Assessment has been on my mind lately. Part of my job is to be our building test coordinator and I have helped to administer on-line assessments in reading and math to all of our students in grades 2-5. This has taken a tremendous amount of time on my end - and at least an hour of lost instructional time from each classroom. I have concerns about how students interact with these tests, including:
1. Students do not have much experience in "close" reading on a computer. They typically have not had experience with needing to read ALL of the information on the screen. Rather, they often play games that provide feedback for incorrect responses. The online tests we are giving do not provide feedback as to whether or not they are answering correctly as they take the test.
2. Students need stamina so they do not rush through the test. Again, students have had experiences where the response time is quick on the computer. In contrast to those experiences, when taking these on-line tests, students need to read and think carefully before choosing a response.
3. Adaptive testing makes assumptions about what is "less challenging" or "more challenging". The next test item the child sees is based on whether their previous response was correct or incorrect. Who makes these decisions about the difficulty of content? If a child answers an addition problem correctly, should they see an item that probes more deeply about their understanding of addition? Or should they see a multiplication problem - where they may or may not make the connection to addition?
Any time students are spending time testing, they are losing instructional time. If we are going to take time from instruction to gather assessment information, then we need to be sure this information can inform our practice and benefit students. How much time are we willing to sacrifice for assessment? How will the new Common Core assessments impact our instructional practices?
It is a lot to consider....
Sunday, September 29, 2013
Sunday, September 22, 2013
So, where do you find some rich mathematical tasks?
It can feel like a daunting task - finding engaging lessons that help students understand the conceptual foundations of mathematics. I'm often asked where to find ideas for lessons. One of my favorite resources is the Ohio Resource Center (ORC).
www.ohiorc.org
The ORC has more than just mathematics - it is also a great resource for language arts, social studies, and science! However, mathematics is near and dear to my heart and when I use the ORC it is typically for math ideas.
http://www.ohiorc.org/for/math/
When you visit the Mathematics page of the ORC, you can click on the first link at the center of the page. This will take you to the standards - and you will find both the "old" Ohio Academic Content Standards/NCTM's Principles and Standards as well as the "new" Common Core State Standards for Mathematics.
http://www.ohiorc.org/standards/math/
If you click on the Common Core link, it will take you to the ORC's resources that have been aligned for Common Core. There are suggestions for activities to help develop the Mathematical Practices as well as content-specific lessons. Many of the lessons come from NCTM - the National Council of Teachers of Mathematics.
A wonderful feature about the ORC is that all of the lessons that are on the site have been reviewed by mathematics educators in Ohio. With so many resources available on the internet, I find that the ORC helps narrow the resources so that I am looking at high-quality suggestions for teaching. It is also helpful to look at assessment items (from NAEP and others) that have been aligned to standards so that you get a sense of what sort of content is specific to that mathematics standard.
There is also a Mathematics Bookshelf and Problem Corner as well as some other features on the main page for mathematics. If you haven't had a chance to explore the ORC, take time to check it out!
www.ohiorc.org
The ORC has more than just mathematics - it is also a great resource for language arts, social studies, and science! However, mathematics is near and dear to my heart and when I use the ORC it is typically for math ideas.
http://www.ohiorc.org/for/math/
When you visit the Mathematics page of the ORC, you can click on the first link at the center of the page. This will take you to the standards - and you will find both the "old" Ohio Academic Content Standards/NCTM's Principles and Standards as well as the "new" Common Core State Standards for Mathematics.
http://www.ohiorc.org/standards/math/
If you click on the Common Core link, it will take you to the ORC's resources that have been aligned for Common Core. There are suggestions for activities to help develop the Mathematical Practices as well as content-specific lessons. Many of the lessons come from NCTM - the National Council of Teachers of Mathematics.
A wonderful feature about the ORC is that all of the lessons that are on the site have been reviewed by mathematics educators in Ohio. With so many resources available on the internet, I find that the ORC helps narrow the resources so that I am looking at high-quality suggestions for teaching. It is also helpful to look at assessment items (from NAEP and others) that have been aligned to standards so that you get a sense of what sort of content is specific to that mathematics standard.
There is also a Mathematics Bookshelf and Problem Corner as well as some other features on the main page for mathematics. If you haven't had a chance to explore the ORC, take time to check it out!
Monday, September 16, 2013
Trusting the kids....
In order to be a facilitator in a mathematics classroom, a teacher needs to be willing to give up control in their classroom. This does not mean that "anything goes". Rather, there should be parameters for how classroom discussions will take place with a focus on respect for all participants. The teacher also needs to be willing to let the students' conjectures and thinking drive the conversation. While the teacher has an ultimate destination in mind, the path to that destination is determined by the students and their ideas.
A beautiful example of this occurred last week. A fifth-grade class was working on the idea of how numbers change when multiplying by 10 (or 100 or 1,000). The teacher had students explore the magnitude of 1, 10, and 100 using base-10 blocks. Students then predicted what it would look like if they were to have a 2-D version of 1,000, 10,000, and 100,000. Groups used paper to build these models. After building their models, the class had a discussion about their observations. They built the rule that when multiplying by 10, a digit moved one place to the left. This conjecture was tested using calculators. When students were confident in the rule, they wrote it on the chart paper. Students were eager to explain their thinking and were engaged throughout the lesson.
Rather than teaching the students to "add 0 when multiplying" (I'll need another post to talk about why that is confusing language for students), this teacher build upon students' observations and reasoning to help them develop the mathematical rule.
In order to facilitate this lesson, the classroom teacher had to trust that the students would discover the rule - and they did! :-)
A beautiful example of this occurred last week. A fifth-grade class was working on the idea of how numbers change when multiplying by 10 (or 100 or 1,000). The teacher had students explore the magnitude of 1, 10, and 100 using base-10 blocks. Students then predicted what it would look like if they were to have a 2-D version of 1,000, 10,000, and 100,000. Groups used paper to build these models. After building their models, the class had a discussion about their observations. They built the rule that when multiplying by 10, a digit moved one place to the left. This conjecture was tested using calculators. When students were confident in the rule, they wrote it on the chart paper. Students were eager to explain their thinking and were engaged throughout the lesson.
Rather than teaching the students to "add 0 when multiplying" (I'll need another post to talk about why that is confusing language for students), this teacher build upon students' observations and reasoning to help them develop the mathematical rule.
In order to facilitate this lesson, the classroom teacher had to trust that the students would discover the rule - and they did! :-)
Sunday, September 8, 2013
Partnering with Parents
Parents often want to be partners with schools and support their child's education. However, these same parents might suffer from their own math anxiety and they are uncertain about how to help their child - especially since so much of the ways in which students are solving problems seem "new". When responding to parents about "new" math, I explain that it isn't that the math is new but rather that we have learned more about how to better teach math.
One particularly confusing aspect to many adults is why students would work left to right when solving a computation problem when many of us were taught in school that you should start in the right column and then work your way left. Research has shown that, when given the opportunity, a majority of students invent strategies or algorithms by working left to right. Encouraging students' invention of strategies and having them talk about their thinking provides an essential foundation as they move into expanded algorithms and traditional algorithms - allowing students to see the place value that becomes "hidden" by the traditional algorithms.
To help parents understand some of the ways that their students might be solving problems, I created a guide for parents. Parents can refer to the guide as they help their students with math at home - and hopefully remove some of the anxiety parents face about the "new" math.
http://bit.ly/13x5LYD
I hope that in discussions with parents, you can be encouraging, help parents to be less anxious about mathematics, and forge strong partnerships to support our future mathematicians!
One particularly confusing aspect to many adults is why students would work left to right when solving a computation problem when many of us were taught in school that you should start in the right column and then work your way left. Research has shown that, when given the opportunity, a majority of students invent strategies or algorithms by working left to right. Encouraging students' invention of strategies and having them talk about their thinking provides an essential foundation as they move into expanded algorithms and traditional algorithms - allowing students to see the place value that becomes "hidden" by the traditional algorithms.
To help parents understand some of the ways that their students might be solving problems, I created a guide for parents. Parents can refer to the guide as they help their students with math at home - and hopefully remove some of the anxiety parents face about the "new" math.
http://bit.ly/13x5LYD
I hope that in discussions with parents, you can be encouraging, help parents to be less anxious about mathematics, and forge strong partnerships to support our future mathematicians!
Sunday, September 1, 2013
Classroom Conversations
I have been reading Caitlin Tucker's Blended Learning in Grades 4-12: Leveraging the Power of Technology to Create Student-Centered Classrooms. It is an easy read and gives many useful ideas to use in your classroom. While the focus of the book is using technology as a tool in teaching, I am struck by the suggestions she emphasizes that are just good teaching practices. Many of her ideas can be applied to primary grades as well.
One of my favorite quotes so far is:
"Online work frees teachers from their role as the only source of information and feedback. When students engage in dynamic online discussions and collaborative group work, they become valued resources in the class. They ask each other clarifying questions, compliment strong ideas, provide suggestions for improvement, and offer alternative perspectives. This also allows for improved student engagement and immediate peer feedback."
Tucker's description could certainly apply to online learning but it just as easily could describe the classroom conversations that should occur during our mathematics teaching. Teachers can help students make sense of the mathematics and discuss them with students by acting as a "guide on the side". Introduce a problem and allow students to work through the problem together. Try to avoid answering questions directly - instead, ask other students in the group what they think or ask students how they might test a theory. How will they decide if they are correct? Where might they find needed information?
By having a strong understanding of the mathematical content to be taught, the teacher can guide students towards understanding through questioning rather than telling. I have often told students it is not enough to trust something if it does not make sense. It is important for them to continue thinking about it, asking questions, and trying until they have made sense of the topic in their own way.
Tucker provides great suggestions for how we might use technology to enrich these mathematical conversations - but regardless of whether the conversations are in person or online, it is important that the students are involved in making sense of the mathematics!
One of my favorite quotes so far is:
"Online work frees teachers from their role as the only source of information and feedback. When students engage in dynamic online discussions and collaborative group work, they become valued resources in the class. They ask each other clarifying questions, compliment strong ideas, provide suggestions for improvement, and offer alternative perspectives. This also allows for improved student engagement and immediate peer feedback."
Tucker's description could certainly apply to online learning but it just as easily could describe the classroom conversations that should occur during our mathematics teaching. Teachers can help students make sense of the mathematics and discuss them with students by acting as a "guide on the side". Introduce a problem and allow students to work through the problem together. Try to avoid answering questions directly - instead, ask other students in the group what they think or ask students how they might test a theory. How will they decide if they are correct? Where might they find needed information?
By having a strong understanding of the mathematical content to be taught, the teacher can guide students towards understanding through questioning rather than telling. I have often told students it is not enough to trust something if it does not make sense. It is important for them to continue thinking about it, asking questions, and trying until they have made sense of the topic in their own way.
Tucker provides great suggestions for how we might use technology to enrich these mathematical conversations - but regardless of whether the conversations are in person or online, it is important that the students are involved in making sense of the mathematics!
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