• Self - assessments are important because it helps students keep track of their progress. By assessing their growth, students are developing an important life - long learning skill. It encourages students to be active and not passive learners.
  

• When students take part in the assessment process they are being motivated and encouraged to monitor and make changes to their learning.
  

• Self - assessments should be used to keep a record of how students perceive their strengths and weaknesses as they begin to take responsibility for their learning.
  It is important for teachers to have other forms of measurement besides self - assessments since the way a student perceives their learning progress is not always reliable.
  

• There are several ways that a teacher can gather student self- assessment data. Examples include: preassessments to identify or clarify confusion, exit tickets at the end of a lesson, concept maps, open - ended writing prompts and questionnaires.

1. Write two important things that you learned in class today.

2. Which problem(s) did you find the most challenging? Which were the easiest?

3. How well do you think you understand the work we have been doing on fractions?

• Teachers must convey to students why they are doing a self - assessment. They need to understand that they play a role in their mastery of math and are not just focusing on completing a task. Teachers should encourage students to be honest about their math skills.
  

• It is important to keep in mind that it will take time to infuse self - assessments into the daily schedule. But the benefits that it brings to students are worth making the time.

1. Observations: Teachers are learning new information about their students everyday. With this being said, a student's performance increases during and after a lesson is presented. If teachers are well prepared and well aware of their students behavior and mannerisms during classroom instruction they should be able to gather important information while observing and listening to students during classroom instruction. Teachers will begin to notice two positive results occur. First, material that may have been misunderstood or even unnoticed becomes highlighted and important when observing and listening. Second, any data collected through observation at this time can be added to previous data, and will only help the teacher with planning future lessons, providing student feedback, parent conferences, and determining student grades. Depending on what exactly you are trying to observe, observations can range from a few days to a few weeks. Observing a classroom full of 25 students is work, and work takes time. One system for recording observations is using anecdotal notes. This is when teachers write notes during or directly after a lesson has be taught. Check lists are another way to observe, which helps the teacher cut down their writing while focusing their attention. This type of observation can be easily modified for each student and their specific needs. Lastly, you have observation through questioning. This is all about talking to your students. Observations do NOT need to be done quietly. Ask your student what he or she understands or what they may be struggling with. Talk , talk, talk. 

2. Interviews: This kind of formative assessment is done using diagnostics. This is a way to get in depth information on an individual student. This is done one on one and is used to get students thinking about a specific topic, concept, or process. What it tough is that diagnostic interviews are assessment opportunities, which means NO teacher input. Teachers want to see what the students knowledge is about said topic and what the students thinking process is, or how they come up with a certain strategy. Students are given a problem and asked to verbalize their own break down of the problem. This assessment is used best when you need more information on how the student is mentally constructing and solving problems. With the information collected from an interview assessment, you the teacher can see just how effective your instruction is.

3. Tasks: Refer to written artifacts and includes performance based texts, writing, and tests. Examples of this would be: journals, math notebooks, and even student self assessments. Translation Tasks or what the book calls "atranslation task" use seven representations for concepts. Students are asked to use several of these representations (tools, words, or numbers), to demonstrate their understanding of single problem. As students move about these representations, there are better odds that a concept will be formed correctly, creating room for meaningful new ideas. Translation tasks are best used when the teacher wants to find out more about the students potential. Like how he or she can represent ideas in more than one form, and explain why the representations are simiar or different.

• How valid or accurate this grade is depends on the information used in making the grade, judgement of a teacher and how the assessments align with goals.

• When determining a score, it should not be solely based on averaging what's available but also any other information.
  

• It is important that pieces of work such as observations, exit tickets, journals and rubric scores are used when deciding on a grade. Students should be given more positive feedback to continue encouraging them to work hard on all assessments. At the same time though, converting the rubric scores, such as 3 out of 4, to a percentage can deter the focus to grades rather than learning and improving.
  

• Grading should focus on the performance, as well as any other activity that was assigned, so students will understand the importance. Grades at the end of a grading period should represent an overall view of how the student performed all quarter compared to the goals set by the teacher.

By using different forms of assessments when grading, the student has a better chance for a higher grade. It is important for teachers to know how to use assessments to gauge what students have learned and still need to learn. Assessments should be used to design your next lesson and decide which strategy to use. Summative assessments are not very useful when creating a lesson or follow up activity, but formative assessments are.

Some criteria that is often included in rubrics is:

• If the student solved the problems correctly and in enough detail.

• If the student could justify and explain the arguments and/or arguments they used.

• If the student used logical reasoning.

• If  the student showed a grasp of numerical relationships and structure.

• If the student incorporated more than one representation and/or strategy.

• If the student showed an ability to select and use tools and manipulatives.

• If the student communicated with precise language and accurate units.

• If the student identified repeating patterns of ideas, and made connections between big ideas.
  

Rubrics generally range from the best score to the lowest score. The teacher starts making the rubric by describing what excellent work would be since that is what they want their students to strive for. Then they go from there.

The performance indicators are what will be scored. These are also called performance level descriptors, or achievement level descriptors. They are standards or learning targets, and show what the student should be learning or a category they should be working on.

Two groups that are working to make rubrics to align with common-core
standards are:

The Partnership for Assessment of Readiness for College and Careers (PARCC).
They have published grade level indicators and subject specific indicators for grades 3-8.

The Smarter Balanced Assessment Consortium (SBAC). They have similar indicators to assess knowledge, skills, and processes that students show. They have four types of indicators. One for test development and conceptualization (they call them policy achievement level descriptors), one for item-writing guidance (they call them range ALDs), one for cut score recommendation and standard-setting guidance (they call them threshold ALDs), and one for test-score interpretation (called reporting performance level descriptors).

There are two main types of rubrics. Generic rubrics and task specific rubrics.

Generic rubrics are very broad with their categories and are used numerous times. Sometimes it is called the four-point rubric. Usually there are two categories that basically mean the student gets it or two that they need more work. It goes from doing an outstanding job, to doing well, to needing some work, then to needing a lot of work. This rubric can be explained at the beginning of the school year and put up in the classroom where it can be seen. It helps students to know what is expected in general assignments. When students understand the rubric they can use it to do self-assessments.

Task-specific rubrics can be done two ways:

Statements that describe in detail what is expected are put into each possible score and have multiple categories that each can gain that score. These are only applicable to specific assignments and can be used to figure out where work needs to be done not only for the student, but for the teacher to see where they aren’t reaching their students. It helps so that the teacher knows where their lesson might have had weaknesses that could be overcome. These rubrics should be given to students before they start their assignment so they know what the expectations are. Afterward these rubrics can be given back to the students or used in student-teacher conferences to help the students know where they went wrong, what they can do to work on that, and where they did well.

Observation or anecdotal notes rubrics that are also for specific tasks. These have categories that range from going beyond expectations, being on target, and not quite being where they need to be. For this rubric the students names are placed into the blank area beside which category they fall in on the assignment they are doing.

- There is never a grade to young to start using writing. For example, a flipchart is one way you can use writing in Kindergarten.

-There are many different ways you can tie in writing with math such as having a Math journal for your students or creating exit slips for them to complete before class is over.

-Using writing opens a door to the students' mind and the way they are thinking and understanding about a concept.

-On the teacher side: having writing example are great to show parents during conferences through the year. If you have a student that doesn't do well on tests their writing can example more of what they understand and what they don't.

-When having discussion in class, having the students write about the solution can help them write out their thoughts and practice what they want to say. For those students that typically keep quite, this can help them get organized. 

POSSIBLE PROMPT TOPICS:

-"I think the answer is... I think this because...." Giving the students a sentence to finish to organize their thoughts.

- Working together as a class to write an explanation of why 4x7 is the same as 7x4. Once you go over it together give the students another situation like this and have them work on it by themselves or in groups.

-Asking the students how they felt about the lesson today and getting feedback from them.

GETTING INFORMATION ON THE STUDENT PROMPTS:

-"What I like about math?"

-Tell your experience with math outside of class.

-What did you learn this week that you didn't know before?

Explicit: Having a student rate themselves confident, somewhat confident, and guessing when taking a test.

Implicit: Giving students options when answering questions. Example: A or B, A or C, B or C, No idea.

These tests will give the teachers evidence on if their teaching methods are working or not.

If the student answers confidently and gets the answer right then your teaching methods are probably working well. If the student gets the answer wrong while stating they are confident then you should reflect on how you are teaching material. If the student answers correctly but is not confident about it, working with that individual student might help them with any anxiety they have when it comes to assessments.

Activity: Imagine that you have a student in your classroom by the name of Johnny. Little Johnny has been struggling with taking assessments especially when it comes to math tests. During lessons Johnny appears to understand the material when participating in white board activities and other classroom informal assessments. After each formal assessment however Johnny does not do well. His mother Janet is very upset that Johnny is not doing well. She took offense to his bad test scores and is blaming you as his teacher for his struggling. In your groups discuss some different strategies a teacher might use to help a student who is struggling with assessments or may have test anxiety. List at least three different strategies on a piece of paper. Then discuss how you as the teacher would handle talking to, and involving Johnny's mother Janet to help improve Johnny's assessment ability, without offending her or creating conflict between the two of you.

Assessment is how the teachers collect evidence showing students’ content knowledge and how well they will be able to use this knowledge. Assessments should not be limited to tests and quizzes, but should also be how they do work in class and how well they are able to participate because of their knowledge.

Formative Assessment

• Formative Assessment can be described as students actively thinking.

• This type of assessment is used to check what the misunderstandings are on specific topics.

• The teacher should be able to look at these and come up with ways that misunderstood topics can be retaught.

• This type of assessment usually gets the teachers thinking and makes it so most of the students in the class are learning and retaining information.

• It is very helpful if the teacher asks the students for their feedback and what they think they need to work on.
• Plans for future action must be created after using a formative assessment.
• Three Key Processes
• Identify where the learners is at.
• Identify the goal for where you want them to be at by the end of the lesson.
• Identify a path for how the learner is going to reach that goal.

• Summative Assessment is what students know at one moment. 

• This is an assessment that will create one single grade such as a mid term test or a state standardized test. 
• These can be helpful for teachers and schools to look at to check where their students are making mistakes. Though this is true, it will most likely not help the teachers see the students and understanding and help them focus on what they need to reteach. 

What Should Be Assessed?

Students should be able to do many things foreach mathematical process in order to show their understanding. Here are a Few:

Problem Solving- The student can come up with more than one way to solve a problem.

  Reasoning- The student shows their work and can justify their reasoning.

Communication- The student uses the correct math language and can explain the problem using writing, pictures, and numbers.

Connections- The student can make a connection between mathematics and real life situations.

Representations- The student can use drawings, graphs, and models to solve and explain math problems.

They can be designed to find out what students understand and how their concepts are connected.

If a test is well constructed, you will gain much more information than whether an answer is wrong or right. You can gain insight into the students thinking and their understanding of the concepts you've taught.

Strategies for maximizing effectiveness of tests in your classroom:

1. Permit students to use calculators on test. The allows you to really focus on testing the skills you want them to learn.

2. Let students use manipulative and drawings while working through the test.

3. Include opportunities for students to give explanations on their tests. Let them describe their thinking and their use of strategies.

4. On the test, use open ended questions. Tests that have only one correct answer limit what you can learn about students understanding.