Improve Mathematical Thinking

Share your plans for improving the mathematical thinking of the students in your classroom. When sharing this plans please explain your: 1) Classroom setting, 2) Need for the change, 3) How much change in student performance you expect, 4) What instructional change you plan to implement, and 5) How you plan to measure the change in student performance.

A.SSE-Using the Quadratic Formula with Technology

richarta Algebra Teaching Issues, Common Core State Standards Mathematics, HS Algebra, HS Modeling, Improve Mathematical Thinking, Technology Teaching Issues

This is a lesson for teaching students how to use the quadratic formula with the use of a SMART Board. How the students learn to use the quadratic formula is broken down into three steps: identifying the coefficients (a, b, and c) in a quadratic equation, correctly plugging them into the quadratic formula, and executing the formula correctly. What the teacher is trying to accomplish is attempting to get the students to learn a new mathematical skill by the use of technology. The teacher hopes that students will be more engaged in this lesson rather than writing on a regular whiteboard. You can view this lesson by following the link:

LessonPlanTemplate(1)

  • Integrating Technology in the Mathematics Curriculum

How technology is integrated into the curriculum of mathematics is by using a electronic white board, otherwise known as the SMART Board, to conduct a lesson and do practice problems with the students. The SMART Board will allow multiple students, maximum of 6 at a time, to do physical work on a given problem using their hands or a pen. Also, the SMART Board has access to a presentation website called the SMART Exchange. This website contains mathematical presentations that teachers can access and use in their classroom and the students can work on problems from the presentation physically. This piece of technology could help students reach the Common Core State Standard by getting the students more motivated and excited to participate in the activities offered. Because students are more interested in their computers and phones, this is a touch screen whiteboard that is much like some of their phones. There are high hopes to get students more engaged and motivated when using this piece of technology.

  • Participation in Community of Mathematics Educators

SMART Boards are giving the community of mathematical educators a much easier and mess free experience when conducting a lesson. When using the SMART Board, the teacher can create her or his own presentation or find one on the SMART Exchange. If a teacher wants to add anything to the presentation they can right in the moment by just writing on the SMART Board. Also, your days or erasing chalk or expo pens and writing with chalk or expo pens are over. The SMART Board is a mess free board. This is a great piece of technology that is easy to use, easy to display lessons, and mess free.

  • Ability to Contribute to Program and School Improvement

The SMART Board will help contribute to school improvement and to the program by getting students to be more engaged and by giving teachers a better way to communicate lessons to students. Students already have a hard time paying attention in class because they are distracted by their own pieces of technology. In using an electronic whiteboard that has a touch screen, there are high hopes to get students more interested in participating class and using the SMART Board to solve problems. Teachers can also choose lessons that best fit their classroom. Based on the students’ knowledge and skill level, the teacher can find a lesson on the SMART Exchange website that best helps students learn. Or the teacher can create their own lessons on the SMART Board. The SMART Board can display easy to read instructions, practice problems, or pictures. For example, if a teacher need to show a picture of a graph but also write down what the different parts of the graph are, the SMART Board can easily display all the information needed or the teacher can display the picture through the SMART Board and write on it what the parts of the graph are. SMART Boards have the ability make teaching more effective and could get students more engaged in participating during class.

  • Planning for Mathematical Understanding

Learning targets will be discussed with students before the lesson begins. The teacher will set up the SMART Board presentation form the SMART Exchange website. Students have had practice with squaring binomials and solving quadratic expressions by factoring. Pre-assessment will consist of giving the students a quadratic that cannot always be factored into two binomials. This will show them that there is another way to solve quadratic equations. The teacher will then assess if the students can identify the coefficients, a, b, and c, in the quadratic equation and determine if the students can correctly plug them into the quadratic formula. Students will be asked to identify a, b, and c of a quadratic equation. One student can volunteer to come to the board and physically write on the board what a, b, and c are. If the students can correctly plug in the coefficients into the quadratic formula, then they can move on to executing the formula to find the zeros of the quadratic equation. Another student will be able to come to the board and plug a, b, and c into the quadratic equation correctly. After a few practice trials of identifying a, b, and c and correctly plugging them into the quadratic formula, the teacher will move forward to effectively solving for the zeros of the quadratic equation. Multiple students can come to the board to solve multiple problems displayed. The students can explain what they are doing as they are going through the problem solving process. Their peers can voice helpful tips or advice if it is needed. After the class activity with the SMART Board in completed, the students will be given a worksheet with more practice problems on them to help master this new skill. This is a step by step process to ensure each student can first identify the correct coefficients, plug them correctly into the quadratic formula, and to correctly execute the equation to find the zeros.

  • Planning to Support Varied Learning Needs

Students have a lot of trouble grasping new mathematical concepts and skills. To accommodate for a large difference in mathematical ability, the teacher will use a SMART Board and a SMART Exchange presentation to help students grasp this new skill. Because it is a new technology, the teacher hopes that the students will be more engaged and will have more fun coming to the board. The teacher will go over step by step how to use the quadratic formula to ensure that students know how to use it correctly and have students come to the board to practice. Also, using the SMART Exchange will give teachers presentations or practice problems to display. It gives the teacher extra tools to help her students learn. The students will also work individually and at their own pace to complete the problems on a worksheet. Students who have misconceptions will work with the instructor and with peers in order to guide the student in the right direction and get immediate feedback.

  • Using Knowledge of Students to Inform Teaching and Learning

Because students have had practice with squaring binomials and solving quadratic expressions by factoring, they need to see a quadratic equation that cannot be factored back into two binomials. The teacher will break up the lesson into smaller steps so the students can keep up and learn how to use the quadratic formula more easily. Pre-assessment will consist of giving the students a quadratic that cannot be factored. This will show them that there is another way to solve quadratic equations. The teacher will then assess if the students can correctly identify a, b, and c in the quadratic equation and determine if the students can correctly plug them into the quadratic formula. If the students can correctly plug in the coefficients into the quadratic formula, then they can move on to executing the formula to find the zeros of the quadratic equation. It is more effective to break up each step in using the quadratic formula because students can be easily confused of how to identify and plug in the coefficients into the formula and can make an error trying to execute the equation. By breaking up the process into smaller steps, students can better grasp how to correctly use the quadratic formula. Also because the students have a hard time participating in the activity, the teacher will use a SMART Board to conduct her lesson. By using the technology in the process of learning, the teacher hopes that the students will be more engaged in the activity. They get to use a touch screen whiteboard to do their work on that is easy to use and mess free. The students use technology everyday; since the teacher knows that the students enjoy using touch screens and using technology, she hopes that the students will have more fun and be more engaged in the lesson.

  • Planning Assessment to Monitor and Support Student Learning

There are no formal rubrics for this lesson. The learning targets are as follows:

  1. I can identify when to use the quadratic formula.
  2. I can identify the correct coefficients, given by the quadratic equation, and plug them into the quadratic formula correctly.
  3. I can execute the quadratic formula and find the zeros of the quadratic equation.

In this lesson, the formative assessment will consist of the students coming to the SMART Board to physically identify a, b, and c, correctly plug them into the quadratic formula, correctly execute the formula to find the zeros, and given practice problems on a worksheet to continue to master this new skill.  The teacher will be observing the students while they quietly work. The teacher will comment on the students’ work to help guide them in the right direction during the problem solving process. At the end of the class period, the worksheet will be handed into the teacher for further assessment. The teacher will then evaluate the worksheets to determine what the students still need to work on.

A Friendly Reminder

cootsj Improve Mathematical Thinking, Technology Teaching Issues

As Teachers, we are constantly busy and  battling with our students to get them to do their work and get it in on time.  Last year, I came across this wonderful piece of technology that I believe can helps us to better connect with our students. This “technology” is called Remind 101. It is a free, safe,easy, and appropriate text messaging program that allows teachers to communicate with their students and parents.

Today, students are constantly on their phones and most of students’ communication is done through text messaging. So maybe it would help if we put forth the effort to communicate with our students the way they prefer to be communicated with? Remind 101 can be used on any cell phone and has an app for both the IPhone and Android.

What is great about this Program/App is that you can send any type of message! It can be used to send homework, quiz, or test reminders, while you can also let parents know that grades are coming up, or state testing dates are approaching.  I also know of teachers who sends, at the end of the week, all of the CCSS Math standards/learning targets that their students accomplished so that parents can have a better sense and update of what their student was doing that week in class. It is also a great way to communicate with students who were gone form your class that day. I know that many teachers have a website where they post homework, but Remind 101 can be a faster and more effective way to connect with your students.

Not only does this program help improve communication, but I believe it also builds rapport with your students. This technology allows us to connect with our students and show that we do acknowledge their interests and the way that they go about their life.

If at all interested in this, go to www.remind101.com.

Collaborative Mathematics Projects

oursland Improve Mathematical Thinking, Lesson Planning Issues, Technology Teaching Issues

A classroom math project can be come more meaningful by collaborating with classrooms all around the world through the Internet. In this blog I will suggest features that are part of good collaborative projects and some examples of ways to make math activities from existing global collaborative projects.

Features of good collaborative projects:
1. Central question engages student to think.
2. Students can share data, solutions, and strategies.
3. Students can peer assess and tutor via the internet.

Guidelines and requirements:
1. Teachers should know who and how students are collaborating.
2. Teachers must make sure that students are following district Internet policies.
3. It is easiest to use existing Internet sites.
4. Get parent permission to internet publish reports, artwork, pictures, or video.

Math activities ideas using existing global projects:
The Big Mac index was invented by The Economist in 1986 as a lighthearted guide to currencies but now it is used for much more. This index allows teachers and students to ask mathematically testable questions, such as, “In what countries could the average person work for one hour and buy a Big Mac?” Collaboration comes from reading the blog posts on The Economist website and posting a hypothesis or some analysis through the teacher.

The Down the Drain Project is a collaborative community that analyzes how much water people use everyday. This project has worksheets and guidelines that support the teaching of creating hypothesis, making predictions, analyzing data to test predictions, and write conclusions. There is a worksheet calculating daily water use and sharing the data with the collaborative project members.

Site for starting a new collaborative project:
Class2class is an Internet service where math teachers can come to join in new projects and collaborations.

Implementing Student Voice into Mathematics Teaching

oursland Assessment of CCSS-Math, Improve Mathematical Thinking, Lesson Planning Issues, Uncategorized

Just like Performance-Expectations (PE) Student-Voice is a Washington State term that refers to teaching practices focused on the student involvement. Some of the principles of Student-Voice are: 1. Eliciting student understanding of the learning targets; 2. Supporting student use of resources to learn and monitor their own progress; and 3. Teachers reflection on Student-Voice evidence to improve instruction. Recently two mathematics masters students and Washington State teacher conducted action research projects related to Student-Voice. The reading of these action research projects will help mathematics teachers and pre-service teachers understand what Student-Voice is, why it is important, and how to implement teaching practices related to this area teaching best practices.
Emphasizing Performance Expectations to Increase Student Achievement, by Jennifer Coulson Emphasizing PE to Increase Math Achievement-Jennifer Coulson

Using Learning Targets to Encourage Student Self Assessment and Increase Student Achievement in Geometry, by Katelyn Marie Pierce UsingLearningTargets_Geometry_Pierce_project

Requirements for classes at THS

Nunez Assessment of CCSS-Math, Improve Mathematical Thinking, Technology Teaching Issues

One of the many issues that we have today at THS is that students are not at their level for the classes that they signed up for. Sometimes the students are transferring from other districts with incomplete transcript and other times the counselors signed them up because it was the “only” class available in their schedule. Some of the classes that we offer at THS should be used as incentives for the students and not be able to get in because they have friends in that class like the engineering classes. I suggest a flow chart on what classes they should take and pass before moving on to another class. Some of the classes have a double arrow like Statistics because you can enter right after Algebra II and after the student can go back to take either Trigonometry or Pre-calculus.
Flow chart for THS

How do we increase math achievement?

oursland Assessment of CCSS-Math, Common Core State Standards Mathematics, Improve Mathematical Thinking, Uncategorized

Watch this video by Uri Treisman, Keeping Our Eyes on the Prize. What is your reaction to Uri’s analysis of the math education in the United States and what changes in math education does this analysis suggest?

Individual Post
What can math teachers do to increase mathematics achievement in their schools districts (as a change agent)?

Group Post
What roles do you think a student focused assessment system plays in increasing mathematics achievement (at the district and classroom levels)?

Give improvement feedback to peers on their learning progressions, benchmark assessments, and classroom assessments.

An Investigation of Three-Dimensional Problem Solving and Levels of Thinking Among High School Geometry Students

oursland Geometry Teaching Issues, Improve Mathematical Thinking

Attached is Josh Wheatley’s MAT research project.  Josh did a great job of creating van Hiele based activities for surface area and volume.  If you teach geometry at the middle or secondary level this is a must read. JoshThesis is the main body of the project and JoshThesis.2 is the rubric he used to score the van Hiele activities.  JoshThesis  JoshThesis.2

Balancing Depth and Territory

pierckat Improve Mathematical Thinking

Mathematics education is often described as “an inch deep and a mile wide”.  Most teachers would agree that mathematics courses often lack depth.  As teachers, we are expected to cover a prescribed amount of territory throughout a course.  However, covering such a large amount of material rarely allows students to learn and understand the concepts at a deeper level.  Feeling the pressure to try to teach all standards assessed on state exams, teachers often settle for basic student understanding rather than deeper student understanding.

This has several negative consequences.  Since few students really had a good initial understanding of the material, too much time is being wasted at the beginning of the year to review what should have been “previously learned”.  Also, teachers often focus on transferring information (and hoping it’s received!) rather than having students problem solve and use higher order thinking to make sense of it.  This can lead to a much lower level of understanding.

I find there are several teacher characteristics that contribute to this problem.  One is that teachers (myself included!) too often teach procedures.  When teachers lay out a step by step guide to solving problems, all higher level thinking is thrown out the window!  We need to have students think about strategies to solving these problems and then determine whether their strategy works.

Clearly, this is a quite a problem in the world of mathematics education.  If we expect to see change from student performance, I believe teachers must first be willing to make the change.  This leads to a couple big questions:

  • How do you balance eliciting deeper student understanding while still covering all of the content?
  • What additional common teaching characteristics can prevent students from using their higher order thinking skills?  How can these characteristics be changed to elicit deeper understanding?

 

-Katelyn

How to optimize 55 minutes?

radmathteacher Improve Mathematical Thinking

This summer much of our focus in this class has been focused on writing lessons and thinking about ways of improving our students mathematical thinking.  This is a very important discussion and I have learned a lot through this process.  Though it may seem obvious, this is my purpose in teaching math.  I want my students to become better problem solvers, and to learn to think deeply about math.

I preface all of this, because I foresee this next academic year being more challenging for me to accomplish this goal than in any of the previous years.  As my title to this post suggests, at West Valley High School this next year we are transitioning back to a “traditional” delivery schedule of 55 minute class periods.  For the past three year, my entire teaching career, we have had 78 minute periods.  Needless to say, this is a dramatic change.  It also must be noted that we are transitioning from trimesters to semesters, so there is really no loss in “contact” time with students.

During these past years I have seen great value in much of the daily routines that we part of a 78 minute period (entry task/warm-up, time to answer questions from the previous homework, time to teach a complete lesson, and often some time to allow the students to begin working on their homework).  I realize that in losing 23 minutes, some things are going to need to change.  So my question is this: for those of you with experience teaching with 55 minute periods, or any of you with helpful ideas, what is the best way to use the 55 minutes I will have to optimize my students’ math performance?

-Aaron