Mathematics and Statistics Article review

Mathematics and Statistics Article review

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Any topic (writer’s choice)

Type of paper:

Article review


Mathematics and Statistics

Format or citation style:

Not applicable

Paper instructions:

Read through the interview data

Go to the text and read through any referenced content.

Use what you read about

Take notes of what you learned about the students’ understanding of two-digit numbers.

Make an instructional plan for the next steps for students.

Submit to D2L the following:

The notes you took – half a page typed, double spaced. Include references from the book, pages numbers and quotes.

Instructional plan for next steps.

Assignment 8. Second Grade Interview Data

Directions:  Below is a set of interview data that used diagnostic interview tasks that you read about on page 237 under the FORMATIVE ASSESSMENT Notes. These were taken over a week in the early part of the year with a class of second grade students. THIS IS REAL DATA!

Your task is the following:

  1. Read through the interview data
  2. Go to the text and read through any referenced content.
  3. Use what you read about
  4. Take notes of what you learned about the students’ understanding of two-digit numbers.
  5. Make an instructional plan for the next steps for students.
  6. Submit to D2L the following:
    1. The notes you took – half a page typed, double spaced. Include references from the book, pages numbers and quotes.
    1. Instructional plan for next steps.
  7. Bring a copy of this to class on Tuesday for us to discuss.

The interview went as follows…

  • “Please write the number sixty-seven.” (All can do this.)

“Now write the number that is one more than that number.” (Most can do this, also.)

“Now write the number that is 10 more than 67.” In the sample, all of the students counted using their fingers and only a few were successful. Not a single child was able to write the number that was ten less. All tried to do so by counting backwards.

  • The digit correspondence task was done using 53 counters exactly as described in the text on page 223. There were no students in the group that evidenced a place-value understanding of the 5 in 53 (Figure 11.1 page 225).

Again, you will find a full explanation of how to conduct the digit correspondence task, Formative Assessment Notes, is on page 237.

  • Students were shown a clear plastic baggy of 57 small counters and asked, “About how many do you think are in the bag?” Students were fairly successful at making reasonable estimates. Note that this first aspect of the task requires no place value understanding.

Then the students were asked to help count out the contents by putting the counters into groups of ten. That was followed with beginning the “Fill the Tens” task (shown in Figure 11.5 p 230 in the text). The teacher then filled one ten-frame card and began the second. “If we keep on filling up these cards like this, how many cards will we need before we run out of these 57 counters?” Not one child got this correct. Many said we would need 57 cards. Most students simply had no idea.

In the classroom, these same students were able to write the number for a tens and ones picture of rods and cubes, could read and write numbers, and could find numbers easily on the hundreds board.

Notes from the interview data

  1. The second graders were able to;
  2. write one and two digit numbers that do not involve calculations,
  3. Perform calculations that involve one digit.
  4. They had trouble in;
  5. Calculations that involved two digits and changing from one decade to another such that the addition and subtraction of 10 to/from 67. They could not figure it out even after counting backwards.
  6. Grouping numbers in according to their place value, either in tens or in ones for the case of the 57 small counters. They could not establish how many tens ar there in the number 57. 
  7. They could read the numbers but had trouble assigning their place values for the case of 5 in 53.
  8. In a class setting, they could assign the values easily using the rods and cubes but once the materials were changed, they had problems.

In general, the second graders have problems with two digits and require more practice as they progress to three digit numbers.


The article on “Research suggests timed tests cause math anxiety” by Jo Boaler is well outlined and researched with convincing evidence on the implication stated in the topic. The use of timed tests is common in most learning institutions.  But is there research evidence backing up the initiative? The article present a research on the topic and find convincing evidence against the initiative as it contribute to the negative attitude towards math by leaners. The major points that derived from the article are that the timed tests cause math anxiety, create negative attitude towards math and the use of number talks and automaticity can help build math confidence for the leaners.

Timed tests creates a sense of anxiety in the learners as they are pressured to present their best during assessments. When students are faced with anxiety, there is the likelihood of poor performance, avoidance of the subject and weak foundation in math especially for early learners. An anxious situation speeds up brain activity in sections associated with fear and lowers those associated with problem solving. The leaners cannot access information stored in their memory during the times of panics. By the time they recover, the time set for the tests is up hence low performance.

The timed tests creates a mindset that math is a subject for the fast learners and fast performance imply good performance. A review on how students felt about timed tests implied a negative attitude about the whole strategy regardless of if they were high or low achievers. The tests requires more answering and memorizing time hence leaving less time for learning. Eventually, the learners do not get the time to enjoy the lessons and the practices that they end hating the subject.

The timed tests requires the students to know math facts by heart, through automaticity. Except for the memorization of the facts, there are other ways to get the students to understand the facts easily. The use of number sense and talks give the students the chance to participate actively in their learning process despite their different learning abilities. Though the involvement, they understand the concepts and are able to recall them at ease when solving the math problems during the test.  

Upon reading the article, I agree with the author that the policies used in teaching and assessing math usually lead to the young learners not succeeding and hating the subject. While the teachers am at building a strong background love for math in the learners, the pressure in the system push them away. I also agree with the approach of involving the students in the learning process without allowing intimidations. Giving them a chance to present their approach in solving the problems allow them to build confidence and learn from their peers.

The article imply that anxiety can block the learner in accessing information stored in the brain. This is presented as neuroscience evidence against the use of timed tests on the students. However, I do not understand the whole theory surrounding the matter. Is the theory still relevant when the students are undertaking non-mathematical tests?

Students have different learning and achievement abilities. The timed tests requires the teachers to teach the learners on how to answer questions quickly that they end up compromising the teaching process. There is no time to address the learner’s problems and shortcomings that they might have in class. The teachers goes through the math basics and present practice tests to assess the ability to complete the tests within the scheduled timeline. The learning abilities of the students is overlooked in the process.

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