5 Practices for Orchestrating Productive Mathematics Discussions

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This book was an interesting read.  It really makes you think about both what you have been doing in your classroom as well as ways you can improve your teaching.  I think it is important for students to have authorship in their own problem solving methods.

I do think that implementing this method would require a lot of work up front.  If you teach the same topics every year, it is not the same level of work each school year.  I do think that the level of work that has to be put in to implement this method could be a detractor for many teachers.  It’s something that I definitely think should be implemented if you have a strong, collaborative PLC because you have both extra support and feedback.

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Classroom Culture, Challenging Mathematical Tasks, and Student Persistence

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This article discussed the importance of creating a classroom culture that supports students in persisting with mathematical tasks.  The goal is to create an environment where students feel comfortable tackling more cognitively challenging problems and persisting in finding a solution.

The key components of successfully accomplishing this are:

1. The way the tasks are introduced. If students are given preliminary experience, they were more comfortable in engaging in the task and persisting with it.

2.  Providing support to students. It is important to allow students time to struggle individually, followed by working collaboratively, as well as overcoming the tendency to give students “hints” and to use prompts that differentiate the task.  The authors make the point that you can provide support for students without detracting their opportunity to understand the math.

3.  Providing an extension task.  It allows students who have finished to explore the topic with more depth and allows those students who are still working adequate time to work with the task to a conclusion.

4.  The sharing of student solutions.  The authors note that is important to observe students as they’re working and to thoughtfully choose students to contribute.  This allows students to explain their strategies and see that they are making an important contribution to the classroom.

5.  The method of assessment.  Students who feel like they are being assessed competitively (compared to their peers) are less willing to participate. Using a criterion-based rubric encourages students to participate and persist, because they can see up front how they will be graded, as well as encouraged them to reflect on their learning.

Overall, the authors concluded that a positive classroom environment is not just rules and procedures, but ongoing and interactive support from the teacher.

Chapter 4 – Wikis

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Wikis combine technology and collaboration.  Having this combination is not only just essential for the educational environment, but for everyday life as well.  Collaboration allows for a greater perspective on a topic, as well an expansion of ideas.  It allows students to develop teamwork skills, something that is vital for their futures.  Building a wiki with your class allows your students to work together, creating a site that covers the material in a way that is helpful to them and that they can be proud of.

In addition to building teamwork skills, a class-built wiki allows students to present information in a way that they can understand.  It is also an effective tool for students to use a reference guide, both throughout the school year, but also in later course work.  And because of the collaborative effort, students will also be exposed to different view points, allowing for a deeper, richer understanding of the material.

As with all technology-based classroom activities, there are some concerns.  Richardson mentions that with the use of wikis, the role of the teacher becomes a bit vague.  It can also be difficult to assess student work, since any of the students can add to or edit a wiki entry.  Content becomes an issue.  It can be difficult to find a balance between allowing students to explore and create, but also ensure that they are creating entries that are relevant to the class.

Chapters 3 & 8 – Blogs, Multimedia, and the Classroom

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If a teacher plans to bring technology into their classroom, it is important for them to be the first student.  Teachers need to be sure they can use blogs, podcasts, and other technology before asking their students to use them.  However, with how quickly technology is changing, this can be a difficult task.

In chapter 3, Richardson posits that blogs are one of the best tools a teacher can use in the classroom.  I can see their potential.  It creates more avenues of collaboration, feedback, quick responses, and extending a topic beyond the classroom.  But I think it can also be detrimental in the classroom as well.  Richardson stresses that blogging can bring in and utilizing a larger, more diverse audience.  While that has its positives, it can also be dangerous or intimidating for students.

In chapter 8, Richardson introduces podcasting and video streaming as other technologies that can be useful in the classroom.  Like with blogs, it has its advantages and disadvantages.  Richardson points out that it is quick and easy to record and publish your thoughts.  However, that speed could be to the detriment of thoughtful consideration.  Do you really want to address the topic that way?  Once that thought is published, there really is no way to remove it (the internet never forgets).

With both blogs and multimedia tools (podcasting, video streaming), I think it is important to stress to students the importance of being thoughtful of what they are putting out there.  Is what you wrote/recorded what you really want to say?  Is there anything that needs to be clarified?  Students should be encouraged to put just as much thought into their postings as they would in a traditional essay or class speech.

Chapters 1 & 2 – The Read/Write Web

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When Tim Berners-Lee began developing the Internet in 1989, he had a vision of it becoming a large, collaborative space.  While in the beginning it wasn’t quite the collaborative space he desired, it has clearly grown to be that way in the years since.

Richardson makes a strong case for the use of online collaborative tools in the classroom.  And I agree that having so many tools to work with our students is incredibly beneficial, not just for students, but for the teachers as well.  It allows us to reach all of our students, as well as see where some students may need extra help.  It also allows more avenues for students to work together and to learn from each other, rather than being solely reliant on the teacher for learning.

Though technology will become more and more prevalent in the classroom, there are still concerns.  When you can publish anything with the click of a finger, it is important for students (and teachers) to think about what they are putting out there.  Students are less likely to consider the consequences of posting something that could lead to unwanted attention, or affect the lives of students in the future.  As educators, we should be aware of what our students are putting up and help them to make good decisions, as well as protecting them from those dangers.

Richardson also mentioned that there is a gap between those who are “digital natives” and those who are “digital immigrants”.  This can be especially acute in the classroom, when often the students have a better understanding of how to use the technology than the teacher does.  As educators, we need to work to bridging this gap and not be afraid of new technology or things that we don’t know.  We should aim to be learning at the same time our students do, so we too can continue to grow.  As we educate ourselves, we can make better, more informed decisions on what tools are appropriate for our students to use and guide their use.