Nicole

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Background

Broad Context

- These data were collected as part of a larger study of transfer and the effectiveness of formula learning.

Materials

All participants solved the Polygon Problem, a growth pattern problem in which the solver’s task is to determine the perimeter of a row of regular polygons arranged in a singe line, as in Figure 1. These figures consisted of shapes ranging from 3 sides (triangles) to 6 sides (hexagons) in rows of 3 to 10 shapes. The relationship between the total perimeter and these two variables can be expressed in various formulae which simplify to this canonical form: Perimeter = (s-2)n + 2 , where s represents the number of sides per polygon and n represents the number of polygons in a row. The Polygon Problem has been used in professional development programs with teachers as an example of growth pattern problem that allows for a general abstract solution to be built from a range of possible contexts (Koellner et al., 2007).

Trial Paradigm

The trial procedure is shown in the figure below. To ensure that potential differences in brain activations to the different conditions would not simply be an effect of different visual stimuli, the presentation of each problem was the same for all trials. As shown below, this screen consisted of the graphic representation of the problem, the formula, and the values of the variables ‘s’ and ‘n’ such that it provided all of the necessary information to use the formula or use the spatial strategy. In each trial, participants clicked a button to indicate that they had solved the problem. On the next screen, participants used the trackball to scroll to their answer.

The study timing was self-paced, a method that has been used in other studies of cognitive processing (e.g. Kalbfleish, VanMeter, & Zeffiro, 2006). The interstimulus interval (ISI) was jittered between each trial.

Blocks consisted of 24 trials with varying lengths and types of shapes presented. Each block lasted approximately six to eight minutes depending on the participants’ efficiency in working through the problems.

Study Design

In this study, participants received training about the Polygon Problem prior to entering the scanner, solved several blocks of problems in the scanner, and were tested on transfer questions after scanning. The study included a between subjects manipulation of instruction. In the Formula + Spatial condition, participants built up the formula from the referent, learning both the formula and an analogous spatial strategy involving skip-counting along the figure to geometrically represent the formula. The Formula Only condition simply learned the formula to be able to do the task but did not learn about its relationship to the spatial referent. This design is outlined below.

In the present investigation, data from seven participants in the Formula Only condition are examined. In particular, I considered data from the first two scanner blocks, during which the participants are using the formula to solve the problems.

The present investigation: Subject Motion

(Example of subject motion graph(s).)

Methods

Subjects

Seven healthy volunteers participated in this study. Their mean age was 23.8 years old and four participants were male. These data were collected as part of a larger sample of 16 healthy volunteers (mean age 23.2 years old).

MR acquisition

Data were obtained on a 3T GE scanner at Stanford's Center for Cognitive and Neurobiological Imaging (CNI)

MR Analysis

The MR data was analyzed using SPM software tools. (PUT LINK TO SPM HERE!) Specifically, ART repair was used (LINK)

Pre-processing

All data were slice-time corrected, motion corrected, and repeated scans were averaged together to create a single average scan for each subject.

MNI space

MNI is an abbreviation for Montreal Neurological Institute.

After a pRF model was solved for each subject, the model was trasnformed into MNI template space. This was done by first aligning the high resolution t1-weighted anatomical scan from each subject to an MNI template. Since the pRF model was coregistered to the t1-anatomical scan, the same alignment matrix could then be applied to the pRF model.
Once each pRF model was aligned to MNI space, 4 model parameters - x, y, sigma, and r^2 - were averaged across each of the 6 subjects in each voxel.

Group Level Analyses

No Motion Correction

Some text. Some analysis. Some figures.

Using Motion Correction

Some text. Some analysis. Some figures.

Dropping A Subject With Too Much Motion

Some text. Some analysis. Some figures. Maybe some equations.

Equations

If you want to use equations, you can use the same formats that are use on wikipedia.
See wikimedia help on formulas for help.
This example of equation use is copied and pasted from wikipedia's article on the DFT.

The sequence of N complex numbers x₀, ..., x_N−1 is transformed into the sequence of N complex numbers X₀, ..., X_N−1 by the DFT according to the formula:

$X_k=\sum _{n=0}^{N-1}{x}_n{e}^{-\frac{2\pi i}{N}kn}k=0,\dots ,N-1$

where i is the imaginary unit and $e^{\frac{2\pi i}{N}}$ is a primitive N'th root of unity. (This expression can also be written in terms of a DFT matrix; when scaled appropriately it becomes a unitary matrix and the X_k can thus be viewed as coefficients of x in an orthonormal basis.)

The transform is sometimes denoted by the symbol $ℱ$, as in $𝐗=ℱ\left\{𝐱\right\}$ or $ℱ\left(𝐱\right)$ or $ℱ𝐱$.

The inverse discrete Fourier transform (IDFT) is given by

$x_n=\frac{1}{N}\sum _{k=0}^{N-1}{X}_k{e}^{\frac{2\pi i}{N}kn}n=0,\dots ,N-1.$

Conclusions

Here is where you say what your results mean.

References - Resources and related work

Software

Art Repair

For more information about the SPM plugin ArtRepair, see: Art Repair