Fourth Courses

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School districts and high schools are working diligently to create a course that will satisfy ODEs requirement for current juniors and anyone after them to have four credits of high school math to graduate. Course names like Consumer Math and Financial Math are starting to come out of the discussions of what a fourth course should be. Many consultants are working diligently to help with this transition. Here are some suggestions for you while working on the creation of a fourth course for your building.

1. The course MUST be aligned with the Common Core State Standards (CCSS). There is no way around this. Unfortunately the fourth course will not be tested under the current testing plans but it is important to recognize why this requirement is in place. A large number of high school students in Ohio are required to take remedial math upon entry to college. This causes a lot of problems for colleges, headaches for students and an enormous amount of lost productivity for the state. The fourth course requirement is one of the many changes made to help curb this trend.

2. The course needs to not only address the letter of the CCSS but also the spirit of the CCSS. In other words the course needs to be created with the 8 Standards for Mathematical Practice (SMP) as a guiding light. These standards are immensely important in creating a sense of mathematics beyond the standards. Mathematics is logical and consistent. Patterns exist that can explain most anything. These ideas are summarized in the 8 SMPs.

3. Creating this course is providing an enormous opportunity to teach in a way that is exciting not just for students but also for teachers. Create your course to be as project-based as possible. Project-Based Learning is not a new concept in any way but has been paved over by standards and standardized testing. The CCSS have created a wonderful opportunity to slow down and allow students to learn in a way that makes more sense and is more like the real world.

If you follow the three suggestions above you should end up with a course that will be a perfect stepping stone for your students as they transition from high school to their career training. There are several places you can get ideas for fourth courses. North Carolina has a list on their website of approved fourth course vendors, the Dana Center has a fourth course and locally some educators in Columbiana County are creating a fourth course. The course is being created through a grant to help close the gap between high school and post-secondary options. If you have questions about the course you may email Matt Nicholas, Columbiana County Mathematics Consultant, at

CCSS Curriculum

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Many teachers have been working to implement the Common Core State Standards. In Columbiana County mathematics teachers from nine school districts have been creating the curriculum they will use for the new standards for over a year now. All the standards have been deconstructed and are posted at this link. Find the grade level/course you need in the table on the right side then click on the standards document at the top of the grade level/course page. The work we are doing is something that should be an ongoing process. Please let me know if you find mistakes, updates, hints, suggestions, etc. for any of the standards documents available. A huge thank you goes to all the mathematics teachers in Columbiana County that have contributed to this work. Your dedication inspires me.

Project Based Learning

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The Common Core State Standards are more than just a new set of standards to teach. The pedagogical implications behind the CCSS are more important than the standards themselves. The days of simply checking off a list of standards are fading faster than the tributes in Hunger Games. There is a great need to begin the process of identifying new and more effective strategies for learning. One of these strategies, though it is not very new, is Project Based Learning (PBL).

The idea has been around for a while though it has had several iterations; inquiry instruction, discovery instruction, problem based instruction. The purpose regardless of what you call it is to allow students the opportunity to direct their own learning with little direction from the teacher. The teacher in this approach is meant to be a resource and advisor rather than a planner and director.

PBL is not something to jump right into though. Like any new strategy it takes time and effort to build competency. There are numerous resources to help guide teachers. Edutopia and Buck Institute for Education (BIE) are two of them. Once you decide to begin working toward PBL take it slow and do some research. There are pre-made projects available for those of you that want to try it without the huge time investment needed to do one on your own.

WARNING. PBL is not creating activities that involve “real-world problems”. It is way more than that. PBL is a drastic change in the point of view of learning. Go on, try it. Your presentations are getting stale, your students are not as engaged as you would hope them to be, it’s time for a change. All subjects and all grade levels can use PBL as a way for students to learn.

ANOTHER WARNING. Students will come to you with questions that you may not know the answer to. That’s okay. You don’t have to know everything. Your job in PBL is to guide students to the right answers, not to give the answers to them. Think of yourself as a guide rather than an instructor. Direct students toward the right resources and information.

Most teachers that have introduced PBL into their classroom have been very happy they did. Teachers feel more students are learning, they are learning more about their students, and they feel students are becoming better thinkers. Students will not just be able to spew out information on a test. They will begin to be able to find the information on their own. A novel idea.

Gulp: You Want Me to Use Technology?

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Using technology in the classroom is scary, unpredictable at times, and down right nerve-racking to some people. Students have the ability to run technological circles the size of Jupiter around us. These two ideas come together in each of our classrooms every day. Meeting students, the digital natives as it were, needs technologically is very difficult for us to figure out. However, that does not mean we have the right to say that this technology has no place in our schools or even say that it is harmful. Though it is likely our society will never be the same because of social networking and online media it is safe to say that society would never be the same at any stage in history. Using the latest and greatest technology is as important as using the latest and greatest teaching styles. Math, Language, History, and any other subject taught in school rarely changes. But the way in which students learn best has changed. That is the primary focus of the new standards. Take some time to find a new way to present the same content using technology. Also, take a moment to read this article about using a few pieces of technology in your next unit of study. I think you will find some of the data surprising.

Integrated Math vs. Traditional Math

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What’s the difference? Integrated math is a series of courses that “integrate” all the main topics in mathematics, i.e. algebra, geometry, data, and trigonometry. Traditional math is an approach that breaks those topics down into their individual parts, i.e. Algebra I, Geometry, Algebra II, and Pre-Calculus. Many high schools offer both course pathways. However, the integrated pathway is typically offered as an alternative for students that are not confident enough in math to take the traditional path. When this is the case the integrated pathway is also typically “watered down” to make it easier for students to pass. With the adoption of the Common Core State Standards ODE, and the writers of the CCSS, are strongly recommending that high schools no longer offer an alternative pathway for the sole purpose of giving students a way to obtain their math credits. Many people oppose the integrated pathway. So, which should you choose? It is the recommendation of this writer that you base that decision on what is best for your students. However, if you are on the fence, choose the integrated approach. Students receive an integrated approach in middle school. The traditional path tends to leave students behind because the topics are segregated and it is not apparent how everything fits together. When choosing this pathway though be sure to consider the implications on instruction. Allow teachers time to be trained and become familiar with the new method of presenting mathematics. The standards are the same but the daily lessons will be quite a bit different. Set teachers up for success and students will be successful too. Click here to read an article on NCTMs website about this topic.

To Google it or not to Google it?

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I saw a forum on Tech and Learning that asked the question “Can you Google-proof a question using Bloom’s Taxonomy?”. It was an interesting conversation. You can check it out here. It made me think though about what we are doing in our classrooms that would be Google-able. Simple math questions (i.e. 2+2) are easily answered by Google. But much more rigorous questions require students to think about the context of the question, the information that is unnecessary, the information that is important, the process to solve, etc. You can’t google many of those things. Google can help students get to the right answer and give suggestions but the problem must be solved by the student. When considering whether a question is rigorous enough try this test. Put it into a search engine. If the search comes back with the correct answer quickly perhaps the question needs to be more challenging. If the search comes back with an answer that is vague and, at best, helpful then maybe you have a question that will truly make students think.

What is Web 2.0?

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Let’s take a step back. Web 1.0 is an internet experience that is strictly meant for consumption. Interaction with and modification of content is not possible. Websites like those provided by corporations are a good example. Browsing Lowe’s website only allows you to view the available products, not to add any new products. “You can look but not touch”. Web 2.0, however, is much different. The content and modification of content is now in the hands of those consuming the information. Things like wikis, blogs, and other interactive types of information media are good examples. This allows the consumer control over some of what is being presented. You can add comments, attempt to correct previous statements that are misleading or incorrect, have discussions, etc.

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