Math Journal Writing and Blogs as an Assessment Tool

By Dawn Woods, RME Elementary Mathematics Coordinator 

Assessment is more than a test at the end of a unit to gauge learning; it is an integral component of classroom instruction (National Council of Teachers of Mathematics, 2013). Not only does assessment provide information needed to adjust teaching and learning as they are happening, but it becomes a fundamental part of mathematics instruction, done for students instead of to students. However, it is important to consider that some students can produce correct answers on a test item but may not understand the solution or question behind it (Garfield, 1994). Therefore, classroom assessments should follow multiple approaches allowing students to showcase his or her strengths while focusing on how students think about mathematics.

According to Marilyn Burns, mathematics teachers gain a wealth of information by investigating the thinking behind students’ answers, not just when they are wrong but when they are correct (2005). One way to investigate the thinking behind students’ answers is by journal writing. Keeping a journal helps students to think about problem solving in a meaningful context while giving insights into their learning (Barlow & Drake, 2008). Open-ended journal writing enables students to analyze, synthesize, and evaluate the lesson thereby growing in mathematical achievement! Through writing prompts or open-ended questions, math journals can

• Stretch students thinking. 
• Help make sense of problems. 
• Express feelings and thoughts about mathematics. 
•  Reveal conceptual understanding. 
• Personalize learning, and 
• Evaluate progress and recognize strengths.

But why not put a technology twist on the traditional written math journals since technology plays an important role in everyday life of our digital native students? According to the National Council of Teachers of Mathematics, technology is vital in teaching and learning mathematics (2008). Through the use of technology, mathematics education and assessment strategies could be transformed to seize the attention of today’s wired students. Through blogging students can

• Post solutions to problems. 
• Post mathematical insights. 
• Post questions. 
• Interact with peers and teachers through online discussions. 
• Embellish online entries with sounds, video, and graphics, creating potential for project-based learning, and 
• Nurture higher order thinking skills

To sum up, journal writing and math blogs provide an authentic, motivating, assessment tool, where students communicate and explain mathematical concepts through writing, taking ownership of mathematical ideas in a creative and meaningful way.

Resources to Get You Started

Writing in Mathematics Drake, J.M., & Barlow, A.T. (2008). Assessing students’ levels of understanding multiplication through problem writing. Teaching Children Mathematics, 14(5), 272-277.

Kawas, T. (2010). Writing in Mathematics. Retrieved June 24, 2013 from http://mathwire.com/writing/writing1.html

Blogging in Mathematics Tubbs, J. (2007). Blogs in the Mathematics classroom. Retrieved June 24, 2013 fromhttp://futureofmath.misterteacher.com/blogs2.html

Pyon, S.M. (2008). Why math blogs. Teaching Children Mathematics, 14(6), 331-335.

References

Barlow, A.T., & Drake, J.M. (2008). Assessing understanding through problem writing. Mathematics Teaching in the Middle School, 13(6), 326-332.

Burns, M. (2005). Looking at how students reason. Educational Leadership, 63(3), 26-31.

Garfield J. (1994). Beyond testing and grading: Using assessment to improve student learning. Journal of Statistics Education, 2(1). Retrieved June 24, 2013 from http://www.amstat.org/publications/jse/v2n1/garfield.html.

National Council of Teachers of Mathematics (2013). The assessment principle. Retrieved June 24, 2013 from http://www.nctm.org/standards/content.aspx?id=26803

National Council of Teachers of Mathematics (2008). The role of technology in the teaching and learning of mathematics. Retrieved June 24, 2013 from http://www.nctm.org/about/content.aspx?id=14233.

Conferences to Attend This Summer!

By Toni Buttner, RME Assistant Director

Come Unlock the Mathematical Mind with CAMT next month! 
San Antonio, TX 

CAMT is an annual Texas conference for K-12 mathematics teachers. The conference is sponsored jointly by the Texas Council of Teachers of Mathematics, the Texas Association of Supervisors of Mathematics, and the Texas Section of the Mathematical Association of America. The three-day conference is conducted each summer, on a rotation basis, in Dallas, Houston, and San Antonio.

Great speaker line up including Rachel Cruze, daughter of Dave Ramsey, financial guru, and Dan Meyer, dynamic speaker one of Tech & Learning’s 30 Leaders of the Future.

 Come be inspired and equipped to teach math in a whole new way!

Interdisciplinary Synthesis in Advancing Education Science 
Society for Research on Educational Effectiveness - September 26-28, Washington, D.C.

SREE endeavors to advance and disseminate research on the causal effects of education practices and interventions. The Society recognizes and supports research in neuroscience, cognition, learning, and socio-behavioral or meta-cognitive influences, broadly and within specific domains such as mathematics and science.

The theme of the SREE Fall 2013 Conference, Interdisciplinary Synthesis in Advancing Education Science, recognizes the value of incorporating diverse branches of education science, including applying causal methods in challenging field settings to improve opportunities and outcomes for students. The application of cognitive science principles to curriculum design, the implementation of evidence-based standards in mathematics and science programs, and the evolution of education technology from a focus on technical features to an emphasis on how principles of learning may encourage productive uses of technology, provide a few examples of research that would be appropriate for this meeting.

Questions of particular interest include:

• How may research findings in cognitive science and other fields be applied to the design of education interventions? 
• How is research evidence being utilized to improve mathematics and science programs along the developmental continuum, including initiatives for at-risk learners? 
• How may we conceptualize and measure capacities beyond academic achievement that are important to lifelong growth and development? 
• How may technology be employed most effectively to improve education in diverse settings? 
• What is the best means to develop expertise in the art and science of completing experiments in school settings?

Teach. Inspire. Hire. 
2013 U.S. News STEM Solutions National Conference 

This week was the National STEM Solutions Conference, right here in Texas. More than 2,000 leaders and visionaries in business, education and government from around the United States convened in Austin, Texas June 17-19th to advance the agenda for national change in STEM education, policy and workforce development.

Last year myself, and several of my colleagues from SMU, attended this summit and found it to be one-of-a-kind. It’s hallmark of having representatives from business, education and government, is what makes this event effective as it has been noted that all of these entities need to form a partnership to truly bring change in STEM education and careers.

What’s in it for you? Not only were there an incredible slate of speakers, but there were also tailored conference tracks for you to plug into the area that is most representative of your profession. If you are a K-12 teachers or a CEO, there is something for everyone here and you are able to network with like-minded colleagues from across the US.

OK, so it's a bit late to attend this year, but there is always next year in Washington, D.C.! Or you if you want to keep abreast of the latest STEM news, join STEMconnector - be the first to get updates on what is happening in STEM across the nation.

What conference are you attending this summer? Recommend a great resource to your colleagues – leave a comment!

Writing to Learn Mathematics

By Yetunde Zannou, RME Postdoctoral Research Fellow

As a mathematics teacher, were you ever blind-sided by students’ performance on an assessment when they seemed so knowledgeable in class? I most certainly was! I decided to do an action research project in several of my classes to better understand that gap and how to bridge it.

My initial investigation led me to look more closely at my assessment techniques and what other teachers were doing to “know what their students know.” I decided to deliberately, and regularly, incorporate writing into my mathematics instruction as a tool to help me support students during the learning process, not near the end of a unit. Writing ultimately helped me to help my students learn.

Some Benefits of Writing to Learn Mathematics

Writing to learn mathematics benefits students and teachers. For students, the process of writing can help them think through and explain their reasoning, which may not always happen when the goal is to find a solution. Students learn over time how to be good note-takers, but often struggle to apply their notes meaningfully. Writing about their thinking forces this process to happen. For instance, instead of asking students to find a solution, ask them to evaluate whether a solution is correct or not and to justify their reasoning. Students have to examine a solution carefully, identify whether or not there are any errors, and explain their position. This type of assignment requires students to access their knowledge in a new way, which facilitates real ownership of new knowledge, not just regurgitation.

As a teacher, my students’ writing made clear where they struggled with a concept or procedure. Particularly as someone who understands mathematics and enjoys it, it was difficult to see some of the little things that may confuse students. However, their writing made those visible to me. As a result, I could address common misconceptions in future classes, provide additional specific support for individual students, and strategically reorder problems in consideration of possible challenges.

Practical Application

There is a wealth of information available on using writing to learn mathematics. In the upper grades, students may be unaccustomed to writing about their mathematical knowledge; however, with sufficient guidance, clear examples, and regular opportunities to practice, they can do well. A good initial writing activity is a mathematics biography. I’ve seen this done primarily with numbers or as a history of students’ experiences in mathematics. I used it as a history and gained valuable insight into my students’ feelings about their mathematical ability. It may be helpful to write your own and share! Writing can be used at almost any stage of a lesson or unit. I’ve used writing to get students thinking about previous lessons and connections between concepts at the beginning of class. I’ve also used writing as an on-the-spot assessment, as well as on summative assessments. Here are my top five assessment prompts:

1. Evaluate a problem and its solution for accuracy and justify your response
2. Create a problem to certain specifications (solvable or not), include a correct response, and identify possible errors a friend might make
3. Write a note to a friend who was absent, describing what you learned today. Include an example problem, solution, and detailed steps to solve
4. Describe how you would solve a problem and your reasoning without including the answer. Great for scale problems
5. Describe what would happen if… This is a good prompt for geometry, proportions, rate, and many others

At the end of a lesson sometimes I would ask students to describe: one thing you know well, one thing you sort of get, and one thing you don’t get at all. I’d use these to revamp the next day’s lesson.

Making it Work

For writing to learn mathematics to work, you and your students have to “buy in.” Students have to understand the value of writing as a tool to help them “know what they know,” as well as a way to assist you in determining how to proceed. You have to be committed to learning from students in this way. Incorporating writing takes class time and time to evaluate assignments. Here are some suggestions to make it work:

• Plan writing assessments in advance. Students will take the writing exercises seriously when they see that you do. Avoid using writing as a way to “pass time” or “on the fly.” Even if you decide an on-the-spot writing assessment is needed, you should already have an idea of a prompt to use or a question that could work as a written assignment.
• Make sure prompts are clear and direct. Writing alone does not guarantee these benefits. Make sure instructions clearly communicate what you want so that students know how to respond and their writing serves as an effective assessment tool.
• Decide in advance how and when you will evaluate it. Planning to write should accompany a plan for evaluation and action. The likelihood of reviewing a written assignment in a timely manner increases when you know what you’re looking for. If you want to know common errors across classes, sampling entries is better than reading each students.’  I’ve given written assignments in lieu of traditional homework problems at times and discussed them in class the next day before moving on.
• Provide feedback, individually or to the class. Even if you don’t provide each student with a detailed response, students should be aware that you are reading their answers. This will help them to see the value of their writing efforts and the immediate impact it has on your instruction.

What are some other advantages of using writing to learn and assess in mathematics? What might be challenges to incorporating it into your instruction? What supports are available to make it work?

All Resources are Not Created Equal! A Closer Look at Algebra I Textbooks

By Dr. Candace Walkington, Assistant Professor of Mathematics Education & Elizabeth Howell, RME Research Assistant

Quite often teachers inherit the textbooks that will be used as a primary teaching tool and resource in their classrooms. Textbook choices may be district-level decisions or may be decided in a multi-year cycle. As a classroom teacher, the decision may be out of your immediate control. However, as the ultimate instructional leader in your classroom, it IS possible to use current research about textbooks in order to improve outcomes for your students, regardless of the required curriculum.

Background
Experts agree that algebra is a crucial course in students’ mathematical trajectory, and success in this course has been identified as important to college and career readiness (Stein, Kaufman, Sherman, & Hillen, 2011; Cogan, Schmidt, & Wiley, 2001; Kaput, 2000; Moses & Cobb, 2001). A key learning goal in algebra is the use of symbols to represent and analyze situations and problems, and many textbooks are written with a heavy emphasis on symbolic usage and presentation.

However, working with symbolic representations is challenging for students (Walkington et al., 2012), and evidence suggests that students actually have improved learning when they first learn about a new concept using concrete and familiar formats (Goldstone & Son, 2005) - like verbally presented algebra story problems. By giving students story scenarios first, instead of symbols alone, we can draw on the things they already know and understand. Over time, these verbal supports can be faded, as students begin to understand and work with symbols more.

Textbook Classifications
Current Algebra I textbooks are classified as being traditional or reformed. Traditional texts have the lion's share of the textbook market (Holt, Pearson, Saxon, etc.), and introduce concepts by showing definitions and worked examples, and then presenting problem sets. These texts are typically expected to go along with a teacher-directed approach to instruction. Reformed textbooks are more rare in Algebra I, and often follow NCTM standards for reformed teaching, taking a student-centered approach. They may present students with more complex, open-ended problems or mathematical investigations, and accentuate the use of problem-based learning. Differences have emerged in the way that traditional and reformed curricula introduce the use of symbols in Algebra I, and many reformed textbooks in mathematics have taken less of a symbolic approach and adopted a more verbal presentation style.

Example of problem presented in VERBAL format:

• Maria just got a new cell phone, and on her phone plan each text message she send costs $.10. Write an algebraic expression that relates the number of texts Maria sends to the cost in dollars. How much will it cost to send 7 texts?

Example of problem set presented in SYMBOLIC format:

• Solve for y when x = 7:
  y = 3x + 5
  y = 0.25x
  y = 2x - 3

Current Research
In a recent study, researchers found that the presentation format of the examples and homework problem sets in commonly used Algebra I textbooks varied depending on the type of textbook, traditional or reformed (Sherman, Walkington, Howell, 2013). Reformed texts favored a verbal presentation first, and this verbal first approach was faded over time in the text. Thus in reformed texts, when students are first learning about algebra, they get a lot of verbal problems, but as their expertise develops, they get more symbolic problems.

Traditional texts favored symbols first - in each section, symbolic problems were presented to students before verbal problems. Traditional texts also had fewer single format only sections - there were fewer sections that had only verbal problems, or only symbolic problems. Most traditional texts contained a mixture of symbolic and verbally presented problems in the homework, yet the instructional examples provided in the text trended toward symbolic. Other research has also suggested that in traditional texts, the student recommended exercises in the teacher’s edition sometimes excluded the verbal problems from the students’ assignment.

Implications
Because many schools are using traditional textbooks, it is likely that your district adopted text has a heavy prevalence of symbol-first presentation. Be aware of the challenges that this approach may present to your beginning Algebra I students, and use verbal presentations in your initial classroom examples whenever possible. When assigning homework, be aware that the recommended exercises may exclude all of the rich verbal contextual problems, and add a few back in to your homework assignment. Better yet, choose a few to discuss and work on together as a class.

The choice of an Algebra I textbook may not be a decision that you can determine, but how to best use the examples and problems presented in the book is always your choice as the teacher. What type of textbook are you currently using? Take a closer look, and be aware of the presentation style that the book favors. If verbal scaffolding is not prevalent, it is easy to add those supports back in to help your students to succeed. A closer look will help you to see those places in the curriculum where a verbal presentation could be beneficial.

Resources:
Texas State Adopted Textbooks: http://www.tea.state.tx.us/index2.aspx?id=2147499935

References:
Cogan, L.S., Schmidt, W.H., & Wiley, D.E. (2001). Who takes what math and in which track? Using TIMMS to characterize U.S. students’ eighth-grade mathematics learning opportunities. Educational Evaluation and Policy Analysis, 23, 323-341.

Goldstone, R., & Son, J. (2005). The transfer of scientific principles using concrete and idealized simulations. Journal of the Learning Sciences, 14(1), 69-110.

Kaput, J. J. (2000). Teaching and learning a new algebra with understanding. U.S.; Massachusetts: National Center for Improving Student Learning and Achievement.

Moses, R., & Cobb, C. (2001). Radical Equations: Math Literacy and Civil Rights. Boston: Beacon Press.

Sherman, M., Walkington, C., & Howell, E. (April, 2013). A comparison of presentation format in algebra curricula. Presented at National Council of Teachers of Mathematics Research Pre-session, Denver, CO.

Stein, M.K., Kaufman, J. H., Sherman, M., Hillen, A.F. (2011). Algebra: A Challenge at the Crossroads of Policy and Practice. Review of Educational Research, 81(4), 453-492.

Walkington, C., Sherman, M., & Petrosino, A. (2012). ‘Playing the game’ of story problems: Coordinating situation-based reasoning with algebraic representation. Journal of Mathematical Behavior, 31(2), 174-195.