Blog Post #13: Assessment Articles

Assessing Problem Solving Thought

As the emphasis on problem solving increases, teachers need to prepare themselves to assess student problem solving understanding. The easiest way to assess student understanding of story problems is through a well-developed rubric. To create the rubric, teacher must first locate or write a high order thinking problem and work through the problem to reach a solution. Next, Teachers need to decide what are the various thinking skills that students need to display in their own solutions. The authors of the article decided to assess students on the following criteria: 1) understand or formulate the question in a problem, 2) select or find the data to solve the problem, 3) formulate sub-problems and select appropriate solution strategies to pursue and 4) correctly implement the solution strategy or strategies and solve sub-problems. These criteria may change based upon the problem(s) teachers are giving to their students.

After determining the grading criteria, the teacher should determine how many levels each criteria should be divided into. The authors suggest three levels for each criterion. Next, point values are assigned to each level within the criterion. The lowest level should be zero for students who do not attempt or do not show evidence of the criteria. Additionally, teachers should consider placing greater weight on harder level skills.

When assessing student work using the created rubric, the teacher should take great care not to assume they know what students were thinking as they were solving the problem. However, there will be instances when score must be given based upon inferences. It should be avoided whenever possible. The teacher should work through the problem as the student and assess the student on each criteria. The teacher may notice that his/her rubric needs adjusting for the next time he/she uses it while assessing the whole group of students. It is important for teachers to always give honest and complete feedback to students in order to help them improve.

This article provided valuable insight into how mathematics teachers (and teachers of other subjects too) should think about assessment. If an assessment tool is used only to have written documentation of whether a student did or did not do something correctly, it is not really assessing much. The well thought out rubrics that the article describes enables teachers to truly get at the root of student understanding and knowledge.  Once this types of rubrics are created, the teacher can use them over and over again and tweak it when necessary. Therefore, it may take some time initially to create these kinds of rubrics but it will be well worth it in the end.

Assessment Design: Helping Pre-service Teachers Focus on Student Thinking

This article describes an activity for pre-service teachers that was designed for such teachers to think more deeply and critically about assessments. This critical thinking included not only the content of the tests but also the type of assessments and the time the assessments are given to students. The project began by introducing pre-service teachers to literature about effective assessments and assessing student understanding. Next, the pre-service teachers selected an NCTM standard and created an assessment with the intention that it would align to such standards. Pre-service teachers discussed their rough draft assessments with their peers and made any necessary changes from the feedback they received. Finally, the pre-service teachers implemented the assessments to a group of students and reflected on the outcomes. Many of the pre-service teachers were amazed about the small details they did not consider when originally creating their assessments. The main point received was that just because students compute the right answer, it does not necessarily mean that the student understood the material or could use it in a real-life situation.

I find assessment to be one of the hardest parts of lesson planning. It is so easy to throw several multiple choice problems on a sheet of paper and give them to your students rather than taking the time and the effort to think about the best method and time to assess them. It would be fantastic if all teachers could share their assessments with their colleagues to get feedback but unfortunately that is not really possible in a real-life situation. When I create my next assessment, I hope to use the ideas of this article especially the section that discussed when to deliver assessment. Assessment should not just be at the end of a lesson or a unit but throughout the lesson in order to tailor instruction to meet the needs and skill levels of all the students in the classroom. Additionally, I hope to remember to consider the best method of assessing my students and if the assessment I created actually matches the original goal and standard.

Assessing Students' Mathematical Problem Posing

As the emphasis on problem solving is increasing in today's  schools, problem posing is receiving more and more attention. Problem posing can be integrated into assessments or it can be assessed as its own entity. When problem posing is integrated into assessment, teachers could potentially provide students with mathematical statements and ask them to create questions based upon those statements. The articles example of this type of problem included: Pose problems that all can be solved using the same division statement 540 ÷ 40 = 13.5 ?. When problem posing is assessed, teachers can potentially provide their students with a set of information and ask them to create specific questions using that information. Their example included this problem: Ann has 34 marbles,  Billy has 27 marbles, and Chris has 23 marbles. Write and solve as many problems as you can using this information. Assessing these types of problems can be difficult for teachers and it largely depends on the instructional goals of the lesson. The authors of the article, however, suggest the following three criteria for assessment: quantity, originality, and complexity. Quantity refers to the number of questions students can create. Originality refers to the unique quality of the questions students posed. Complexity refers to the mathematical concepts and skills within the questions .

I think it is a great idea for teachers to ask students to participate in the question generating process. This allows the teacher to know what types of ideas or skills students are comprehending and those that students are struggling with. Additionally, it allows students to be creative. However, I do not think that students should be assessed based upon the quantity of questions they can come up with. This type of assessment seems a bit superficial and does not take into consideration any kind of mathematical ability. The criteria of originality and complexity seemed more appropriate for these types of activities.