Math - no problem! evaluation guides (2023)

What is the rating?

In short, we can define evaluation asdata collection processto better understand students' learning strengths and weaknesses.

The evaluation can be divided into three types.:

  1. EvaluationforTeach
  2. EvaluationifTeach
  3. EvaluationvonTeach

They may look almost identical on paper, but they are different and serve different purposes. Let's examine one by one.

to learn assessment

Assessment for Learning is also known as formative assessment. Describe one of several methods teachers use to determine how well students understand the math they are being taught.

It's the type of assessment thatbenefits the studentand is used as a tool to support learning outcomes.

Formative assessment answers the question: Where are the students at in terms of learning and what should be done next in teaching based on this knowledge?

It can be viewed as a daily, cross-workstation or real-time assessment.

Formative assessment can be formal and informal, ranging from teacher observations to testing. It usually contains data in the form of numbers, descriptions, comments and checklists.

Here are some examples offorms of formative assessment:

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make questions

Asking skillful questions during the lesson helps teachers check depth of understanding, identify progress against learning objectives, and diagnose the causes of incorrect answers.

ThisTips for good questionsthey were summarized from a list compiled by Steve Reinhart, a professor of mathematics in Wisconsin, USA:

  • Never say anything a student might say.
    • If you are tempted to say something to the students, ask a question.
  • Ask questions that require more than remembering facts
    • The student must be able to learn something from the question and the teacher must be able to learn something about what the student does and does not know.
  • Use more process questions than product questions
    • Product questions require short answers and don't provide much information about what the student knows; Process problems require students to reflect, analyze, and think at much higher levels
  • Replace conversation with interrogative sentences
    • Often, lesson time involves very little active thinking and discussion, resulting in a low percentage of student attention.
  • be patient
    • Increasing wait times to five seconds or more can result in more and better answers.

Skillful questioning may sound like a mundane skill, but it's actually essential.

Asking yes/no or right/wrong questions candelay the development of children's metacognition and communication skillsexplains Alex Laurie, a primary school mathematics teacher in New Zealand who has extensive experience with the Singapore Method. This is because these "lower" questions don't give students an opportunity to think about how they arrived at an answer.

Instead, by focusing on a complex problem and using higher-order questioning techniques, students' answers show different levels of understanding as well as how they approach math problems in general.

Flora Taxonomy, named after the American educational psychologist Benjamin Bloom, is aLearning model consisting of three domains– cognitive, affective and psychomotor – each with different levels of thought, ordered from the simplest to the most complex.

As you level up, your thinking skills become more sophisticated. For example, remembering and understanding are lower-order skills, while evaluating and creating are lower-order skills.superior order.

To encourage higher-level thinking:

  • Ask questions that give students a starting point, such as:
    • How could I ask that?
    • How many ways can you find to...?
    • What happens if we...?
    • What can you make of it...?
    • How many different [ ] can you find?
  • Ask questions that stimulate mathematical thinking, such as:
    • What's the same?
    • What is different?
    • Can you group these objects somehow?
    • Can you spot a pattern?
    • What do you think next?
    • Is there another way?
  • Ask evaluation questions like:
    • what did you discover
    • How did you find out?
    • Why do you think that?
    • What made you decide to do it this way?
  • To develop students' metacognition skills, ask concluding discussion questions such as:
    • Who has the same answer/pattern/grouping as this one? As you know?
    • Anyone have another solution? Where's the difference?
    • Have we found all possibilities? How do we know?
    • Have you thought of another way to do this?
listen to your students

Finally, we sometimes forget that the really good questions in class don't always come from the teacher.

children's questionscan give you valuable information about your learning. Have the children quiz each other and you.

Shaw Primary Academy principal Dawn Copping says there are dozens of methods you can use to monitor your students and move everyone forward when it comes to classroom assessment. But after months of interrupted learning, ensuring efficient and effective assessment is a top priority.

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The best proof is to listen to children. Create an opportunity to talk to them about what they are learning.

You could ask her:

  • what do you know now
  • What didn't they know?
  • How do they know they're making progress?

Introduction of questions or plenary activities

questions or plenary activitiesCheck that students are ready to continue at the end of the lesson. In Mastery programs, students perform independent work that requires progressively deeper understanding. This carefully structured work allows you to easily assess how well a child understands the purpose of the lesson by assessing the amount of independent work they can do.

Implementation of quick scan routines

Some teachers opt for a quick check-in routine where children use a signal, e.g. For example, give a thumbs up to show their confidence and set the tone for the lesson. This quick review can determine next steps, e.g. B. whether the majority of the class can continue and complete the work independently, while those who are still unsure can continue in a guided environment with the teacher or peers.

assessment as learning

Assessment as learning, another type of formative assessment, occurs when students actively monitor their own math learning, asking questions and using a variety of strategies to decide what they know, what they don't know, and what they partially know.

Esthe process of developing and supporting students' metacognition, Encourage students to self-reflect and ask questions about their learning.

These comments by a teacher in aStudy 2017show how to approach a domain, in this case with theMathematics: no problem!shows that developing a classroom learning environment that involves difficulties and mistakes is intertwined with collaborative learning, formative assessment, and development through metacognition as a self-regulated learner:

"It's that idea that as an apprentice you build maturity."

“Errors really become a core process. Now, in our classes, we're going to be really happy when someone does something wrong because it's something to run away from. And it also models these self-control skills, so the child talks out loud about what they are doing and maybe making a mistake, they monitor and regulate themselves, which is actually a very important skill. ."

Why are metacognitive skills important?

Put simply, metacognition is the ability to reflect on one's thinking.

Research suggests there isdirect correlation between students' metacognition and their performance in mathematics. When you compare high-performing and low-performing behavior in troubleshooting tasks, you often find important differences.

High-performing students:

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  • Explain things to themselves while working through examples.
  • Try to build relationships between the new processes and what they already knew
  • Tends to derive additional information not directly provided

Underperforming students:

  • Follow step-by-step examples without referring to what you already know
  • Don't try to build a broader understanding of the procedure in order to generalize it to new situations.


As a teacher and former Inspector of Ofstedjohn dabeldeclares children have adecisive roleTaking responsibility for their own learning and supporting the learning of their peers. One of the core principles of formative assessment is to help children take an active part in accurately evaluating their own understanding and actions.

Teachers can create amazing lessons through technical discussions, structured learning, and guidance on next learning steps, but students must be able to calibrate, self-evaluate, and reflect.

Teachers and students can create learning goals together to guide their next steps towards peer review, self-assessment and reflection.

math diary

Mathematics curricula around the world emphasize the importance of developing mathematical fluency, conceptual understanding, and reasoning skills in their students. However, these skills are not always easy to assess. Cue the humble math diary, says Alex Laurie.

Math journals give children a chance to reflect on their learning and reinforce their understanding.

But what is a math journal?? And what does a good math journal look like?

Math notebooks are workbooks (grid, lined, or plain paper) in which students record their methods, explanations, and ideas for problem solving and learning concepts.

Journals provide teachers with information about a student's thinking and understanding of mathematical ideas and allow them to correct any misunderstandings that arise.

How should they look?

  • Add the date and title.
    • Each journal entry must begin with the date and a title.
  • Add a learning intent
    • In math, we often start the lesson by telling the children what math concept they are going to learn that day. We give them the intent to learn, or We Learn (WALT), to write at the top of the page.
    • A journal's title is similar to WALT, but instead of communicating the math concept to students, the journal's title comes from the student and reflects what they believe they learned during the class.
  • set expectations
    • A good magazine cover should reflect the mathematical idea that the lesson focuses on. Magazine titles indicate the student's level of understanding of the concept.
    • Take the following examples of math magazine titlesMathematics: no problem!NZ Textbook 2A Chapter 7 Lesson 6 (the exploration task)
      • Subtract from 10: This may indicate that the child understands the math concept and can use formal math language.
      • Remove Notes: This may indicate that the child understands the math concept but is using informal math language.
      • Amira and her notes: This may indicate that the child is not relating the mathematical idea to the context of the problem.

creative diary

The math journal can play an important role in actively engaging children, allowing them to focus on their learning journey and articulate their own understanding. This allows them to accept mistakes and think critically.

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Laut Roger Hitchin, Singapur Maths and Drama Director an der Wellington Prep School.
creative diaryencourages students to develop models and stories and to show the full range of their understanding.

Creative journals are also a safe place to explore misconceptions or build on more advanced students who have mastered a concept.

Fullfive different types of mathematics journals, Datahell douglas.

  • Descriptive questions ask children to describe methods they used or explain a concept. For example: "How do you multiply a two-digit number by another two-digit number?"
  • Assessment tasks ask children why they chose a method and how it helped solve the problem. Children need to justify their decisions.
  • The creative journal allows children to develop models and stories to show their understanding. Example: "The answer is 25. What might the question be?"
  • Children can investigate a problem and write down their findings, such as “I buy a toy from a store. I get 20 cents in change. What coins have I earned?
  • Children share what they have learned and understood in formative journal entries. This is an opportunity for them to reflect on what they found challenging and why.

In short, the journal is a tool that students can use to communicate their knowledge and feelings about mathematics and help them solidify their understanding. It is also a tool for teachers to assess student learning and growth.

learning assessment

Learning assessment or summative assessment is the process of assessing individuals to determine their understanding of mathematics. It can be used to assess a child's placement in the class and as a comparison to their peers.

The summative assessment summarizes what has been learned so far. The question arises: did the students learn or master what was taught? This often resembles questionnaires, tests, and numerical data, but can take many forms. Summative assessment is often viewed as a tool for assessing accountability.

While summative assessments are typically conducted at the end of the learning process in a traditional testing environment, they can also be used formatively as an opportunity to enhance learning.

However, its effectiveness really depends on the type and quality of the feedback. The results should not be used to find errors but to work with formative assessment to provide the right learning environment for each child.

How summative assessment is used

Some of the uses of summative assessment include:

  • Plan future goals and learning paths for students.
  • Provide proof of achievement for students, teachers and parents.
  • Providing data to the general community and external groups.
  • Offer a snapshot of learning.
  • To determine where further additional resources are needed

Ifassess responsibility, metrics-based goals and predefined numbers are the focus, says Mirkka Jokelainen, product manager at Oxford University Press. This can help improve learning outcomes, but what prints on the student report is sometimes prioritized over other information that teachers can use to take positive action in the classroom.

We like to pretend that the accountability assessment is not happening. Nobody wants to think about six-year-olds taking tests just so someone can have a great chart on their slideshow somewhere. However, the reality is that most schools need to produce data that shows leadership or outside stakeholders that they have achieved their goals.

Adam Gifford, Senior Strategic Leader in the NCETM Maths Hub pilot program and aMathematics: no problem!The series' editor, writer, and coach says summarizing a child's learning is a difficult task.

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It takes a great deal of skill to write questions that can help gain insight into a child's understanding. The summary assessment is sometimes viewed negatively on its own, but works well as part of an overall, cohesive assessment program.

Rating in Insights

Mathematics: no problem!Assessment documents serve to provide performance data across different content domains; Numbers, addition and subtraction, geometry, measurement, statistics, multiplication and division and fractions, decimals, percent and proportion.

But when used in conjunction with thatInformationstoolthe results can also be evaluated at individual, class and school level.


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