, productive interactions of students with their peers can break some of the barriers of equity in the classroom.

I discovered another blog titled “8 Characteristics of an Equitable Mathematics Classroom”.

It promotes conversation for problem-solving which opens communication pathways for students to access understanding. The blog also states that “achieving equity is meaningless if it sacrifices excellence”. This should be the challenge of all math teachers to connect with students’ needs to achieve both of these things.

Access and Equity in Mathematics Education


I read an article titled “Access and Equity in Mathematics Education” from the NCTM website. In this article, the writer asked, “What is required to create, support, and sustain a culture of access and equity in the teaching and learning of mathematics?”

The writer believes that these things must happen in order to create, support, and sustain a culture of access and equity:

  • Be responsive to the background, experiences, perspectives, traditions, and knowledge of students
  • Acknowledge and address factors contributing to different outcomes among students
    • Critical in making sure students have chances to experience quality math instruction, learn challenging content, and receive necessary support

To achieve equity and access, you must make sure all students attain math proficiency and increase the number of students who attain the highest math achievement regardless of factors such as; race, ethnicity, language, gender, and socioeconomic group.

After sharing ideas on how to create such an environment, the writer offers a few practices that myself and other teachers can use to achieve access and equity. A few of these practices are; holding high expectations, allow time for students to learn, and ensuring quality math curriculum and instruction. By keeping high expectations for each student, I can ensure that I will have high expectations for myself in needing to do my best to help each student. Each student will learn at a different pace, by allowing each student adequate time before moving on will help them completely grasp a concept.

Another article I found titled “Equity and Mathematics Education” comes from the James C. Kennedy Institute for Educational Success. This article concludes that providing classroom equity starts at an early age. Based on what type of education they receive as a child has a large part to play in how successful they will be in mathematics as they continue to progress through school.

Tracking In The Mathematics Classroom

The article that I read was “Promoting Equity in Mathematics: One Teacher’s Journey” by Alan D. Tennison, published by NCTM (link: After searching for articles involving equity in the mathematics classroom, I stumbled upon this article when I began to look through the NCTM website. Throughout the article, Tennison describes his personal experience with equity in the mathematics classroom as a teacher. The specific topic of discussion in this article is tracking, or grouping students based on their abilities in different mathematics classrooms. He discusses that although tracking may be helpful to students who are high-achieving, it has proven to be detrimental to poor and minority students in the past. At the end of the article, Tennison describes his own experience with creating a heterogeneous classroom where there is a standards-based curriculum and students with differing mathematical abilities are put in the same classroom. The curriculum was split up into units where there would be a central problem relating to other areas of study that the students would investigate throughout the unit. Within Tennison’s school, he found that students who participated in this track were more likely to enroll in four-year mathematics courses in high school, and had a higher average ACT score by 3 points. The article overall begged the question about the value of tracking in high school, causing me to reflect on what I consider its value to be in the classroom, as I had always considered tracking a positive part of schools because it challenges the students that need more challenge, and gives the students who may need more support in their classes the support they need to be successful. However, there are more questionable aspects of tracking than meet the general onlookers eye.

Tracking is a controversial topic in education as often times the students who are in the “lower” track are often overlooked, and as Tennison writes in his article, they are trained to memorize formulas rather than problem solve. The problem there lies within the instruction itself, which is at the core of equity in schools. Teachers ask that students in “lower” tracks memorize formulas because do not believe that the students are capable of learning the material to the same standard that students in the “higher” track are. Tracking inherently predisposes teachers to have prejudices about students in the different tracks. While in general tracking may seem like it has benefits, the way in which it is too often carried out negates these benefits.

The information that Tennison provided can be used in the future when designing my own curriculum, especially if I am given the opportunity to teach students who consistently struggle in mathematics. A portion of the problem that he mentioned in the article is that students in tracks that are not advanced focus on drilling different formulas for memorization, not problem solving. Problem solving, critical thinking, and other skills that can be developed in the mathematics classroom are focused on in the higher-level tracks. Therefore, if working in a school where tracking is part of the curriculum, the students in “low” tracks may especially benefit from a curriculum that focuses on problem solving, and critical thinking. Thus, the modification I would then make is to implement the standards-based curriculum heavily into tracks where students more noticeably struggle in mathematics to promote equity in mathematics. Tracking in itself does not allow for full equity in the classroom because it separates students based on ability, but there are ways that teachers can work toward creating the most equity they can if working in a school where tracking is present. Tennison’s proposal for creating a heterogeneous classroom prompted me to:

  1. Ponder the value of tracking in the classroom
  2. What teachers can do to help students who have been placed in a lower track if a school does implement tracking
  3. What the underlying benefits are of having a heterogeneous classroom

Therefore, I found a chapter of a book that discusses tracking in schools, and its implications. This chapter addresses the concerns listed above about tracking, and discusses its strengths and weaknesses. The link to the chapter: